A note on testing for a unit root in an ARIMA(p,1,0) signal observed with MA(q) noise

Dongwan Shin, Sahadeb Sarkar

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An ARIMA(p,1,0) signal contaminated by MA(q) noise is a restricted ARIMA(p,1,p + q + 1) process. For this model restricted by nonlinear constraints, it is shown that the maximum likelihood estimator of the unit root is strongly consistent and its limiting distribution is the same as that of the least squares estimator of the unit root in an AR(1) process tabulated by Dickey and Fuller.

Original languageEnglish
Pages (from-to)195-203
Number of pages9
JournalStatistics and Probability Letters
Issue number3
StatePublished - 15 Oct 1993

Bibliographical note

Funding Information:
The research of the first author was supported by Korea Research Foundation. The research of the second author was partly supported by the Dean’s Incentive Grant from the College of Arts and Sciences at Oklahoma State University. The authors wish to thank Professor Wayne A. Fuller for kindly suggesting the problem and providing the example of Labor Force Survey conducted by Statistics Canada. The authors would also like to thank the referee for several useful suggestions.


  • Measurement error
  • large sample properties
  • maximum likelihood estimation
  • nonstationarity
  • unit root


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