Andrews, Donald (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica 61, 821-856.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....our findings is the presence of structural breaks in the data generating processes of the variables themselves. To allow for this possibility, we check for a structural break in the unbiasedness and e#ciency test regressions based on (4) In particular, we use the sup Wald test as developed by Andrews (1993): SupW = sup # 1 ##B## 2 W T (# B ) 7) where W T (# B ) denotes a Wald statistic of the hypothesis of constancy of the parameters #, # and # in (4) against the alternative of a one time change for fixed break data # B , given by f X t t k X t = # # 1 # 1 t k X t W # t k # 1 # I[t ....

Andrews, D.W.K. (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica 61, 821--856.

....# = TB T . Consider two estimation strategies. The first is to test the individual series for stable means, 3 and if there is evidence of shifts in mean, use the estimated break dates to form dummy variables 3 This can be achieved using one or more of the tests available in the literature e.g. Andrews (1993), Andrews and Ploberger (1994) Perron (1991) Vogelsang (1997) or Vogelsang (1998) The date of the shift can be consistently estimated by least squares following Bai (1994) 8 and to obtain y t = y t D U t #. We can then form a VAR for y t . 4 We refer to this as the two step ....

Andrews, D. W. K. (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica 61, 821--856.

....of testing whether a parameter in a statistical model remains constant over time. Most tests in the literature concerning change point problems are retrospective tests, that is given a set of observations, it is the aim to decide if a change has occured within a span of data see for example Andrews (1993) and Ploberger, Kramer Kontrus (1989) among many others. In contrast a monitoring procedure for structural change allows us to check parameter constancy, any time new data become available. The purpose of the monitoring procedure described in Chu et al. 1996) is to detect a change in a ....

Andrews, D. W. K. (1993), `Test for parameter instability and structural change point', Econometrica 61, 821--856.

....as OOS t and will reference the latter as the OOS F test. The limiting distributions of both the OOS t and OOS F tests are non standard. Each can be written as functions of stochastic integrals of quadratics of Brownian Motion. The distributions bear some resemblance to those derived by Andrews (1993), in the context of testing for changepoints in the regression function, but are distinct. Tables are provided in order to facilitate the use of these distributions. Furthermore, since the limiting distributions do not lie within any well known class of distributions it is unclear how well the ....

Andrews, Donald W.K. (1993): "Tests for Parameter Instability and Structural Change with Unknown Change Point", Econometrica, 61, 821-856.

.... endogenizing of the timing of break did not provide a useful distributional theory for hypothesis testing purposes (Quandt, 1960; Brown et al. 1975) The asymptotic distributions of the sup Wald, sup LM and sup LR test statistics for structural break at unknown timing were recently puzzled out by Andrews (1993). These distributions are constructed based Fax: 852 2603 5805. E mail address: b792703 mailserv.cuhk.edu.hk (T. Tai leung Chong) 0954 349X 99 see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S0954 349X(99)00013 2 422 T. Tai leung Chong Structural Change and ....

....is to verify Corollary 2. Using the definition of W T (#) in (3.1) Table 1 (A C) shows the critical value c such that: Pr # sup ## (#,1 #) W T (#)#c # =#. Table 1 (A) shows the critical values in the absence of specification errors, the values are very close to those obtained in Andrews (1993); B) and (C) display the critical values under specification errors a (A) b=1, No specification errors) C(#,1,1,1,1) 1 #=2 #=3 #=1 C(3, 1, 1, 1, 1) 1 C(1, 1, 1, 1, 1) 1 C(2, 1, 1, 1, 1) 1 0.1 0.05 0.01 0.1 0.05 0.01 0.1 0.05 ### 0.01 0.25 11.06 7.70 6.23 11.13 6.43 7.73 6.25 11.40 7.97 6.69 ....

Andrews, D.W.K., 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821 -- 856.

....known a priori generally involves standard test statistics and estimators (Chow (1960) When the break point is unknown the problem becomes more difficult because the break point must be estimated and, under the null of no break, this parameter is unidentified. Andrews, Lee and Ploberger (1996) Andrews (1993), Hansen (1992) Christiano (1992) and others have studied this problem in various contexts. When considering multiple break points the problem becomes further complicated since it requires specification of the number of breaks and inclusion of enough parameters to account for each regime. This ....

....motions and no longer normal. This arises because the regressor in the test equation becomes nearly integrated as approaches one. A possible choice is = 0.8. A second strategy is to take the infimum of t over feasible values of as suggested by Davies (1977) and elaborated on by Hansen (1996) Andrews (1993) and others. The null distribution of this statistic is well defined but will depend on the correlation of t across various different values of which will in general depend on the distribution of # t . In this case, the simulated values prove reasonably robust to GARCH(1,1) and excess kurtosis. ....

ANDREWS, D.W.K. (1993): "Tests for Parameter Instability and Structural Change with an Unknown Change Point," Econometrica, 61, 821-856.

