SCAD Regularized HAR Model For Volatility Prediction

Volatility is a vital indicator of risk in financial market.With increasing accessibility to high-frequency trading data and reduction of processing cost,a great many research has been done to model and forecast the realized volatility constructed from high-frequency intra-day returns,which covers the information of intra-day transaction.The Flexible HAR Model based on SCAD regularization constructed in this paper can characterize the long-memory property of realized volatility.Realized volatility can be defined over various horizons.The multi-period volatilities are normalized sums of the daily realized volatilities.The Flexible HAR Model is proposed to capture that volatility over longer time intervals has a stronger influence on volatility over shorter time intervals.We propose two methods of defining the lag structure.The volatility cascade over different time horizons leads to a regression of high dimensional data.It's effective to use SCAD regularization method to select the variable subset which has large contribution to the model,thereby reducing the number of variables and improving the out-of-sample forecasting performance.We transfer the original problem into an adaptive LASSO type problem based on local linear approximation to the nonconvex penalty function,then re-scale the data set and further simplify the adaptive LASSO type problem into an ordinary LASSO problem using the LARS algorithm to solve.The data set consists of Shanghai composite index.We compute realized volatility prediction with the Flexible HAR Model based on SCAD regularization and LASSO regularization,and compare the forecasting errors.Numerical experiments show clearly the accuracy of the Flexible HAR Model based on SCAD regularization.