In addition to clear-cut seasonality in mean and variance, weekly Dutch temperature data appear to have a strong asymmetry in the impact of unexpectedly high or low temperatures on conditional volatility. Furthermore, this asymmetry also shows fairly pronounced seasonal variation. To describe these features, we propose a univariate seasonal time series model with asymmetric conditionally heteroskedastic errors. We fit this (and other, nested) model(s) to 25 years of weekly data. We evaluate its forecasting performance for 5 years of hold-out data and find that the imposed asymmetry leads to better out-of-sample forecasts of temperature volatility.

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Keywords Forecasting, Nonlinearity, Seasonality, Temperature data, Time series
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Franses, Ph.H.B.F., Neele, J., & van Dijk, D.J.C.. (2001). Modeling asymmetric volatility in weekly Dutch temperature data. Environmental Modelling & Software, 16(2), 131–137. doi:10.1016/S1364-8152(00)00076-1