"Frontmatter". In: Analysis of Financial Time Series

APPLICATION 165unem. rate4 6 8 10••• • • ••••••• • • • • ••• •• • ••• • ••••••• •• • •• • •••• •• •• ••• • •• ••••• ••• ••• ••• ••••• • • •••• • ••• •••• •• ••••• ••••• •• •••••• •• •• •••• •• •• • ••••• ••••••••• ••••• • •• ••• ••••••••••••••• ••••• •••••• •••••1950 1960 1970 1980 1990yearFigure 4.8. Time plot of the U.S. quarterly unemployment rate, seasonally adjusted, from1948 to 1993.Using a modeling procedure similar to that of Tsay (1989), Montgomery et al.(1998) build the following TAR model for the x t series:x t ={ 0.01 + 0.73xt−1 + 0.10x t−2 + a 1t if x t−2 ≤ 0.1,0.18 + 0.80x t−1 − 0.56x t−2 + a 2t otherwise.(4.51)The sample variances of a 1t and a 2t are 0.76 and 0.165, respectively, the standarderrors of the three coefficients of Regime 1 are 0.03, 0.10, and 0.12, respectively,and those of Regime 2 are 0.09, 0.1, and 0.16. This model says that the change inthe U.S. quarterly unemployment rate, x t , behaves like a piecewise linear model inthe reference space of x t−2 − x t−3 with threshold 0.1. Intuitively, the model impliesthat the dynamics of unemployment act differently depending on the recent changein the unemployment rate. In the first regime, the unemployment rate has had eitherTable 4.3. Nonlinearity Test for Changes in the U.S. Quarterly Unemployment Rate:1948.II-1993.IV. An AR(5) Model Was Used in the Tests, Where LST Denotes the Test ofLuukkonen et al. (1988) and TAR(d) Means Threshold Test with Delay d.Type Ori-F LST TAR(1) TAR(2) TAR(3) TAR(4)Test 2.80 2.83 2.41 2.16 2.84 2.98p value .0007 .0002 .0298 .0500 .0121 .0088