www.gusucode.com > econ 案例源码程序 matlab代码 > econ/EstimateMultiplicativeARIMAModelExample.m
%% Estimate Multiplicative ARIMA Model % This example shows how to estimate a multiplicative seasonal ARIMA model % using |estimate|. The time series is monthly international airline passenger % numbers from 1949 to 1960. % Copyright 2015 The MathWorks, Inc. %% Load the Data and Specify the model. % Load the airline data set. load(fullfile(matlabroot,'examples','econ','Data_Airline.mat')) y = log(Data); T = length(y); Mdl = arima('Constant',0,'D',1,'Seasonality',12,... 'MALags',1,'SMALags',12); %% Estimate the Model Using Presample Data. % Use the first 13 observations as presample data, and the remaining 131 % observations for estimation. y0 = y(1:13); [EstMdl,EstParamCov] = estimate(Mdl,y(14:end),'Y0',y0) %% % The fitted model is % % $$\Delta {\Delta _{12}}{y_t} = (1 - 0.38L)(1 - 0.57{L^{12}}){\varepsilon _t},$$ % % with innovation variance 0.0014. %% % Notice that the model constant is not estimated, but remains fixed at % zero. There is no corresponding standard error or t statistic for the % constant term. The row (and column) in the variance-covariance matrix % corresponding to the constant term has all zeros. %% Infer the Residuals. % Infer the residuals from the fitted model. res = infer(EstMdl,y(14:end),'Y0',y0); figure plot(14:T,res) xlim([0,T]) title('Residuals') axis tight %% % When you use the first 13 observations as presample data, residuals are % available from time 14 onward. %% % References: % % Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. _Time Series Analysis: Forecasting and Control_. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.