....and asymmetric alternatives in Section 4.5 Such tests should allow for uncertainty about where a breakpoint may lie, due to the many potential candidates, including the different phases in the oil market and the change in Federal Reserve operating procedures from 1979 to 1982. Thus I use the Andrews (1993) test for a structural break at an unknown changepoint. When this test is applied to the middle 70 of the sample (Andrews recommended choice) for the core inflation equation, the maximal 2 statistic is 59.1, which greatly exceeds the critical value for a 1 test, strongly supporting a ....

Andrews, Donald W.K. (1993), "Tests for Parameter Instability and Structural Change with Unknown Change Point", Econometrica 61, 821-856.

....of z(t) and the grid for # covered the bottom quartile, with the restriction that # mp,T and # mp,B be non zero in at least eight quarters. The restriction avoids the econometric problems associated with threshold models where the threshold is close to the boundary of the parameter space. See Andrews (1993, p. 826) for a discussion of these problems. 23 Alternative results on the asymptotic normality of maximum likelihood estimators, which do not require a smooth objective function, exist but are beyond the scope of this paper. 24 Hansen (1996b) describes a procedure to estimate a confidence ....

Andrews, D. W. K., 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821--856.

....performance of two alternative approximations to the finite sample distributions of test statistics for structural change, one based on asymptotics and one based on the bootstrap. We focus on tests acknowledging that the break point is selected endogenously in particular, the supremum tests of Andrews (1993). We explore a variety of issues of interest in applied work, focusing particularly on smaller samples and persistent dynamics. The bootstrap approximation to the finite sample distribution appears consistently accurate, in contrast to the asymptotic approximation. The results are of interest not ....

....data based procedures are typically used to determine the most likely location of a break, thereby invalidating the distribution theory associated with conventional tests. Tests formally incorporating selection effects are therefore desirable. Important such tests are the supremum test of Andrews (1993) and the related average and exponential tests of Andrews and Ploberger (1992) Andrews, Lee, and Ploberger (1992) and Hansen (1991a, 1991b) At issue, however, is how best to approximate their finite sample distributions under the null hypothesis of structural stability. One obvious ....

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Andrews, D.W.K., 1993, Tests for parameter instability and structural change with unknown change point, Econometrica 61, 821-856.

....on the finding that coefficients in simple specifications of the Fed s policy rule shift over time [e.g. Clarida, Gali and Gertler (1998) and Taylor (1999) The simple rules emerge from restrictions on the policy behavior embedded in VARs. For our 17 They use a Lagrange multiplier variant of Andrews s (1993) test, which checks every possible break point and tests the significance of the associated LM statistics. Using quarterly data, Sims and Zha (1998b) corroborate Bernanke and Mihov s results by comparing a model fit from 1964:1 to 1994:1 to one fit separately to 1964:11979: 3 and 1983:1 1994:1. ....

Andrews, Donald W. K. (1993). "Tests for Parameter Instability and Structural Change with Unknown Change Point." Econometrica 61, July, 821-856.

....even in the presence of structural breaks will therefore need to be employed. Second, a time period free of structural breaks in the cointegration relationship has to be identified otherwise the interpretation of the cointegration vector will result in misleading conclusions. As Quandt (1960) Andrews (1993), Diebold and Chen (1996) and Hansen (1992) show, a supremum F test allows the exact determination of the timing of such a structural break. Once the break has been determined, the complete cointegration analysis can then be conducted for the pre and post break periods separately. In particular, ....

....dependent variable and the policy rate x t of the same country as the independent variable: 3) y t = g 1 g 2 x t u t To test for structural breaks a supremum F (supF) test is calculated. This test was first proposed by Quandt (1960) and has recently been the focus of various studies (e.g. Andrews 1993, Diebold and Chen 1996, Hansen 1992) This test can be seen as a rolling Chow test and is more flexible than the standard Chow test because it allows simultaneously to test for the significance and the timing of a structural break in the cointegration relationship 5 . If a break is present, the ....

Andrews, D.W.K., 1993, Tests for parameter instability and structural change with an unknown change point, Econometrica 61, 821-856.

....rank three curvature in aggregate data is limited. 13 We consider two additional tests of the empirical adequacy of this model. The first is a test for stability of the coe#cients (that are not statistically di#erent from zero in the full sample) For both sets of instruments, the sup LM test of Andrews (1993) is maximized at # = 2, where #T is the breakpoint for a sample of size T . The test statistic is 16.38 and 11.43 for the two sets of instruments respectively, and the 5 critical value for seven parameters is 21.07. Thus, we cannot reject the null hypothesis of parameter constancy. The second ....

Andrews, D. W. K. (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica 61, 821--856.

....allows agents to be less informed about possible policy regimes than would be the case for a shifting regimes analysis. 15 In the learning simulations referenced in this paper, agents test for intercept shifts in a twelve order autoregression in inflation using critical values extrapolated from Andrews (1993). The search by simulated agents for significant changepoints is in real time as new observations are added in expanding monthly samples over the period 1954m1 1997m9. To account for heterogeneous expectations among bond traders, agents are viewed as subscribing to one of m market forecast ....

