By Professor Dr. Walter Krämer, Dr. Harald Sonnberger (auth.)

This monograph grew out of joint paintings with a variety of devoted colleagues and scholars on the Vienna Institute for complex stories. we might most likely by no means have began with no the impetus of Johann Maurer, who for a while used to be the spiritus rector at the back of the Institute's macromodel of the Austrian financial system. Manfred Deistler supplied sustained stimulation for our study via many discussions in his econometric examine seminar. comparable credit are because of Adrian Pagan, Roberto Mariano and Garry Phillips, the econometrics visitor professors on the Institute within the 1982 - 1984 interval, who via their lectures and recommendation have contributed enormously to our attempt. Hans SchneeweiB provided worthy reviews on an previous model of the manuscript, and Benedikt Poetscher was once constantly keen to lend a aiding . hand after we had hassle with the math of the exams. remember that that any blunders are our personal. a lot of the programming for the checks and for the Monte Carlo experiments used to be performed through Petr Havlik, Karl Kontrus and Raimund Alt. with out their suggestions, our study venture could were very unlikely. Petr Havlik and Karl Kontrus additionally. learn and criticized parts of the manuscript, and have been of serious assist in decreasing our mistakes fee. a few of the extra theoretical leads to this monograph may by no means have come to gentle with out the mathematical services of Werner Ploberger, who supplied many of the statistical heritage of the bankruptcy on trying out for structural swap . .

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3) Under Bo, C has again an F distribution, with T-To and TO-K degrees of freedom. 2). When TO = T-K, ~ = 0, Le. ii 'ii = iiI 'iiI and C and Fare identical. When TO < K (Le. 3) applies with ~ in place of iiI. The Chow test cannot be applied when both TO:;;;K and T-To:;;;K. 3) of the Chow test can be viewed as a test for predictive failure. 4) where 0 = EY2-x,[:J1 is a (T-To) vector of unknown coefficients, which equal the mean errors when predicting Y2 from the first period. The hypothesis that the mean prediction errors are all zero therefore amounts to Bo': 0 = O.

1) separately, with residual vectors ul and ~, and the ML estimate for i is ~2 = ii 'ii/T. The maximised value of the log likelihood function is therefore T T T -2 II = - -In(27r) - - - - In(a ) . ) - In(~2) ] , STRUCTURAL CHANGE 4S xi. 2). 2) if its eKact finite sample null distribution were known. When TO> T-K (Le. 1) cannot be computed due to rank deficiency in ~. 3) Under Bo, C has again an F distribution, with T-To and TO-K degrees of freedom. 2). When TO = T-K, ~ = 0, Le. ii 'ii = iiI 'iiI and C and Fare identical.

G. 21) (T_K)1I2 where Q(Z)=(2'1rrl/2J~exp(-u212)du. 850 . 23). First, the Wr's were replaced by the better manageable W's. Second, the W's were r r assumed to be discrete observations of a continuous process with a similar covariance structure, and fmally, we disregarded the probability that a sample path crosses both critical lines. As a result, the CUSUM test will in general not attain its nominal significance level 01 in fmite samples (a property it shares with many of the procedures 54 TESTING REGRESSORS discussed so far), and we will for selected X-matrices determine this discrepancy via Monte Carlo experiments.