Model-Free vs. Model-Based Volatility Prediction

Abstract

The well-known ARCH/GARCH models for financial time series have been criticized of late for their poor performance in volatility prediction, i.e., prediction of squared returns. 1 Focusing on three representative data series, namely a foreign exchange series (Yen vs. Dollar), a stock index series (the S&P500 index), and a stock price series (IBM), the case is made that financial returns may not possess a finite fourth moment. Taking this into account, we show how and why ARCH/GARCH models-when properly applied and evaluatedactually do have nontrivial predictive validity for volatility. Furthermore, we show how a simple model-free variation on the ARCH theme can perform even better in that respect. The model-free approach is based on a novel normalizing and variance-stabilizing transformation (NoVaS, for short) that can be seen as an alternative to parametric modelling. Properties of this transformation are discussed, and practical algorithms for optimizing it are given.

Comparison of forecasting performances: Does normalization and variance stabilization method beat GARCH(1,1)‐type models? Empirical evidence from the stock markets

“…Owing to the fact that the variance stabilizing is simple and the assumed structure of the return series is known, this means that a local scale predictor must be built for normalization. Hence the following constraints are needed (Politis, ): It can be assumed that the series { W t , α } has unconditional variance from Equation , but there is no doubt that the coefficients p and a i must be carefully selected to enable a degree of conditional homogeneity. To do this, p must be small enough.…”

“…In this section, the NoVaS method is used to predict the squared return series. Equation can be rearranged as follows (Politis, ): After taking the square root of Equation , Equation is obtained in the following form: The process of the prediction to be given is described by taking a step forward. Hence let g be a measurable function.…”

“…In this section, the NoVaS method, which is model free and not necessary to estimate parameters, will be introduced as an alternative technique to the popular ARCH/GARCH models in forecasting volatility. The NoVaS method includes two calculation techniques: simple and exponential NoVaS (Politis, ).…”

Model Free Inference on Multivariate Time Series with Conditional Correlations

“…With these designations, our empirical measure of the time-localized variance becomes a combination of an unweighted, recursive estimator s t−1 of the unconditional variance of the returns σ 2 = E X 2 1 , or of the mean absolute deviation of the returns δ = E|X 1 |, and a weighted average of the current. The necessity and advantages of including the current value is elaborated upon by Politis [3][4][5][6][36][37][38] and the past p values of the squared or absolute returns.…”

“…In this paper we present a novel approach for modeling conditional correlations building on the NoVaS (NOrmalizing and VAriance Stabilizing) transformation approach introduced by Politis [3][4][5][6] and significantly extended by Politis and Thomakos [7,8]. Our work has both similarities and differences with the related literature.…”