季节性持续过程的非正则似然推断
Non-Regular Likelihood Inference for Seasonally Persistent Processes
摘要：
研究了季节性平稳随机过程的频谱参数估计问题。对于季节性持久性与一个极点位于远离频率零的频谱，一个新的惠特尔型的可能性，明确承认的极点的位置。该Whittle似然是对所选择的频率网格上的周期图的分布的大样本近似，并且经由与解调相结合的离散傅立叶逆变换的线性变换构成对数据的时域似然的近似。新的可能性是简单的计算，并将被证明具有良好的，但非标准的，属性。建议的似然估计的渐近行为进行了研究，特别是，$N$ -一致性的谱极点位置的估计建立。给出了分数和观测费舍尔信息的大样本和渐近分布，并推导了相应的极大似然估计量的分布.的小样本性质的似然近似的研究，并显示其优越的性能，以前建议的方法，以及与发达国家的分布近似协议。
英文摘要：
The estimation of parameters in the frequency spectrum of a seasonally persistent stationary stochastic process is addressed. For seasonal persistence associated with a pole in the spectrum located away from frequency zero, a new Whittle-type likelihood is developed that explicitly acknowledges the location of the pole. This Whittle likelihood is a large sample approximation to the distribution of the periodogram over a chosen grid of frequencies, and constitutes an approximation to the time-domain likelihood of the data, via the linear transformation of an inverse discrete Fourier transform combined with a demodulation. The new likelihood is straightforward to compute, and as will be demonstrated has good, yet non-standard, properties. The asymptotic behaviour of the proposed likelihood estimators is studied; in particular, $N$-consistency of the estimator of the spectral pole location is established. Large finite sample and asymptotic distributions of the score and observed Fisher information are given, and the corresponding distributions of the maximum likelihood estimators are deduced. A study of the small sample properties of the likelihood approximation is provided, and its superior performance to previously suggested methods is shown, as well as agreement with the developed distributional approximations.
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