Evaluating Realized Volatility Models with Higher Order Cumulants: HAR-RV Versus ARIMA-RV

Abstract

The objective of this paper is to introduce a new Realized Volatility (RV) Model. The model solves the problems of capturing long memory and heavy tales, which persist in current Heterogeneous Auto Regressive Realized Volatility Models (HAR-RV). First, an extensive empirical analysis of the classical RV model is provided by coupling Digital Signal Processing (DSP), Non Gaussian Time Series Analyses (NG-TSA) and volatility forecasting concepts. All models are built and tested on 30 min quotations of closing spot prices: USD/JPY, CHF/USD, JPY/EUR USD/GBP and GBP/EUR for the period from May 14, 2013 to July 31, 2015, taken from Bloomberg. The independence of the model’s innovations is tested by using the second, third and fourth cumulants, known as Higher Order Cumulants (HOC).Two tests are used, the Box-Ljung (B-Lj) test and Hinich test. The model is compared with the more natural Autoregressive Moving Average model (ARMA-RV). The empirical analysis shows that neither classic HAR-RV nor ARMA-RV models produce independent residuals. In addition, DSP recent findings are used to build a new HOC-ARMA-RV model. It was shown that only HOC-ARMA model fully captures fat tails and the long memory of FX returns.