Seasonal integration and cointegration.

*(English)*Zbl 0709.62102Summary: This paper develops tests for roots in linear time series which have a modulus of one but which correspond to seasonal frequencies. Critical values for the tests are generated by Monte Carlo methods or are shown to be available from critical values of D. A. Dickey and W. A. Fuller [J. Am. Stat. Assoc. 74, 427-431 (1979; Zbl 0413.62075)] or D. A. Dickey, D. P. Hasza and W. A. Fuller [ibid. 79, 355- 367 (1984; Zbl 0559.62074)]. Representations for multivariate processes with combinations of seasonal and zero-frequency unit roots are developed leading to a variety of autoregressive and error-correction representations. The techniques are used to examine cointegration at different frequencies between consumption and income in the U.K.

##### MSC:

62P20 | Applications of statistics to economics |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

##### Keywords:

tests for roots; linear time series; seasonal frequencies; Critical values; Monte Carlo; multivariate processes; error-correction representations; cointegration
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\textit{S. Hylleberg} et al., J. Econom. 44, No. 1--2, 215--238 (1990; Zbl 0709.62102)

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##### References:

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