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Abstract:
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Previous studies have shown that the structure of time series may change at any time due to the change in mean and/or variance of the series, which violates the assumption of stationarity and creates uncertainty in parameter estimates and forecasting. This paper, discusses a method of analyzing non-stationary time series, by breaking the series into smaller locally stationary series. The specific focus in this paper will be on financial time series. To achieve the main goal, which is locating beak-points: a point in the series where occurs a sudden change in mean and/or variance, this method uses Maximum Likelihood Estimation (MLE) by means of Simulated Annealing (SA) optimization. Then the originally non-stationary time series is divided into locally stationary time series according to the number of break points found. The analysis by this method considers each interval on which the series is stationary as an independent time series with its specific parameters, which enhances the accuracy in parameter estimates and forecasting. Applications to simulated and real financial data are presented.
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