Inference for asymmetric exponentially weighted moving average models

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.