Testing in unobserved components models

Abstract

This article reviews recent work on testing for the presence of non‐stationary unobserved components and presents it in a unified way. Tests against random walk components and seasonal components are given and it is shown how the procedures may be extended to multivariate models and models with structural breaks. Many of the test statistics have an asymptotic distribution belonging to the class of generalized Cramér – von Mises distributions. A test for the number of common trends, or equivalently, co‐integrating vectors, is also described. Copyright © 2001 John Wiley & Sons, Ltd.

Foreign Property Shocks and the Impact on Domestic Securitized Real Estate Markets: An Unobserved Components Approach

“…While Harvey (2001) presents a methodology to test for the rank of a system (with and without breaks) using unobserved components models, the preferred approach here is the Inoue (1999) method since it also provides an outcome independent of the unobserved component methodology and ensures the structural breakpoints are chosen exogenously. Part (a) of Table 2 shows the trace and maximum eigenvalue statistics from each run of the Inoue Models A, B and C (as described in Appendix A) using the pure real estate price index series from each country, while part (b) does the same for the 80/20 portfolio.…”

Foreign Property Shocks and the Impact on Domestic Securitized Real Estate Markets: An Unobserved Components Approach

“…While Harvey (2001) presents a methodology to test for the rank of a system (with and without breaks) using unobserved components models, the preferred approach here is the Inoue (1999) method since it also provides an outcome independent of the unobserved component methodology and ensures the structural breakpoints are chosen exogenously. Part (a) of Table 2 shows the trace and maximum eigenvalue statistics from each run of the Inoue Models A, B and C (as described in Appendix A) using the pure real estate price index series from each country, while part (b) does the same for the 80/20 portfolio.…”

Seasonal Changes in Central England Temperatures

“…The 5% and 1% critical values of the † j -, j = 1, 2, 3, 4, 5, statistics are 0.247 and 0.329 respectively. The critical values are obtained from Harvey (2001). Italic values are significant at the 1% level.…”

“…The test statistic for H 0 : σ 2 j = 0, for a specific j = 1, 2, : : : , 6, takes the same form as equation (9), with e t representing the residual from the regression of y t on a set of explanatory variables x t = .1, t, z t , tz t / : We label the test + j . Its asymptotic null distribution is Cramér-von Mises with time trend; the critical values are available in Table I(b) of Harvey (2001).…”

Testing for the Presence of a Random Walk in Series with Structural Breaks

“…If all the seasonal frequencies are included, the asymptotic distribution of the resulting test statistic under the null is CvM(s À 1). As shown in Harvey and Streibel (1997), the inclusion of a time trend does not 144 affect this asymptotic distribution. Thus CvM 2 (s À 1) is not appropriate unless seasonal slopes, as used, for example, by Proietti (1998), are included in the model; this can be shown by an extension of the argument in Harvey and Streibel (1997, Appendix).…”

Foreign Property Shocks and the Impact on Domestic Securitized Real Estate Markets: An Unobserved Components Approach

“…While Harvey (2001) presents a methodology to test for the rank of a system (with and without breaks) using unobserved components models, the preferred approach here is the Inoue (1999) method since it also provides an outcome independent of the unobserved component methodology and ensures the structural breakpoints are chosen exogenously. Part (a) of Table 2 shows the trace and maximum eigenvalue statistics from each run of the Inoue Models A, B and C (as described in Appendix A) using the pure real estate price index series from each country, while part (b) does the same for the 80/20 portfolio.…”

Seasonal Changes in Central England Temperatures

“…The 5% and 1% critical values of the † j -, j = 1, 2, 3, 4, 5, statistics are 0.247 and 0.329 respectively. The critical values are obtained from Harvey (2001). Italic values are significant at the 1% level.…”

“…The test statistic for H 0 : σ 2 j = 0, for a specific j = 1, 2, : : : , 6, takes the same form as equation (9), with e t representing the residual from the regression of y t on a set of explanatory variables x t = .1, t, z t , tz t / : We label the test + j . Its asymptotic null distribution is Cramér-von Mises with time trend; the critical values are available in Table I(b) of Harvey (2001).…”

Testing for the Presence of a Random Walk in Series with Structural Breaks

“…If all the seasonal frequencies are included, the asymptotic distribution of the resulting test statistic under the null is CvM(s À 1). As shown in Harvey and Streibel (1997), the inclusion of a time trend does not 144 affect this asymptotic distribution. Thus CvM 2 (s À 1) is not appropriate unless seasonal slopes, as used, for example, by Proietti (1998), are included in the model; this can be shown by an extension of the argument in Harvey and Streibel (1997, Appendix).…”

Foreign Property Shocks and the Impact on Domestic Securitized Real Estate Markets: An Unobserved Components Approach

“…While Harvey (2001) presents a methodology to test for the rank of a system (with and without breaks) using unobserved components models, the preferred approach here is the Inoue (1999) method since it also provides an outcome independent of the unobserved component methodology and ensures the structural breakpoints are chosen exogenously. Part (a) of Table 2 shows the trace and maximum eigenvalue statistics from each run of the Inoue Models A, B and C (as described in Appendix A) using the pure real estate price index series from each country, while part (b) does the same for the 80/20 portfolio.…”

Seasonal Changes in Central England Temperatures

“…The 5% and 1% critical values of the † j -, j = 1, 2, 3, 4, 5, statistics are 0.247 and 0.329 respectively. The critical values are obtained from Harvey (2001). Italic values are significant at the 1% level.…”

“…The test statistic for H 0 : σ 2 j = 0, for a specific j = 1, 2, : : : , 6, takes the same form as equation (9), with e t representing the residual from the regression of y t on a set of explanatory variables x t = .1, t, z t , tz t / : We label the test + j . Its asymptotic null distribution is Cramér-von Mises with time trend; the critical values are available in Table I(b) of Harvey (2001).…”

Testing for the Presence of a Random Walk in Series with Structural Breaks

“…If all the seasonal frequencies are included, the asymptotic distribution of the resulting test statistic under the null is CvM(s À 1). As shown in Harvey and Streibel (1997), the inclusion of a time trend does not 144 affect this asymptotic distribution. Thus CvM 2 (s À 1) is not appropriate unless seasonal slopes, as used, for example, by Proietti (1998), are included in the model; this can be shown by an extension of the argument in Harvey and Streibel (1997, Appendix).…”