Time-varying NoVaS Versus GARCH: Point Prediction, Volatility Estimation and Prediction Intervals

The NoVaS methodology for prediction of stationary financial returns is reviewed, and the applicability of the NoVaS transformation for volatility estimation is illustrated using realized volatility as a proxy. The realm of applicability of the NoVaS methodology is then extended to non-stationary data (involving local stationarity and/or structural breaks) for one-step ahead point prediction of squared returns. In addition, a NoVaS-based algorithm is proposed for the construction of bootstrap prediction intervals for one-step ahead squared returns for both stationary and non-stationary data. It is shown that the "Time-varying" NoVaS is robust against possible nonstationarities in the data; this is true in terms of locally (but not globally) financial returns but also in change point problems where the NoVaS methodology adapts fast to the new regime that occurs after an unknown/undetected change point. Extensive empirical work shows that the NoVaS methodology generally outperforms the GARCH benchmark for (i) point prediction of squared returns, (ii) interval prediction of squared returns, and (iii) volatility estimation. With regard to target (J), earlier work had shown little advantage of using a nonzero a in the NoVaS transformation. However, in terms or targets (ii) and (iii), it appears that using the Generalized version of NoVaS-either Simple or Exponential-can be quite beneficial and well-worth the associated computational cost.