Abstract
In this chapter we present several new findings on the NoVaS transformation approach for volatility forecasting introduced by Politis (Model-Free Volatility Prediction, UCSD Department of Economics Discussion Paper 2003–16; Recent advances and trends in nonparametric statistics, Elsevier, North Holland; J Financ Econ 5:358–389, 2007). In particular: (a) we present a new method for accurate volatility forecasting using NoVaS; (b) we introduce a “time-varying” version of NoVaS and show that the NoVaS methodology is applicable in situations where (global) stationarity for returns fails such as the cases of local stationarity and/or structural breaks and/or model uncertainty; (c) we conduct an extensive simulation study on the forecasting ability of the NoVaS approach under a variety of realistic data generating processes (DGP); and (d) we illustrate the forecasting ability of NoVaS on a number of real data sets and compare it to realized and range-based volatility measures. Our empirical results show that the NoVaS -based forecasts lead to a much ‘tighter’ distribution of the forecasting performance measure. Perhaps our most remarkable finding is the robustness of the NoVaS forecasts in the context of structural breaks and/or other nonstationarities of the underlying data. Also striking is that forecasts based on NoVaS invariably outperform those based on the benchmark GARCH(1,1) even when the true DGP is GARCH(1,1) when the sample size is moderately large, e.g., 350 daily observations.
Earlier results from this research were presented in seminars in the Departments of Economics of the University of California at San Diego, University of Cyprus, and the University of Crete, as well as several conferences. We would like to thank Elena Andreou, conference and seminar participants for useful comments and suggestions. Many thanks are also due to an anonymous referee for a most constructive report, and to the Editors, **aohong Chen and Norman Swanson, for all their hard work in putting this volume together.
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Notes
- 1.
See also Politis and Thomakos (2008).
- 2.
- 3.
See the discussion about the calibration of \(\alpha \) and \(\displaystyle \varvec{a}\) in the next section.
- 4.
- 5.
This might well be the case of the EFG data set of Sect. 4 in what follows.
- 6.
See also the recent chapter by Hansen and Lunde (2006) about the relevance of MSE in evaluating volatility forecasts.
- 7.
This part of the NoVaS application appears similar at the outset to the Minimum Distance Method (MDM) of Wolfowitz (1957). Nevertheless, their objectives are quite different since the latter is typically employed for parameter estimation and testing whereas in NoVaS there is little interest in parameters—the focus lying on effective forecasting.
- 8.
- 9.
In our design we do not just go for a limited number of DGPs but for a wide variety and we also generate a large number of observations, totalling over 4 million, across models and replications. Note that the main computational burden is the numerical (re)optimization of the GARCH model over 300 K times across all simulations—and that involves (re)optimization only every 20 observations!.
- 10.
We fix the degrees of freedom to their true value of 3 during estimation and forecasting, thus giving GARCH a relative advantage in estimation.
- 11.
The phenomenon of poor performance of GARCH forecasting when the DGP is actually GARCH may seem puzzling and certainly deserves further study. Our experience based on the simulations suggests that the culprit is the occasional instability of the numerical MLE used to fit the GARCH model (computations performed in R using an explicit log-likelihood function with R optimization routines). Although in most trials the GARCH fitted parameters were accurate, every so often the numerical MLE gave grossly inaccurate answers which, of course, affect the statistics of forecasting performance. This instability was less pronounced when the fitting was done based on a large sample (case of 900). Surprisingly, a training sample as large as 250 (e.g. a year of daily data) was not enough to ward off the negative effects of this instability in fitting (and forecasting) based on the GARCH model.
- 12.
All NoVaS forecasts were made without applying an explicit predictor as all \(W_{t}(\displaystyle \varvec{\theta }^{*})\) series were found to be uncorrelated.
- 13.
Note also the performance improvement from the use of the median GARCH versus the mean GARCH forecasts for the MSFT series. Recall that our simulation results showed that the performance of a GARCH model could be way off the mark if the training sample was small; here we use only 157 observations for training the MSFT series and the GARCH forecasts cannot outperform even the Naive benchmark.
- 14.
For the MSFT series the benchmark forecasts are also significantly better than the GARCH forecasts.
- 15.
Changing the value of \(\alpha \) did not result in improvements in the other three series.
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Politis, D.N., Thomakos, D.D. (2013). NoVaS Transformations: Flexible Inference for Volatility Forecasting. In: Chen, X., Swanson, N. (eds) Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1653-1_19
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