A Class of Permanent Component Time Series Models.
Joseph A. Machak · Deep Blue (University of Michigan) · 1981
We consider a class of models of the form Y(,t) = Y(,t)('p) + (epsilon)(,t), where the (rx1) vector Y(,t) is observed and the unobserved vectorsY(,t)('p) and (epsilon)(,t) are to be regarded as the permanent and transitorycomponents of Y(,t) respectively. This class of models will haveseveral important features. First, Y(,t) will be an (rx1) vector where in general r (GREATERTHEQ) 1, so we can deal with vector as well as scalar processes. Second, both Y(,t)('p) and (epsilon)(,t) will be stochastic vectors. Third, models with nonstationary, as well as stationary Y(,t)('p), will be considered. Finally, when r = 1, this class of models will allow for parametric departures from the st and ard Ordinary Least Squares (OLS) model. An allocation parameter, (gamma), is introduced into the variance-covariance matrices of Y(,t)('p) and (epsilon)(,t). Using this allocation parametera hierarchy of related models possessing the above features is constructed. It is shown that this hierarchy contains many well-known variable parameter regression and time sense models as special cases, as well as introducing many new models. Algorithms are developed to efficiently calculate the maximum likelihood estimates of the parameters in these models. Finally, a subclass of these models is used with the LivingstonConsumer Price Index (CPI) expectations data to investigate the"Rational Expections" hypothesis. Models are constructed whereY(,t) is expected CPI. It is concluded that economic agents "smooth-out" their CPI inflation expectations by moving some of their uncertainty from (epsilon)(,t) to Y(,t)('p).