On the threshold innovation in quasi-likelihood for conditionally heteroscedastic time series

Abstract

This work considers conditionally heteroscedastic time series with possibly asymmetric errors (e.g., skewed t-distributions). Suppose that the error distribution is unknown and estimating functions, so called quasi-likelihood (QL) scores are employed to estimate parameters. The quasi-likelihood can be regarded as a special case of the Godambe’s optimum estimating functions (see, e.g., Hwang and Basawa (2011)). To capture asymmetry in errors, a threshold-innovation is newly suggested to construct an “optimum” quasi likelihood score. It is shown that the threshold innovation is “better” than the standard innovation especially when errors are asymmetrically distributed. A simulation study is reported and a real data analysis is illustrated.