Statistics and Its Interface

Volume 4 (2011)

Number 2

On the threshold hyperbolic GARCH models

Pages: 159 – 166

DOI: https://dx.doi.org/10.4310/SII.2011.v4.n2.a11

Authors

Wilson Kwan (The Hong Kong Polytechnic University, Hong Kong)

Guodong Li (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong)

Wai Keung Li (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong)

Abstract

In the financial market, the volatility of financial assets plays a key role in the problem of measuring market risk in many investment decisions. Insights into economic forces that may contribute to or amplify volatility are thus important. The financial market is characterized by regime switching between phases of low volatility and phases of high volatility. Nonlinearity and long memory are two salient features of volatility. To jointly capture the features of long memory and nonlinearity, a new threshold time series model with hyperbolic generalized autoregressive conditional heteroscedasticity is considered in this article. A goodness of fit test is derived to check the adequacy of the fitted model. Simulation and empirical results provide further support to the proposed model.

Keywords

hyperbolic GARCH model, long memory, threshold model, volatility

2010 Mathematics Subject Classification

Primary 91B84. Secondary 62M10.

Published 22 June 2011