MATLAB code for Heterogeneous Autoregressive (HAR) model forecasting

The HAR model is a simple autoregressive model for realized variance (and all its transformations - log/root etc.), which has the following form:

where the d, w and m superscripts represent daily, weekly and monthly realized variance. The model can be estimated by OLS.

The input for this code is a (n x 1) vector of realized variance or its transformations.

X_mat.m generates HAR regressors (daily, weekly and monthly RV) from the input, har_forecasting.m makes rolling forecasts (one or multi-day horizons) and returns the RMSE value.