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Abstract:
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To describe the seasonal patterns in economic data, we use a weak linear representation of integrated processes. We assume that the polynomial associated to the Wold representation of the process appropriately differenced satisfies a not too restrictive summability condition. Relying on a simple additive decomposition of these integrated processes, the statistical treatment consists of removing from raw data the pure seasonal random walk components present at each seasonal frequencies. These random walk components are separately derived from a Beveridge-Nelson type decomposition of the demodulated process at each seasonal frequency. This framework allows for a simultaneous seasonal adjustment of a set of variables, the use of robust estimation procedures to limit the influence of outlier definition, and gives a rationale for the computation of asymmetric filters at the ends of the sample
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