A Fuzzy Framework for Realized Volatility Prediction: Empirical Evidence From Equity Markets

Abstract

This study introduces a realized volatility fuzzy time series (RV-FTS) model that applies a fuzzy c-means clustering algorithm to estimate time-varying (Formula presented.) latent volatility states and their corresponding membership degrees. These memberships are used to construct a fuzzified volatility estimate as a weighted average of cluster centroids. The final volatility forecast is generated through an exponentially weighted moving average (EWMA) mechanism that combines the most recent fuzzified volatility estimate with the previous forecast, governed by the smoothing parameter (Formula presented.). The two hyperparameters are estimated using a rolling-window cross-validation approach. Our empirical study is based on volatility forecasts for 14 major stock market indices, covering more than 20 years of data. We predict 1- to 22-day-ahead volatility and compare the RV-FTS model with nine standard volatility model benchmarks: generalized autoregressive conditional heteroscedasticity (GARCH), ARFIMA, AR, heterogeneous autoregressive (HAR), EWMA, and random forest models, as well as conditional combination forecasts. We find that, in the short-term, day-ahead setting, the RV-FTS model tends to outperform the benchmark models under the mean squared error loss and performs similarly to the best models under the QLIKE loss. The conditional combination forecast shows that across all markets and multiple forecast horizons, there are periods when the weight of the RV-FTS model in the conditional combination of eight models reaches 50% or more. The volatility timing strategy also shows that the RV-FTS model leads to higher cost- and risk-adjusted returns compared with a benchmark volatility model.