The remainder of the paper is organized as follow: we explain the weekly IUIC data and highlight their unique statistical properties.
Figure 1 plots the weekly seasonally unadjusted IUIC over 1967-2012.
This is vividly reflected by the dotted line, which is the fitted value from a regression of seasonally adjusted IUIC on a trend (T), an intercept dummy (D) with values of one prior to 1983 and zero afterward, and the product term (DxT), which captures the change in the slope parameter after 1983.
Table 1 summarizes the salient features of the seasonally unadjusted weekly IUIC. Initial claims averaged 363,000 during the sample period with a minimum of 133,000 on 9/6/1969 and maximum of 1,074,000 at the bottom of the trough on 1/9/1982.
Next, we examine the stochastic properties of the weekly IUIC. Table 2 reports the results.
Given the ambiguity regarding the stochastic nature of IUIC, the empirical work that follows will work with the variable in both log level and log first-differences.
Modeling the univariate properties of the IUIC requires identification of the models for the conditional mean and conditional variance.
Visual inspections, along with summary statistics reported earlier, suggest that the conditional mean of IUIC is potentially the outcome of four types of unobservable behavior consisting of seasonal ([y.sup.S.sub.t]), cyclical ([y.sup.C.sub.t]), secular or trend ([c.sup.T.sub.t]), and random ([e.sub.t]) components: That is,