Exponential Smoothing, Long Memory and Volatility Prediction

31 Pages Posted: 5 Aug 2014

See all articles by Tommaso Proietti

Tommaso Proietti

University of Rome II - Department of Economics and Finance

Date Written: August 4, 2014


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 low-pass 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

JEL Classification: C22, C53, G17

Suggested Citation

Proietti, Tommaso, Exponential Smoothing, Long Memory and Volatility Prediction (August 4, 2014). CEIS Working Paper No. 319. Available at SSRN: https://ssrn.com/abstract=2475784 or http://dx.doi.org/10.2139/ssrn.2475784

Tommaso Proietti (Contact Author)

University of Rome II - Department of Economics and Finance ( email )

Via Columbia, 2
Rome, 00133

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