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Abstract:
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An increasing valuable tool for modeling nonstationary time series data is time deformation. However, since the time transformation transforms the scale, equally spaced data become unequally spaced data. Interpolation is therefore often used to obtain regularly sampled data, which can be modeled by the classical ARMA modeling techniques. In this paper, the need for interpolation is eliminated by employing the continuous time autoregressive model. To estimate the parameters, the maximum likelihood function is decomposed by means of the Kalman filter. The resulting modeling improvements include, more accurate estimation of the spectrum, better forecasts, and the separation of the data into its smoothed time-varying components. The technique is applied to simulated and real data for illustrations.
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