A new generalized exponentially weighted moving average quantile model and its statistical inference

Abstract

The exponentially weighting scheme is a simple and pragmatic approach to compute the value at risk (VaR). However, the existing exponentially weighting methods lack a sound statistical inference procedure. To circumvent this deficiency, this paper proposes a new generalized exponentially weighted moving average (GEWMA) quantile model, which allows a much broader weighting scheme than the benchmark one used in “Risk Metrics” document. For the GEWMA quantile model, a systematic statistical inference procedure is provided, including the weighted estimators for the weighting parameters, a t-test for the stability of the conditional quantile, another t-test for the mean invariance of the conditional quantile, a unit root test for the absence of intercept term, and several dynamic quantile tests for the model checking. Under mild conditions, the asymptotics of all proposed estimators and tests are established. Simulations show that all proposed estimators and tests have good finite-sample performances. Applications to four major exchange rates demonstrate that the weighting scheme suggested by “Risk Metrics” document is inappropriate, and the GEWMA quantile model delivers better VaR predictions than its many competitive methods. As an extension, the asymmetric GEWMA quantile model is also studied.