Exponential Smoothing, Long Memory and Volatility Prediction

Tommaso Proietti

No 319, CEIS Research Paper from Tor Vergata University, CEIS

Abstract: Extracting and forecasting the volatility of financial markets is an important empirical problem. Time series of realized volatility or other volatility proxies, such as squared returns, display long range dependence. Exponential smoothing (ES) is a very popular and successful forecasting and signal extraction scheme, but it can be suboptimal for long memory time series. This paper discusses possible long memory extensions of ES and finally implements a generalization based on a fractional equal root integrated moving average (FerIMA) model, proposed originally by Hosking in his seminal 1981 article on fractional differencing. We provide a decomposition of the process into the sum of fractional noise processes with decreasing orders of integration, encompassing simple and double exponential smoothing, and introduce a lowpass real time filter arising in the long memory case. Signal extraction and prediction depend on two parameters: the memory (fractional integration) parameter and a mean reversion parameter. They can be estimated by pseudo maximum likelihood in the frequency domain. We then address the prediction of volatility by a FerIMA model and carry out a recursive forecasting experiment, which proves that the proposed generalized exponential smoothing predictor improves significantly upon commonly used methods for forecasting realized volatility.

Keywords: Realized; Volatility.; Signal; Extraction.; Permanent-Transitory; Decomposition.; Fractional; equal-root; IMA; model (search for similar items in EconPapers)
JEL-codes: C22 C53 G17 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2014-07-30, Revised 2014-07-30
New Economics Papers: this item is included in nep-ets, nep-for, nep-ore and nep-rmg
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Related works:
Working Paper: Exponential Smoothing, Long Memory and Volatility Prediction (2015)
Working Paper: Exponential Smoothing, Long Memory and Volatility Prediction (2014)
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