Converting from GARCH Functions to Model Objects

In R2014a, arima, garch, egarch, and gjr models and associated functionality replace the garchfit, garchinfer, garchplot, garchpred, garchsim, garchcount, garchdisp, garchget, and garchset functions. If you use the older GARCH data analysis functions, then you will receive an error. Use the information on this page to help you convert from the older to the newer functionality.

Suppose that you want to analyze a univariate series y using an ARIMA(3,4) model with GARCH(1,2) innovations, and you have presample observations (y0), innovations (e0), and conditional standard deviations (sigma0). This table shows both ways to complete such an analysis.

Step	Old Functionality	New Functionality
Specify a compound ARIMA-GARCH model	Mdl = garchset('R',3,'M',4,... 'P',1,'Q',2);	Mdl = arima(3,0,4); VarMdl = garch(1,2); Mdl.Variance = VarMdl;
Retrieve model properties	garchget(Mdl,'K')	Mdl.Variance.Constant
Set equality constraints	Mdl = garchset(Mdl,... 'K',0.75,'FixK',1);	Mdl.Variance.Constant = 0.75;
Estimate parameters	EstMdl = garchfit(Mdl,y,[],... e0,sigma0,y0);	[EstMdl,EstParamCov] = ... estimate(Mdl,y,'E0',e0,... 'V0',sigma0.^2,'Y0',y0)
Count the number of fitted parameters	numParams = garchcount(... EstMdl);	numParams = sum(any(... EstParamCov));
Infer conditional variances (sigma2) and obtain the loglikelihood (logL)	[e,sigma,logL] = ... garchinfer(EstMdl,y,... [],e0,sigma0,y0); sigma2 = sigma.^2;	[e,sigma2,logL] = infer(... EstMdl,y,'E0',e0,... 'V0',sigma0.^2,'Y0',y0);
Simulate observations	simY = garchsim(EstMdl,100);	simY = simulate(EstMdl,100);
Filter disturbances	e = randn(100,1); simY = garchsim(EstMdl,[],... [],e);	e = randn(100,1); simY = filter(EstMdl,e);
Forecast observations	fY = garchpred(EstMdl,y,... 15);	fY = forecast(EstMdl,15,... 'Y0',y);

Though similar, the input and output structure of the two functionalities differ in some ways. This example shows how to determine some of the differences between the two, and might help you through the conversion. This example does not show how to reproduce equivalent results between the models, because, in general, the estimates between the two functionalities might differ.

Suppose that you want to analyze a univariate series. You suspect that the model is either an ARIMA(2,1)/GARCH(1,1) or ARIMA(1,1)/GARCH(1,1) model, and want to test which model fits to the data better. Variables representing the new functionality have the suffix 1 (e.g., Mdl1), and those of the older functionality have suffix 2 (e.g., Mdl2).

1. Simulate the data from an ARIMA(2,1) model with GARCH(1,1) innovations.

   % New way
   VarMdl1 = garch('GARCH',0.3,'ARCH',0.2,'Constant',0.75);
   Mdl1 = arima('AR',{0.5,0.3},'MA',-0.7,'Constant',0,'Variance',VarMdl1);
   [y1,e1,v1] = simulate(Mdl1,100);
   
   % Old way
   Mdl2 = garchset('AR',[0.5,0.3],'MA',-0.7,'C',0,...
       'GARCH',0.3,'ARCH',0.2,'K',0.75);
   [e2,sd2,y2] = garchsim(Mdl2,100);

   The differences are:

   • Mdl1 is an arima object, and Mdl2 is a structure array.

   • simulate returns conditional variances, whereas garchsim returns conditional standard deviations.

   • With the new functionality, you must:

     • Specify multiple coefficient values using a cell array.

     • Specify the variance model using garch, egarch, or gjr.

2. Specify template models to use for estimation.

   % New way
   VarMdl1 = garch(1,1);
   Mdl11 = arima('ARLags',1,'MALags',1,'Variance',VarMdl1);
   Mdl12 = arima('ARLags',1:2,'MALags',1,'Variance',VarMdl1);
   
   % Old way
   Mdl21 = garchset('R',1,'M',1,'P',1,'Q',1,'Display','off');
   Mdl22 = garchset('R',2,'M',1,'P',1,'Q',1,'Display','off');
   

   The new functionality has the name-value pair arguments 'ARLags' and 'MALags' to set the polynomial terms of the model. You must specify each term order individually, which allows for a more flexible specification. The models Mdl11 and Mdl12 have properties P and Q corresponding to the autoregressive and moving average orders of the model.

3. Fit each model to the data.

   % New way
   logL1 = [0;0];       % Preallocate
   numParams1 = logL1;  % Preallocate
   [EstMdl11,EstParamCov11,logl11] = estimate(Mdl11,y1,'Display','off');
   [EstMdl12,EstParamCov12,logl12] = estimate(Mdl12,y1,'Display','off');
   
   % Old way
   logL2 = [0;0];       % Preallocate
   numParams2 = logL2;  % Preallocate
   [EstMdl21,~,logl12] = garchfit(Mdl21,y2);
   [EstMdl22,~,logl22] = garchfit(Mdl22,y2);

   The estimate function:

   • Returns the estimated parameter covariance matrix rather than just the standard errors.

   • Lets you decide to see estimates and optimization information, rather than setting it when you specify the model.

4. Count the number of fitted parameters in the estimated model.

   % New way
   numParams11 = sum(any(EstParamCov11));
   numParams21 = sum(any(EstParamCov21));
   
   % Old way
   numParams12 = garchcount(EstMdl12);
   numParams22 = garchcount(EstMdl22); 

   The new functionality does not contain a function that counts the number of fitted parameters in an estimated model. However, if a parameter is fixed during estimation, then the software sets all variances and covariances of the corresponding parameter estimate to 0. The new way to count fitted parameters uses this feature.

5. Assess which model is more appropriate using information criteria.

   aic1 = aicbic(logL1,numParams1);
   aic2 = aicbic(logL2,numParams2);