Memory Choice and Tail Risk in Volatility Forecasting

Shortening the memory of a volatility forecaster can make severe underprediction more frequent. In archived 22-period forecasts for four equity markets, aggressive forgetting raises the extreme QLIKE loss rate from 1.03% to 2.03%, a difference of 1.00 percentage point (95% paired block interval: 0.39 to 1.75). The net increase comes entirely from forecasts that underestimate volatility. The increase remains 0.59 percentage points after excluding 2020 and re-estimating the market-specific thresholds (95% interval: 0.15 to 1.19). With moderate forgetting, sample median loss is slightly lower while mean loss and extreme-loss incidence are higher. A separate S&P 500 experiment shows that the estimated tail effect is sensitive to variance-scale calibration and the loss benchmark. Memory selection should therefore evaluate the frequency and direction of large errors alongside average forecast loss.