Joint estimation of transfer learning on time series data

In the context of time series modeling, historical data influences the current period, but its impact diminishes rapidly. We propose leveraging the transfer learning technique to harness historical data for forecasting and enhance prediction accuracy. Our method comprises a two-step process. Initially, we cluster the data into auxiliary and target groups, while the target group indicates the current period, and the auxiliary groups contain the past periods. Subsequently, we estimate the current period data by incorporating historical periods using two lasso penalty terms. Our method allows for different periods to influence the current period. Under mild conditions, we demonstrate that the estimator enjoys asymptotic properties, including selection and estimation consistency. We apply the proposed method to index tracking in empirical analysis and conduct a comparative evaluation against three alternative methods. Results indicate that our method outperforms others in prediction accuracy and stability in subset selection.