Forecasting volatility from econometric datasets is a crucial task in finance. To acquire meaningful volatility predictions, various methods were built upon GARCH-type models, but these classical techniques suffer from instability of short and volatile data. Recently, a novel existing normalizing and variance-stabilizing (NoVaS) method for predicting squared log-returns of financial data was proposed. This model-free method has been shown to possess more accurate and stable prediction performance than GARCH-type methods. However, whether this method can sustain this high performance for long-term prediction is still in doubt. In this article, we firstly explore the robustness of the existing NoVaS method for long-term time-aggregated predictions. Then, we develop a more parsimonious variant of the existing method. With systematic justification and extensive data analysis, our new method shows better performance than current NoVaS and standard GARCH(1,1) methods on both short- and long-term time-aggregated predictions. The success of our new method is remarkable since efficient predictions with short and volatile data always carry great importance. Additionally, this article opens potential avenues where one can design a model-free prediction structure to meet specific needs.

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Volatility forecasting is important in financial econometrics and is mainly based on the application of various GARCH-type models. However, it is difficult to choose a specific GARCH model that works uniformly well across datasets, and the traditional methods are unstable when dealing with highly volatile or short-sized datasets. The newly proposed normalizing and variance stabilizing (NoVaS) method is a more robust and accurate prediction technique that can help with such datasets. This model-free method was originally developed by taking advantage of an inverse transformation based on the frame of the ARCH model. In this study, we conduct extensive empirical and simulation analyses to investigate whether it provides higher-quality long-term volatility forecasting than standard GARCH models. Specifically, we found this advantage to be more prominent with short and volatile data. Next, we propose a variant of the NoVaS method that possesses a more complete form and generally outperforms the current state-of-the-art NoVaS method. The uniformly superior performance of NoVaS-type methods encourages their wide application in volatility forecasting. Our analyses also highlight the flexibility of the NoVaS idea that allows the exploration of other model structures to improve existing models or solve specific prediction problems.

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To address the difficult problem of the multi-step-ahead prediction of nonparametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of nonparametric time-series model and show that the proposed point predictions are consistent with the true optimal predictor. We construct a quantile prediction interval that is asymptotically valid. Moreover, using a debiasing technique, we can asymptotically approximate the distribution of multi-step-ahead nonparametric estimation by the bootstrap. As a result, we can build bootstrap prediction intervals that are pertinent, i.e., can capture the model estimation variability, thus improving the standard quantile prediction intervals. Simulation studies are presented to illustrate the performance of our point predictions and pertinent prediction intervals for finite samples.