Likelihood-based estimation methods involve the normalising constant of the model distributions, expressed as a function of the parameter. However in many problems this function is not easily available, and then less efficient but more easily computed estimators may be attractive. In this work we study stationary time-series models, and construct and analyse "score-matching'' estimators, that do not involve the normalising constant. We consider two scenarios: a single series of increasing length, and an increasing number of independent series of fixed length. In the latter case there are two variants, one based on the full data, and another based on a sufficient statistic. We study the empirical performance of these estimators in three special cases, autoregressive (\AR), moving average (MA) and fractionally differenced white noise (\ARFIMA) models, and make comparisons with full and pairwise likelihood estimators. The results are somewhat model-dependent, with the new estimators doing well for $\MA$ and \ARFIMA\ models, but less so for $\AR$ models.

中文翻译：

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高斯线性时间序列模型中的 Hyvärinen 评分规则

基于似然的估计方法涉及模型分布的归一化常数，表示为参数的函数。然而，在许多问题中，这个函数并不容易获得，因此效率较低但更容易计算的估计量可能很有吸引力。在这项工作中，我们研究平稳时间序列模型，并构建和分析不涉及归一化常数的“分数匹配”估计量。我们考虑两种情况：增加长度的单个序列和增加数量的独立序列固定长度的。在后一种情况下，有两种变体，一种基于完整数据，另一种基于足够的统计量。我们研究这些估计量在三种特殊情况下的经验性能，自回归（\AR），移动平均 (MA) 和分数差分白噪声 (\ARFIMA) 模型，并与完全和成对似然估计量进行比较。结果在某种程度上与模型有关，新的估计器对 $\MA$ 和 \ARFIMA\ 模型表现良好，但对 $\AR$ 模型效果较差。