Lag structure selection in heterogeneous autoregressive model

The HAR model has the advantage of effectively capturing the characteristics of strongly dependent time series by linearly combining daily, weekly, and monthly lag structures.However, in cases like cryptocurrencies, where the concept of trading days differs from traditional financial markets, using a fixed lag structure may fail to adequately reflect the nature of the data.To address this limitation, this study establishes the structure of the LsHAR model and proposes a method to dynamically estimate the lag structure using the least squares method and 1 step-ahead out-of-sample forecasting.Through simulation experiments, it is shown that both methods converge toward the true lag structure as the sample size grows.In the empirical analysis, the predictive performance of the LsHAR model and the HAR model was compared using realized volatilities of national stock indices and cryptocurrencies.The results showed that the LsHAR model, by estimating the lag structure, outperformed the traditional HAR model in most indices and cryptocurrencies.