By James D. Hamilton, Baldev Raj
This ebook is a set of cutting-edge papers at the houses of industrial cycles and fiscal research. the person contributions hide new advances in Markov-switching versions with purposes to enterprise cycle study and finance. The advent surveys the present tools and new result of the decade. person chapters research positive aspects of the U. S. and eu enterprise cycles with specific specialize in the position of economic coverage, oil shocks and co routine between key variables. The short-run as opposed to long-run results of an fiscal recession also are mentioned. one other zone that's featured is an in depth research of forex crises and the potential of bubbles or fads in inventory costs. A concluding bankruptcy deals invaluable new effects on checking out for this type of regime-switching behaviour. total, the publication offers a state of the art over view of recent instructions in tools and effects for estimation and inference in keeping with using Markov-switching time-series research. a different function of the publication is that it comprises an indication of quite a lot of purposes in line with a typical method. it truly is anticipated that the subject matter of the ebook may be of specific curiosity to the macroeconomics readers in addition to econometrics pros, students and graduate scholars. we want to convey our gratitude to the authors for his or her robust contributions and the reviewers for his or her guidance and cautious realization to aspect of their reports.
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Extra info for Advances in Markov-Switching Models: Applications in Business Cycle Research and Finance
Krolzig ';11 - ~I' which equals 1 - ~I if the regime is 1 and -~I otherwise. Invoking proposition 1, the skewness of the Markov chain is given by: (I = where jJ,x = ~1jJ,1 + (1 - ~1)jJ,2 and ~I = probability of regime one. 5. Hence the matrix of transition probabilities must be symmetric, Pl2 = P21. This also implies that the regime-conditional means jJ,1 and 112 are equidistant to the unconditional mean jJ,y. Hence, in the case of two regimes we can test for non-deepness by testing the hypothesis PI2 = P2l.
With a sample size of T, there would be us 4 T cases to consider; an impractical computational burden. Kim (1994) proposes a method to approximate the likelihood function for state space models with Markov switching in both the measurement and transition equations. The algorithm is computationally efficient, and experience suggests that the degree of approximation is small; see Kim (1994) and Kim and Nelson (1999b). Conditional on SI = j and SI_I = i, the Kalman filter equations can be written as: ~;I;~I = rx~ + F~:_III_I (i,j) F'Pi1-111-1 F' + Q P111-1 = Penn anent and transitory components of recessions (i,)) '7111-1 = J, (i,j) 111-1 = Ll p(ij) III ):(ij) "111_1 HP(i,j) HI 111-1 c;(i,)) = c;(i,j) III H YI - 37 111-1 + p(i,)) HI[J,(i,j)]-ln(i,j) 111-1 111-1 '1111-1 = (1 _ p(i,j) HI[J,(i,))]-I)HP(i,j) 111-1 111-1 111-1 where c;~I;~1 is an inference on c;l based on information up to time t - 1, conditional on SI = j and SI_I = i; ~~I/) is an inference on ,c;l basedon information up to time t" conditional on SI = j and SI--: I = i; P,\;~)I and p,\;,j) are the MSE matrices of c;~I;~1 and ~~I/) respectively; '7~I;~1 is the conditional forecast is the conditional error of LlYt based on information up to time t - 1; .
As noted by Harrison and Stevens (1976) and Gordon and Smith (1988), if there are M possible states at each time period (4 in our case), each iteration of the filter produces an M-fold increase in the number of states to consider. With a sample size of T, there would be us 4 T cases to consider; an impractical computational burden. Kim (1994) proposes a method to approximate the likelihood function for state space models with Markov switching in both the measurement and transition equations. The algorithm is computationally efficient, and experience suggests that the degree of approximation is small; see Kim (1994) and Kim and Nelson (1999b).