Inference for asymmetric exponentially weighted moving average models

Abstract

The exponentially weighted moving average (EWMA) model in ‘Risk‐Metrics’ has been a benchmark for controlling and forecasting risks in financial operations. However, it is incapable of capturing the asymmetric volatility effect and the heavy‐tailed innovation, which are two important stylized features of financial returns. We propose a new asymmetric EWMA model driven by the Student's t‐distributed innovations to take these two stylized features into account and study its maximum likelihood estimation and model diagnostic checking. The finite‐sample performance of the estimation and diagnostic test statistic is examined by the simulated data.