By Werner Ploberger, Walter Krämer, Raimund Alt (auth.), Walter Krämer (eds.)
Econometric versions are made from assumptions which by no means precisely fit truth. one of the such a lot contested ones is the requirement that the coefficients of an econometric version stay good over the years. contemporary years have for that reason obvious a variety of makes an attempt to check for it or to version attainable structural switch while it could not be neglected. This choice of papers from Empirical Economics mirrors a part of this improvement. the purpose of departure of such a lot stories during this quantity is the normal linear regression version Yt = x;fJt + U (t = I, ... , 1), t the place notation is clear and the place the index t emphasises the truth that structural swap is usually mentioned and encountered in a time sequence context. it truly is less of an issue for go part information, even though many exams practice there to boot. The null speculation of so much checks for structural switch is that fJt = fJo for all t, i.e. that an identical regression applies to all time sessions within the pattern and that the disturbances u are good behaved. the well-known Chow try for example assumes t that there's a unmarried structural shift at a identified time limit, i.e. that fJt = fJo (t< t*), and fJt = fJo + t1fJ (t"?:. t*), the place t* is known.
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Ohtani 3 Abstract: In this paper, we set up a switching regression model in which individual coefficients are allowed to shift at different change-points. We also apply it to the energy demand equations and examine structural change in the demands for total fuel oil and for light oil and kerosene at the second oil crisis. It is shown that assuming the different change-points for individual coefficients yields more plausible results than assuming the same change-point for all coefficients. 1 Introduction Since Quandt (1958) proposed a switching regression model, the model has often been used to detect a structural change-point in some economic equations.
54 M. L. King and P. M. Edwards For 1 ~j~m- 2 and m- j odd, let q=(m-l-J)/2. 1 (-1)k(2 q){Sin (2q - 2k)OA/{2q - 2k}] . k=O k For 1~j~m-2andm-j even,letq=(m-2-J)/2. Then Wj=T(q+3/2)n- I / 2{T(q+ l)}-I [2- 2q(-1)q+1 k~O (_1)k(2 q : 1) (cos {(2q+ 1- 2k)Oj}-1)/(2q+ 1-2k)] The resultant Wj,j= 1, ... , m-l, after having been sorted into ascending order can be used to calculate standard test statistics based on the EOF as follows: (i) The Kolmogorov-Smirnov statistics D, D+, D-: D+= max l::5i::5m-1 {i/(m-l)-wY)}, D-= max l::5i::5m-1 [wY)-W-l)/(m-l)}] (ii) The Cramer-von Mises statistic W 2: m-I W2= L ;=1 [wY)-{(2i-l)/(2m-2)}]2+ 1/{12(m-l)}.
It would be silly to build a complicated model when a simple one will do. It is therefore important to be able to test the adequacy of a fitted linear regression model. Typically, little may be known about how and when the regression relationship might change so that the test will need to cast a wide net. One possible approach is to apply a goodness-of-fit test to the linear regression. 1 This research was supported by a grant from the Australian Research Council. It was also supported by the ESRC under grant HR8323 while the first author was visiting the Department of Economics at the University of Southampton.