Abstract

The exponentially weighted moving average (EWMA) could be labeled as a competitive volatility estimator, where its main strongness relies on computation simplicity due to dependency only on the decay parameter, λ. Then, what is the best selection for λ 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. The analysis of the results confirms the time-varying behavior of λ, finding different optimal values as a function of the forecasting horizon. First, using a fixed decay parameter for the full sample, the results show an agreement with the RiskMetrics suggestion for 1-month forecasting; however, for lower forecasting horizons the short-term memory gains importance. Our results show a lower λ than the recommended one for the daily case. However, we could not discard this recommendation because the two λ−values have the same statistical forecasting accuracy. In addition, we provide the full-sample optimal decay parameter for the weekly and bi-weekly forecasting horizon. In a second approach, we also evaluate the forecasting performance of EWMA 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 in case of predictions greater or equal than one week.