Determinism and non-linear behaviour in log-return and conditional volatility time series of the stock market index is examined for twenty-six countries. For this goal, the principal statistical techniques used in this study are a robust estimator of correlation dimension, a normalized non-linear prediction error, and pseudo-periodic surrogate data method. The proposed approach indicates, first, the stochastic behaviour of all log-return time series. Second, the inability of local linear, ARMA, or state- dependent noise models (such as ARCH, GARCH, and EGARCH) to describe its structure for the frontier, emerging, and developed markets. The same stochastic behaviour of conditional volatility time series, estimated by the stochastic volatility model with moving average innovations, is detected. This finding proves the efficiency of the stochastic volatility model compared with some analysed types of GARCH models for all studied markets. JEL Classification: C12, C52, D53, E44
In this paper, a hybrid scheme for time series prediction is developed based on wavelet decomposition combined with Bayesian Least Squares Support Vector Machine regression. As a filtering step, using the Maximal Overlap Discrete Wavelet Transform, the original time series is mapped on a scale-by-scale basis yielding an outcome set of new time series with simpler temporal dynamic structures. Next, a scale-by-scale Bayesian Least Squares Support Vector Machine predictor is provided. Individual scale predictions are subsequently recombined to yield an overall forecast. The relevance of the suggested procedure is shown on the NINO3 SST anomaly index via a comparison with the existing methods for modeling and prediction.
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