Оценка Модели regARIMA Используя Ограничения Равенства

estimate требует, чтобы модель regARIMA и вектор одномерных данных об ответе оценили модель регрессии с ошибками ARIMA. Без данных о предикторе модель задает параметрическую форму компонента регрессии только для прерывания с ошибочной моделью ARIMA. Это не то же самое как условная средняя модель с константой. Для получения дополнительной информации смотрите Альтернативу Представления Модели ARIMA. Если вы задаете T-by-r матрица данных о предикторе, то estimate включает компонент линейной регрессии для серии r.

estimate возвращает адаптированные значения для любых параметров во входной модели со значениями NaN. Например, если вы задаете модель regARIMA по умолчанию и передаете T-by-r матрица данных о предикторе, затем программное обеспечение устанавливает все параметры на NaN включая коэффициенты регрессии r и оценивает их всех. Если вы задаете non-NaN значения для каких-либо параметров, то estimate просматривает эти значения как ограничения равенства и соблюдает их во время оценки.

Например, предположите, что остаточная диагностика от линейной регрессии предлагает интегрированные безусловные воздействия. Поскольку прерывание регрессии не идентифицируется в интегрированных моделях, вы решаете установить прерывание на 0. Задайте 'Intercept',0 в модели regARIMA, которую вы передаете в estimate. Программное обеспечение просматривает это non-NaN значение как ограничение равенства и не оценивает прерывание, его стандартную погрешность и его ковариацию с другими оценками. Чтобы проиллюстрировать далее, предположите, что истинная модель для серии yt ответа

yt=0+utut=εt,

где εt является Гауссовым с отклонением 1. Функция loglikelihood для моделируемого набора данных из этой модели может напомнить поверхность в следующей фигуре по сетке отклонений и прерываний.

rng(1); % For reproducibility
e = randn(100,1);
Variance = 1;
Intercept = 0;
Mdl = regARIMA('Intercept',Intercept,'Variance',Variance);
y = filter(Mdl,e);

gridLength = 50;
intGrid1 = linspace(-1,1,50);
varGrid1 = linspace(0.1,4,50);
[varGrid2,intGrid2] = meshgrid(varGrid1,intGrid1);
LogLGrid = zeros(numel(varGrid1),numel(intGrid1));

for k1 = 1:numel(intGrid1)
    for k2 = 1:numel(varGrid1)
        ToEstMdl = regARIMA('Intercept',...
            intGrid1(k1),'Variance',varGrid1(k2));
        [~,~,LogLGrid(k1,k2)] = estimate(ToEstMdl,y);
    end
end
 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value    StandardError    TStatistic    PValue
                 _____    _____________    __________    ______

    Intercept      -1           0             -Inf         0   
    Variance      0.1           0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.17959          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.25918          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.33878          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.41837          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.49796          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.57755          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.65714          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.73673          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.81633          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.89592          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value     StandardError    TStatistic    PValue
                 _______    _____________    __________    ______

    Intercept         -1          0             -Inf         0   
    Variance     0.97551          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.0551          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.1347          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.2143          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.2939          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.3735          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.4531          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.5327          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.6122          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.6918          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.7714          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value    StandardError    TStatistic    PValue
                 _____    _____________    __________    ______

    Intercept       -1          0             -Inf         0   
    Variance     1.851          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     1.9306          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.0102          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.0898          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.1694          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value    StandardError    TStatistic    PValue
                 _____    _____________    __________    ______

    Intercept       -1          0             -Inf         0   
    Variance     2.249          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.3286          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.4082          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.4878          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.5673          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.6469          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.7265          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.8061          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.8857          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     2.9653          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.0449          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.1245          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.2041          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.2837          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.3633          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.4429          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.5224          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value    StandardError    TStatistic    PValue
                 _____    _____________    __________    ______

    Intercept       -1          0             -Inf         0   
    Variance     3.602          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.6816          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.7612          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.8408          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value     StandardError    TStatistic    PValue
                 ______    _____________    __________    ______

    Intercept        -1          0             -Inf         0   
    Variance     3.9204          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                 Value    StandardError    TStatistic    PValue
                 _____    _____________    __________    ______

