Asset volatility forecasting:The optimal decay parameter in the EWMA model

Abstract: The exponentially weighted moving average (EMWA) could be labeled as a competitive volatility estimator, where its main strength relies on computation simplicity, especially in a multi-asset scenario, due to dependency only on the decay parameter, $\lambda$. But, what is the best election for $\lambda$ in the EMWA volatility model? Through a large time-series data set of historical returns of the top US large-cap companies; we test empirically the forecasting performance of the EWMA approach, under different time horizons and varying the decay parameter. Using a rolling window scheme, the out-of-sample performance of the variance-covariance matrix is computed following two approaches. First, if we look for a fixed decay parameter for the full sample, the results are in agreement with the RiskMetrics suggestion for 1-month forecasting. In addition, we provide the full-sample optimal decay parameter for the weekly and bi-weekly forecasting horizon cases, confirming two facts: i) the optimal value is as a function of the forecasting horizon, and ii) for lower forecasting horizons the short-term memory gains importance. In a second way, we also evaluate the forecasting performance of EWMA, but this time using the optimal time-varying decay parameter which minimizes the in-sample variance-covariance estimator, arriving at better accuracy than the use of a fixed-full-sample optimal parameter.