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A statistical analysis of cointegration for $$I(2)$$ variables. (English) Zbl 1274.62597
Summary: This paper discusses inference for $$I(2)$$ variables in a VAR model. The estimation procedure suggested consists of two reduced rank regressions. The asymptotic distribution of the proposed estimators of the cointegrating coefficients is mixed Gaussian, which implies that asymptotic inference can be conducted using the $$\chi^2$$ distribution. It is shown to what extent inference on the cointegration ranks can be conducted using the tables already prepared for the analysis of cointegration of $$I(1)$$ variables. New tables are needed for the test statistics to control the size of the tests. This paper contains a multivariate test for the existence of $$I(2)$$ variables. This test is illustrated using a data set consisting of U.K. and foreign prices and interest rates as well as the exchange rate.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M07 Non-Markovian processes: hypothesis testing 62P20 Applications of statistics to economics
##### Keywords:
inference for time series; signal analysis
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##### References:
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