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A graphical procedure for determining nonstationarity in time series

Journal Article


Abstract


  • Integrated processes as models for time series data have proved to be an important component of the highly flexible class of ARIMA(p, d, q) models. Determining the amount of differencing, d, has been a difficult task: too little and the process is not yet second-order stationary; too much and the process is more variable than it need be. It is shown that by introducing the notion of generalized covariances, developed by Matheron (1973) for spatial processes, the amount of differencing needed can be read easily from a sequence of graphs showing averages of squares of primary data increments. Formal inference to determine if the last difference really is necessary can then be carried out. Time series data are analyzed in this way and compared with the hypothesis-testing approach illustrated by Dickey, Bell, and Miller (1986). Once the order of differencing has been diagnosed, either the differenced time series can be analyzed or the generalized covariance of the undifferenced series can be estimated. © 1976 Taylor & Francis Group, LLC.

Publication Date


  • 1988

Citation


  • Cressie, N. (1988). A graphical procedure for determining nonstationarity in time series. Journal of the American Statistical Association, 83(404), 1108-1116. doi:10.1080/01621459.1988.10478708

Scopus Eid


  • 2-s2.0-84950436461

Web Of Science Accession Number


Start Page


  • 1108

End Page


  • 1116

Volume


  • 83

Issue


  • 404

Abstract


  • Integrated processes as models for time series data have proved to be an important component of the highly flexible class of ARIMA(p, d, q) models. Determining the amount of differencing, d, has been a difficult task: too little and the process is not yet second-order stationary; too much and the process is more variable than it need be. It is shown that by introducing the notion of generalized covariances, developed by Matheron (1973) for spatial processes, the amount of differencing needed can be read easily from a sequence of graphs showing averages of squares of primary data increments. Formal inference to determine if the last difference really is necessary can then be carried out. Time series data are analyzed in this way and compared with the hypothesis-testing approach illustrated by Dickey, Bell, and Miller (1986). Once the order of differencing has been diagnosed, either the differenced time series can be analyzed or the generalized covariance of the undifferenced series can be estimated. © 1976 Taylor & Francis Group, LLC.

Publication Date


  • 1988

Citation


  • Cressie, N. (1988). A graphical procedure for determining nonstationarity in time series. Journal of the American Statistical Association, 83(404), 1108-1116. doi:10.1080/01621459.1988.10478708

Scopus Eid


  • 2-s2.0-84950436461

Web Of Science Accession Number


Start Page


  • 1108

End Page


  • 1116

Volume


  • 83

Issue


  • 404