Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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ARMA Modeling for Nonstationary Time Series Data without Differencing

  • Published : 1999.09.01
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Abstract

For possibly nonstationary autoregressive moving average, modeling based on the original observations rather than the differenced observations is considered. Under this scheme, sample autocorrelation functions, parameter estimates, model diagnostic statistics, and prediction are all computed from the original data instead of the differenced data. The methods and results established under stationarity of data are shown to naturally extend to the nonstationarity of one autoregressive unit root. The sample ACF and PACF can be used for ARMA order determination. The BIC order is strongly consistent. The parameter estimates are asymptotically normal. The portmanteau statistic has chi-square distribution. The predictor is asymptotically equivalent to that based on the differenced data.

Keywords

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