infer
Infer ARIMA or ARIMAX model residuals or conditional variances
Syntax
[E,V] =
infer(Mdl,Y)
[E,V,logL]
= infer(Mdl,Y)
[E,V,logL] = infer(Mdl,Y,Name,Value)
Description
[ infers
residuals and conditional variances of a univariate ARIMA model fit
to data E,V] =
infer(Mdl,Y)Y.
[ additionally
returns the loglikelihood objective function values.E,V,logL]
= infer(Mdl,Y)
[E,V,logL] = infer(Mdl,Y, infers
the ARIMA or ARIMAX model residuals and conditional variances, and
returns the loglikelihood objective function values, with additional
options specified by one or more Name,Value)Name,Value pair
arguments.
Input Arguments
Output Arguments
Examples
Infer Residuals
Infer residuals from an AR model.
Specify an AR(2) model using known parameters.
Mdl = arima('AR',{0.5,-0.8},'Constant',0.002,... 'Variance',0.8);
Simulate response data with 102 observations.
rng 'default';
Y = simulate(Mdl,102);Use the first two responses as presample data, and infer residuals for the remaining 100 observations.
E = infer(Mdl,Y(3:end),'Y0',Y(1:2)); figure; plot(E); title 'Inferred Residuals';
Infer Conditional Variances
Infer the conditional variances from an AR(1) and GARCH(1,1) composite model.
Specify an AR(1) model using known parameters. Set the variance equal to a garch model.
Mdl = arima('AR',{0.8,-0.3},'Constant',0); MdlVar = garch('Constant',0.0002,'GARCH',0.6,... 'ARCH',0.2); Mdl.Variance = MdlVar;
Simulate response data with 102 observations.
rng 'default';
Y = simulate(Mdl,102);Infer conditional variances for the last 100 observations without using presample data.
[Ew,Vw] = infer(Mdl,Y(3:end));
Infer conditional variances for the last 100 observations using the first two observations as presample data.
[E,V] = infer(Mdl,Y(3:end),'Y0',Y(1:2));Plot the two sets of conditional variances for comparison. Examine the first few observations to see the slight difference between the series at the beginning.
figure; subplot(2,1,1); plot(Vw,'r','LineWidth',2); hold on; plot(V); legend('Without Presample','With Presample'); title 'Inferred Conditional Variances'; hold off subplot(2,1,2); plot(Vw(1:5),'r','LineWidth',2); hold on; plot(V(1:5)); legend('Without Presample','With Presample'); title 'Beginning of Series'; hold off
Infer Residuals from ARMAX Model
Infer residuals from an ARMAX model.
Specify an ARMA(1,2) model using known parameters for the response (MdlY) and an AR(1) model for the predictor data (MdlX).
MdlY = arima('AR',0.2,'MA',{-0.1,0.6},'Constant',... 1,'Variance',2,'Beta',3); MdlX = arima('AR',0.3,'Constant',0,'Variance',1);
Simulate response and predictor data with 102 observations.
rng 'default'; % For reproducibility X = simulate(MdlX,102); Y = simulate(MdlY,102,'X',X);
Use the first two responses as presample data, and infer residuals for the remaining 100 observations.
E = infer(MdlY,Y(3:end),'Y0',Y(1:2),'X',X); figure; plot(E); title 'Inferred Residuals';
References
[1] 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.
[2] Enders, W. Applied Econometric Time Series. Hoboken, NJ: John Wiley & Sons, 1995.
[3] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.