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
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.