ESTIMATION OF THE FRACTIONAL DIFFERENCE PARAMETER IN THE ARIMA(p, d, q) MODEL USING THE SMOOTHED PERIODOGRAM

Valderio A. Reisen

Journal of Time Series Analysis, 1994, vol. 15, issue 3, 335-350

Abstract: Abstract. In recent work on time series analysis considerable interest has been focused on series having the property of long memory. Long memory is a characteristic of time series in which the dependence between distant observations is not negligible. The model that has been most frequently studied, which in some situations shows properties of long memory, is based on the autoregressive integrated moving‐average ARIMA(p, d, q) process. Hosking (Fractional differencing, Biometrika 68 (1) (1981), 165–76) generalized this model by permitting the degree of differencing d to take fractional values. He then demonstrated that for d in the range 0

Date: 1994
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