Proietti, Tommaso (2014): 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.
Item Type:  MPRA Paper 

Original Title:  Exponential Smoothing, Long Memory and Volatility Prediction 
Language:  English 
Keywords:  Realized Volatility. Signal Extraction. PermanentTransitory Decomposition. Fractional equalroot IMA model. 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C53  Forecasting and Prediction Methods ; Simulation Methods G  Financial Economics > G1  General Financial Markets > G17  Financial Forecasting and Simulation 
Item ID:  57230 
Depositing User:  Tommaso Proietti 
Date Deposited:  10. Jul 2014 20:06 
Last Modified:  09. Aug 2015 10:45 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/57230 