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Statistical Signal Extraction and Filtering : Structual Time Series Models

In economics, it is traditional to decompose time series into a variety of components, some or all of which may be present in a particular instance. One is liable to assume that the relative proportions of the components of an aggregate index are maintained, approximately, in spite of the variations in their levels. Therefore, the basic model of an economic index is a multiplicative one; and, if Y (t) is the sequence of values of an economic index, then it can be expressed as