Question about GARCH forecast command

Hello! I would like to ask you about the forecast command. https://www.mathworks.com/help/econ/cvm.forecast.htm The numPeriods represents the number of one-day ahead forecasts or the k-period ahead forecasts? For example if i want to make 1,000 one day ahead forecasts what do I do? Do I fill in "1,000" in numPeriods or i should create a loop filling in "1" in numPeriods?

Answer 1

[Hang Qian]

Hello -

In GARCH models, the input argument ‘numPeriods’ represents forecast horizon, say the conditional volatility for y(t+1), y(t+2),...,y(t+numPeriods). As a result, the output variable ‘V’ is a numPeriods-by-1 vector. The last element of V corresponds to the k-period ahead forecasts. The GARCH conditional variance is a deterministic function of the past observations, so the 1000 one-day-ahead forecast would be identical, conditional on the same dataset and parameter values. However, if we take estimated parameter uncertainty into account, it is possible to make 1000 one-day-ahead forecast values by generating some GARCH coefficients from the MLE coefficients and their covariance matrix.

Regards,

Hang Qian