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Abstract:
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Determining the periodicity of seasonal components (if any) within a time series is an important initial step in analysing data. Traditionally the seasonal scale is either known, e.g. quarterly, or is estimated using peaks in a periodogram or dummy variables in a regression. When estimating seasonality using the Fourier periodogram we have to determine what are "significant" peaks. There are several methods that attempt to automate peak determination but all have parameters that the user has to set to encode significance. We will present an alternative approach for automatically determining seasonality using wavelets. Wavelets are an alternative basis functions to the Fourier sinusoids that give a decomposition of frequency bands over time (compared to the Fourier Transform which gives only a frequency decomposition). Using the theoretical relationship between wavelet coefficients over these frequency bands we can determine the seasonality of a time series automatically whether it has an hourly, weekly, monthly or decadal season. We will illustrate our methodology for automatic seasonality detection and subsequent seasonal adjustment using simulated and economic data.
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