Functional Unit Root Test
29 Pages Posted: 18 Feb 2021
Date Written: January 5, 2021
In this paper, we propose a unit root test for functional time series. We derive a new analytical framework for nonstationary functional time series. Specifically, for the proposed test statistic, we derive its limit distribution under the null hypothesis of a random walk and its asymptotic behavior of alternative hypotheses of trend stationary, weakly dependent stationary, and autoregressive stationary models. For the trend stationary model as an alternative, a theoretical derivation of the test consistency is provided, while for other two alternatives, a combination of theoretical and experimental validation on the statistical power of the test is presented. Simulation studies are conducted to justify the theories and the desirable finite-sample performance of the proposed functional unit root test. The proposed test is also applied to real data of intraday stock price curves and the test results are plausible.
Keywords: Functional time series, Non-stationarity, Unit root test, Asymptotic statistics, Intraday stock price analysis
JEL Classification: C12
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