EWMA covariances and the optimal decay parameter

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Rok publikování 2021
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Popis The exponentially weighted moving average (EMWA) could be labeled as a competitive volatility estimator, where its main strongness relies on computation simplicity due to dependency only on the decay parameter, ?. Then, what is the best election for ? 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 ?, 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 shown a lower ? than the recommended one for the daily case. However, we could not discard this recommendation because the two ?-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.
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