    Intercept     -1            0             -Inf         0   
    Variance       4            0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance          0.1          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.17959          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.25918          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.33878          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.41837          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.49796          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.57755          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.65714          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.73673          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.81633          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.89592          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance      0.97551          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.0551          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.1347          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.2143          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.2939          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.3735          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.4531          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.5327          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.6122          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.6918          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.7714          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance        1.851          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       1.9306          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.0102          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.0898          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.1694          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance        2.249          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.3286          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.4082          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.4878          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.5673          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.6469          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.7265          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.8061          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.8857          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       2.9653          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.0449          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.1245          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.2041          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.2837          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.3633          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.4429          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.5224          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance        3.602          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.6816          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.7612          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.8408          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance       3.9204          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.95918          0             -Inf         0   
    Variance            4          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance          0.1          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.17959          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.25918          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.33878          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.41837          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.49796          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.57755          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.65714          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.73673          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.81633          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.89592          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance      0.97551          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.0551          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.1347          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.2143          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.2939          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.3735          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.4531          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.5327          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.6122          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.6918          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.7714          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance        1.851          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       1.9306          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.0102          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.0898          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.1694          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance        2.249          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.3286          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.4082          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.4878          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.5673          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.6469          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.7265          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.8061          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.8857          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       2.9653          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.0449          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.1245          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.2041          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.2837          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.3633          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.4429          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.5224          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance        3.602          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.6816          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.7612          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.8408          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance       3.9204          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.91837          0             -Inf         0   
    Variance            4          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance          0.1          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.17959          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.25918          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.33878          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.41837          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.49796          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.57755          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.65714          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.73673          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.81633          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.89592          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance      0.97551          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.0551          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.1347          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.2143          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.2939          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.3735          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.4531          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.5327          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.6122          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.6918          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.7714          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance        1.851          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       1.9306          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.0102          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.0898          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.1694          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance        2.249          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.3286          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.4082          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.4878          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.5673          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.6469          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.7265          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf         0   
    Variance       2.8061          0              Inf         0   

 
    ARMA(0,0) Error Model (Gaussian Distribution):
 
                  Value      StandardError    TStatistic    PValue
                 ________    _____________    __________    ______

    Intercept    -0.87755          0             -Inf        ...
surf(intGrid2,varGrid2,LogLGrid) % 3D loglikelihood plot        
xlabel 'Intercept';
ylabel 'Variance';
zlabel 'Loglikelihood';
shading interp

Заметьте, что максимум (самая темно-красная область) происходит вокруг Intercept = 0 и Variance = 1. Если вы применяете ограничение равенства, то оптимизатор просматривает двумерный срез (в этом примере) функции loglikelihood при том ограничении. Следующие графики отображают loglikelihood при нескольких различных ограничениях равенства Intercept.

intValue = [intGrid1(10), intGrid1(20),...
    intGrid1(30), intGrid1(40)];
for k = 1:4
    subplot(2,2,k)
%    plot(varGrid1,LogLGrid(find(intGrid2 == intValue(k))))
    plot(varGrid1,LogLGrid(intGrid2 == intValue(k)))
    title(sprintf('Loglikelihood, Intercpet = %.3f',intValue(k)))
    xlabel 'Variance';
    ylabel 'Loglikelihood';
    hold on
    h1 = gca;
    plot([Variance Variance],h1.YLim,'r:')
    hold off
end

В каждом случае Variance = 1 (его истинное значение) происходит очень близко к максимуму функции loglikelihood. Вместо того, чтобы ограничивать Intercept, следующие графики отображают функцию правдоподобия с помощью нескольких ограничений равенства Variance.

varValue = [varGrid1(10),varGrid1(20),varGrid1(30),varGrid1(40)];
for k = 1:4
    subplot(2,2,k)
%    plot(intGrid1,LogLGrid(find(varGrid2 == varValue(k))))
    plot(intGrid1,LogLGrid(varGrid2 == varValue(k)))
    title(sprintf('Loglikelihood, Variance = %.3f',varValue(k)))
    xlabel('Intercept')
    ylabel('Loglikelihood')
    hold on
    h2 = gca;
    plot([Intercept Intercept],h2.YLim,'r:')
    hold off
end

В каждом случае Intercept = 0 (его истинное значение) происходит очень близко к максимуму функции loglikelihood.

estimate также соблюдает подмножество ограничений равенства при оценке всего другого набора параметров к NaN. Например, предположите r = 3, и вы знаете что β 2 = 5. Задайте Beta = [NaN; 5; NaN] в модели regARIMA и передайте эту модель с данными к estimate.

estimate опционально возвращает предполагаемую ковариационную матрицу отклонения для предполагаемых параметров. Порядок параметра в этой матрице:

  • Прерывание

  • Ненулевые коэффициенты AR в положительных задержках

  • Ненулевые коэффициенты SAR в положительных задержках

  • Ненулевые коэффициенты MA в положительных задержках

  • Ненулевые коэффициенты SMA в положительных задержках

  • Коэффициенты регрессии (когда вы задаете X в estimate),

  • Инновационное отклонение

  • Степени свободы для распределения t

Если какой-либо параметр, известный оптимизатору, имеет ограничение равенства, то соответствующая строка и столбец ковариационной матрицы отклонения имеет весь 0s.

В дополнение к вашим ограничениям равенства estimate устанавливает любой AR, MA, SAR и коэффициент SMA с оценкой меньше, чем 1e-12 в значении, равном 0.

Смотрите также

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