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Regression in Forecasting

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Using Forecasted Explanatory Data Generating Forecasted Explanatory Data

Using Forecasted Explanatory Data

To forecast the conditional mean of a return series y in each period of a 10-period forecast horizon, call garchpred with the following syntax:

NumPeriods = 10;
[sigmaForecast,meanForecast] = ...
      garchpred(spec,y,NumPeriods,X,XF);

where X is the same regression matrix shown in Fitting a Regression Model to a Return Series, and XF is a regression matrix of forecasted explanatory data. In fact, XF represents a projection into the future of the explanatory data in X. This command produces an error if you execute it in your current workspace, because XF is missing.

XF must have the same number of columns as X. In each column of XF, the first row contains the one-period-ahead forecast, the second row the two-period-ahead forecast, and so on. If you specify XF, the number of rows (forecasts) in each column must equal or exceed the forecast horizon, NumPeriods. When the number of forecasts in XF exceeds the forecast horizon, garchpred uses only the first NumPeriods forecasts. If XF is empty ([]) or missing, the conditional mean forecast, meanForecast, has no regression component.

If you use a regression matrix X for simulation and/or estimation, also use a regression matrix when calling garchpred. This is because garchpred requires a complete conditional mean specification to correctly infer the innovations {ε_t} from the observed return series {y_t}. Typically, the same regression matrix is used for simulation, estimation, and forecasting.

Forecasting Only the Conditional Standard Deviation

To forecast the conditional standard deviation (that is, sigmaForecast), XF is unnecessary, and garchpred ignores it if it is present. This is true even if you included the matrix X in the simulation and/or estimation process.

For example, you could use the following syntax to forecast only the conditional standard deviation of the innovations {ε_t} over a 10-period forecast horizon:

sigmaForecast = garchpred(spec,y,10,X);

Forecasting the Conditional Mean

To forecast the conditional mean (that is, meanForecast), specify both X and XF. For example, to forecast the conditional mean of the return series y over a 10-period forecast horizon:

[sigmaForecast,meanForecast] = garchpred(spec,y,10,X,XF);

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Generating Forecasted Explanatory Data

Typically, the regression matrix X contains the observed returns of a suitable market index, collected over the same time interval as the observed data of interest. In this case, X is most likely a vector that corresponds to a single explanatory variable. You must find a way to generate the forecast of X (that is, XF).

One approach is to use garchfit to fit a suitable ARMA(R,M) model to the returns in X, and then use garchpred to forecast the market index returns into the future. Specifically, since you are not interested in fitting the volatility of X, you can simplify the estimation process by assuming a constant conditional variance model, for example, ARMA(R,M)/GARCH(0,0).

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Regression in Simulation

Regression in Monte Carlo

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