Andrews, D., 1993, "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, 61(4), July, 821-56.

.... estimate of a time varying parameter variance has a point mass at zero when the true variance is small (Stock and Watson, 1998) Meanwhile, the estimates are generally consistent with the Wald statistics reported in Table 1, while they avoid the problems, discussed in Zivot and Andrews (1992) and Andrews (1993), associated with an assumption of a known breakpoint. Figure 2 displays the filtered and smoothed inferences about the time varying parameter. The point estimates of long horizon predictability start out negative and potentially significant for both portfolios (k=72 and k=96) but are updated in ....

Andrews, D.W.K., 1993, "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica 61, 821-856.

....: y (n Gamma1) The minimization problem (10) can be solved by means of direct search, although there is a notable difference with estimation of the parameters in the corresponding unconstrained SETAR model, i.e. 1) with p = 1 and s t = y t Gamma1 . In the latter case, it suffices 3 Since Andrews (1993), the default value for 0 appears to be 0.15. 7 to compute the residual variance oe 2 n (fl) only for threshold values equal to the order statistics of y t Gamma1 , i.e. with fl = y (i) for each i such that y (i) 2 Gamma. This is easily understood since no observations are transferred from ....

Andrews, D.W.K., 1993, Tests for parameter instability and structural change with unknown change point, Econometrica 61, 821-856.

....procedure. 3. Bayesian Inference and Model Selection Procedure 6 3.1. Bayesian Inference of the Model For Bayesian inference of the model, given appropriate priors we need the marginal posterior distributions for the followings: 0 1 00 11 ] 0 ; 1 : k ] 0 ; 2 = [ 2 0 2 1 ] 0 ; D T = D 1 : D T ] 0 ; S T = S 1 : S T ] 0 ; p = p 00 p 11 ] 0 ; and q 00 . These marginal posterior distributions may be obtained from the joint posterior distribution, p( 2 ; D T ; S T ; p; q 00 j Y T ) 19) where Y T = y 1 : y T ....

Andrews, Donald W. K., 1993, \Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Vol. 61, No. 4, 821-856.

....may apply with particular force. The historical empirical importance of this Critique can be gauged by econometric stability tests (again, see Oliner, Rudebusch, and Sichel [60] Our estimated equations appear to easily pass these tests. For example, consider a stability test from Andrews [1]: 7 Almost identical parameter estimates were obtained by the SUR and by system ML methods because the cross correlation of the errors is essentially zero. 8 This p value was obtained by simulating the above ination equation 1000 times and ranking the sum of coecients from the unrestricted ....

....likelihood ratio test statistic for structural stability over all possible breakpoints in the middle 70 percent of the sample. For our estimated ination equation, the maximum likelihood ratio test statistic is 9. 77 (in 1972:3) while the 10 percent critical value is 14.31 (from table 1 in Andrews [1]) Similarly, for the output equation, the maximum statistic 7.87 (in 1982:4) while the 10 percent critical value is 12.27. 2.3. Comparison to other empirical estimates It is useful to compare our model with other empirical estimates in order to gauge its plausibility and its conformity to ....

Andrews, Donald W.K. (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica,6 1(4), 821-856.

....may apply 5 with particular force. The historical empirical importance of this Critique can be gauged by econometric stability tests (again, see Oliner, Rudebusch, and Sichel [60] Our estimated equations appear to easily pass these tests. For example, consider a stability test from Andrews [1]: the maximum value of the likelihood ratio test statistic for structural stability over all possible breakpoints in the middle 70 percent of the sample. For our estimated ination equation, the maximum likelihood ratio test statistic is 9.77 (in 1972:3) while the 10 percent critical value is ....

....likelihood ratio test statistic for structural stability over all possible breakpoints in the middle 70 percent of the sample. For our estimated ination equation, the maximum likelihood ratio test statistic is 9. 77 (in 1972:3) while the 10 percent critical value is 14.31 (from table 1 in Andrews [1]) Similarly, for the output equation, the maximum statistic 7.87 (in 1982:4) while the 10 percent critical value is 12.27. 2.3. Comparison to other empirical estimates It is useful to compare our model with other empirical estimates in order to gauge its plausibility and its conformity to ....

Andrews, Donald W.K. (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica, 61(4), 821-856.

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Andrews, D. (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica 61, 821-856.

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Andrews, Donald (1993), Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica 61, 821-856.

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Andrews, Donald W. K. Tests for Parameter Instability and Structural Change With Unknown Change Point, Econometrica, 61(4), July 1993, pp. 821-856.

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Andrews, D.W.K. (1993), "Tests for parameter instability and structural change with unknown change point," Econometrica, 61, 821-856.

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Andrews, D.W.K. (1993). "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica 61, 821-856. 18

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Andrews, D. W. K. (1993), "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica , 61, 821-856.

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Andrews, D. W. K. (1993), Tests for parameter instability and structural change with unknown change point, Econometrica 61, 821-856.

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