Top Highlights

• Currently, the most popular dynamic time series models are ARIMA and GARCH models
• These models are based on the assumption of stationarity of the residual “innovations” in the time series, where market risk is measured by second-order moments only. This assumption is often combined with the assumption of normality (or Gaussian distribution) of these residual innovations
• Our critique of these "stationarity of residuals" models is twofold. First, the innovations of empirical financial time series are demonstrably not Gaussian and the moments of the distributions of these innovations tend to vary over time (Loretan and Phillips, 1994)
• ARIMA models concentrate on the first few (constant) autocorrelations to capture the short- run features of the time series, and that they produce misleading results, when used to estimate long-run properties of time series

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