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Exponential Smoothing, Long Memory and Volatility Prediction

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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.

Suggested Citation

  • Tommaso Proietti, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," CEIS Research Paper 319, Tor Vergata University, CEIS, revised 30 Jul 2014.
    • Handle: RePEc:rtv:ceisrp:319
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Realized Volatility. Signal Extraction. Permanent-Transitory Decomposition. Fractional equal-root IMA model;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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