Functional Unit Root Test

29 Pages Posted: 18 Feb 2021

See all articles by Yichao Chen

Yichao Chen

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Date Written: January 5, 2021

Abstract

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

Suggested Citation

Chen, Yichao and Pun, Chi Seng, Functional Unit Root Test (January 5, 2021). Available at SSRN: https://ssrn.com/abstract=3761262 or http://dx.doi.org/10.2139/ssrn.3761262

Yichao Chen

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

S3 B2-A28 Nanyang Avenue
Singapore, 639798
Singapore

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://personal.ntu.edu.sg/cspun/

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