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Abstract:
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A least absolute deviation approach is considered to estimate fractionally autoregressive integrated moving average models with conditional heteroscedasticity. The time series generated by this model is short memory or long memory, stationary or nonstationary, depending on whether the fractional di®erencing parameter d ? (-1/2, 0) or (0,8),(-1/2, 1/2) or (1/2,8) respectively. Using a unified approach, the asymptotic properties of the least absolute deviation estimation are established. This article also derives the large sample distribution of residual autocorrelations and absolute residual autocorrelations and these results lead to two useful diagnostic tools for checking the adequacy of the fitted models. Some Monte Carlo experiments were reported. A real example is also included.
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