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平稳与非平稳短记忆及长记忆自回归过程的统一模型选择AI 解读

The question of model choice for the class of stationary and nonstationary, fractional and nonfractional autoregressive processes is considered. This class is defined by the property that the dth difference, for −½ ≪ d ≪ ∞, is a stationary autoregressive process of order po ≪ ∞. A version of the Akaike information criterion, AIC, for determining an appropriate autoregressive order when d and the autoregressive parameters are estimated simultaneously by a maximum likelihood…

长记忆参数变化的检验AI 解读

Long-range dependence is often observed in long time series. Correlations decay approximately like |k|2H-2, with H ε (0.5, 1), as the lag k tends to infinity. The long-term features of the data are essentially characterised by the parameter H. Small changes of H have strong implications for the long-term behaviour of the process. In particular, rates of convergence of estimators for the mean, and for many other parameters of interest, differ for different values of H. For…