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Abstract:
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Many standard methods of time series analysis assume that observation times are both known and regularly-spaced. Regular sampling and known observation times are cornerstones of methods such as ARMA models and spectral estimation using the Fast Fourier Transform. When the measurement process is controlled by the experimenter, these assumptions can be largely met by design. However, there are cases in which the measurement process is not under complete experimental control, and the observation times are either irregular or unknown. For example, many data sets in astronomy have irregular sampling due to the effects of orbital geometry and interfering processes such as clouds. In paleoenvironmental studies, time series data consist of core samples of possibly known depth, but unknown age. Extending common time series analysis methods to these types of data is a challenge. We have developed a Bayesian approach based on a spectral representation of the process that decomposes the time series into trend, autoregressive, periodic, and noise components, typical of natural processes. We illustrate the method by application to paleoenvironmental data with latent times.
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