Title :
Best likelihood forecast of volatility in class of linear functions
Author :
Krivoruchenko, Mikhail I.
Author_Institution :
Inst. for Theor. & Exp. Phys., Moscow, Russia
Abstract :
An explicit analytical solution of the problem of constructing the best linear predictor of a stationary stochastic process with the autocorrelation function representing a superposition of several exponents is reported. The proposed method is applied further for volatility forecasting in financial time series. We account for the well-established deviations of financial time series from the Gaussian random walk, such as an approximate scaling and heavy tails of the return distributions, long-ranged volatility-volatility correlations (volatility clustering) and return-volatility correlations (leverage effect). Parameters of the predictor function are determined numerically by fitting the 100+ years of daily price returns of the Dow Jones 30 Industrial Average. Connection of the proposed method to the popular autoregressive conditional heteroscedasticity models is discussed.
Keywords :
Gaussian processes; autoregressive processes; econophysics; finance; functional analysis; random processes; time series; Gaussian random walk; analytical solution; autocorrelation function; autoregressive conditional heteroscedasticity models; daily price returns; financial time series; leverage effect; long-ranged volatility-volatility correlations; return distributions; return-volatility correlations; stationary stochastic process; volatility clustering; volatility forecasting; Autocorrelation; Data analysis; Econophysics; Fitting; Mechanical factors; Microscopy; Power system modeling; Probability distribution; Real time systems; Stochastic processes;
Conference_Titel :
Physics and Control, 2005. Proceedings. 2005 International Conference
Print_ISBN :
0-7803-9235-3
DOI :
10.1109/PHYCON.2005.1514040