Testing the null hypothesis of stationarity against the alternative of a unit root. How sure are we that economic time series have a unit root?

*(English)*Zbl 0871.62100Summary: We propose a test of the null hypothesis that an observable series is stationary around a deterministic trend. The series is expressed as the sum of deterministic trend, random walk, and stationary error, and the test is the LM test of the hypothesis that the random walk has zero variance. The asymptotic distribution of the statistic is derived under the null and under the alternative that the series is difference-stationary. Finite sample size and power are considered in a Monte Carlo experiment. The test is applied to the Nelson-Plosser data [C. R. Nelson and C. I. Plosser, “Trends and random walks in macroeconmic time series: some evidence and implications”, J. Mon. Econ. 10, 139–162 (1982; doi:10.1016/0304-3932(82)90012-5)] and for many of these series the hypothesis of trend stationarity cannot be rejected.

##### MSC:

62P20 | Applications of statistics to economics |

62M07 | Non-Markovian processes: hypothesis testing |

91B84 | Economic time series analysis |

##### Keywords:

difference stationarity; deterministic trend; random walk; LM test; Monte Carlo; trend stationarity; KPSS test##### Software:

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\textit{D. Kwiatkowski} et al., J. Econom. 54, No. 1--3, 159--178 (1992; Zbl 0871.62100)

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