Modelling Financial Time Series
Financial time series, in general, exhibit average behaviour at “long” time scales and stochastic behaviour at ‘short” time scales. As in statistical physics, the two have to be modelled using different approaches — deterministic for trends and probabilistic for fluctuations about the trend. In this talk, we will describe a new wavelet based approach to separate the trend from the fluctuations in a time series. A deterministic (non-linear regression) model is then constructed for the trend using genetic algorithm. We thereby obtain an explicit analytic model to describe dynamics of the trend. Further the model is used to make predictions of the trend. We also study statistical and scaling properties of the fluctuations. The fluctuations have non-Gaussian probability distribution function and show multi-scaling behaviour. Thus, our work results in a comprehensive model of trends and fluctuations of a financial time series.
KeywordsDiscrete Wavelet Transform Probability Distribution Function Financial Time Series Smooth Trend Trend Series
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