Flexible HAR model for realized volatility

Abstract

The Heterogeneous Autoregressive (HAR) model is commonly used in modeling the dynamics of realized volatility. In this paper, we propose a flexible HAR(1, . . . , p) specification, employing the adaptive LASSO and its statistical inference theory to see whether the lag structure (1, 5, 22) implied from an economic point of view can be recovered by statistical methods. The model differs from Audrino and Knaus (2016) [Audrino, F. and S. D. Knaus. 2016. “Lassoing the HAR model: A model selection perspective on realized volatility dynamics.” Econometrics Review 35: 1485–1521]. where the authors apply LASSO on the AR(p) model, which does not necessarily lead to a HAR model. Adaptive LASSO estimation and the subsequent hypothesis testing results fail to show strong evidence that such a fixed lag structure can be recovered by a flexible model. We also apply the group LASSO and related tests to check the validity of the classic HAR, which is rejected in most cases. The results justify our intention to use a flexible lag structure while still keeping the HAR frame. In terms of the out-of-sample forecasting, the proposed flexible specification works comparably to the benchmark HAR(1, 5, 22). Moreover, the time-varying model combinations show that when the market environment is not stable, the fixed lag structure (1, 5, 22) is not particularly accurate and effective.

A Note on the Asymptotic Normality Theory of the Least Squares Estimates in Multivariate HAR-RV Models

“…Assume that {Y t } is another strictly stationary solution of the vector autoregression (3) with E Y t < ∞. Then we haveY * t = B * 0 + FY * t−1 + E * t in the same way as above in (5). For any positive integer m we…”

“…Since its introduction, various adaptive versions of the HAR model are used to analyze the volatility along with empirical data analysis. Here, we refer to [2][3][4][5] for univariate data and [6][7][8][9][10][11] for multivariate data.…”

Forecasting stock return volatility: The role of shrinkage approaches in a data‐rich environment

“…Our paper is related to the work of Audrino and Knaus (2016) and Audrino et al (2019) as the two studies both rely on lasso. On the contrary, we can provide at least three new contributions or major differences.…”

“…On the contrary, we can provide at least three new contributions or major differences. First, Audrino and Knaus (2016) and Audrino et al (2019) make an empirical analysis on several individual stocks returns volatility, while our paper focuses on the stock market return volatility. Second, Audrino and Knaus (2016) and Audrino et al (2019) explore whether the lag structure imposed by the simple HAR-RV model can be recovered by the lasso or adaptive lasso.…”

“…First, Audrino and Knaus (2016) and Audrino et al (2019) make an empirical analysis on several individual stocks returns volatility, while our paper focuses on the stock market return volatility. Second, Audrino and Knaus (2016) and Audrino et al (2019) explore whether the lag structure imposed by the simple HAR-RV model can be recovered by the lasso or adaptive lasso. However, we collect all the predictors from its various extensions and investigate whether all these predictors can be efficiently used by the lasso, adaptive lasso, elastic net and ridge.…”