By R.I. Porter
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Extra resources for A school course in vectors
L , then we have the generalization of SETAR to a set of self-exciting threshold autoregressive/moving average models of order l; k, k, . . , k; k 1, . . , k 1 . 26 iD0 conditional on Xt d 2 Rs , s D 1, 2, . . , l. A more general form would be SETARMA l; k1 , . . , kl ; k10 , . . , kl0 , where ks and ks0 refer to AR order and MA order, respectively, conditional on Xt d 2 Rs . 27 iD0 conditional on Yt d 2 Rs ; s D 1, . . , l , where εt s ; s D 1, 2, . . , l, are strict WN sequences, with zero mean and finite variances and each are independent of fYt g.
The important assumption is that although fYt g series affects fXt g series, the reverse is not necessarily true. 3 Closed loop threshold models fXt , Yt g is called a closed loop threshold autoregressive system, denoted by TARSC, if fXt , Yt g are both TARSO. The assumption is that all WN sequences involved are independent of one another. This type of models allows both series to affect the corresponding regime in the other series. 29 and r is the threshold. If we choose the indicator function to be any ‘smooth’ function F where the only requirement on F is to be continuous and nondecreasing, we get a smooth threshold autoregressive (STAR) model.
Gray (1996) develops a generalized regime switching model of the shortterm interest rate that allows the short rate to exhibit both mean reversion and conditional heteroscedasticity and nests the GARCH and square root process specifications. Similarly Evans and Lewis (1995) estimate a regime switching model of exchange rates where they test the hypothesis that spot and forward rates move together one-for-one in the long run. They can’t reject this hypothesis and note that a long-run relationship between spot and forward rates is likely to be biased when a sample contains infrequent shifts in regime.
A school course in vectors by R.I. Porter
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