In empirical studies selection of the order of a model is routinely invoked. A common example is the order selection of an autoregressive model via Akaike's AIC, Schwarz's BIC or Hannan and Quinn's HIC. The criteria are based on the conditional sum of squares (CSS). However, the computation of the CSS might be difficult for some models such as Bloomfield's exponential model and/or when we allow for long memory dependence. The main aim of the article is thus to propose an alternative way to compute the criterion by using the decomposition of the variance of the innovation errors in terms of its frequency components. We show its validity to obtain the correct order the model. In addition, as a by-product, we describe a simple (two-step) estimator of the parameters of the model.

中文翻译：

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长内存相关数据的顺序选择和推理

在实证研究中，通常会调用模型顺序的选择。一个常见的例子是通过 Akaike 的 AIC、Schwarz 的 BIC 或 Hannan 和 Quinn 的 HIC 选择自回归模型的阶数。该标准基于条件平方和 (CSS)。但是，对于某些模型（例如 Bloomfield 的指数模型）和/或当我们允许长期内存依赖时，CSS 的计算可能会很困难。因此，本文的主要目的是提出一种替代方法，通过使用创新误差方差在其频率分量方面的分解来计算标准。我们展示了它的有效性，以获得模型的正确顺序。此外，作为副产品，我们描述了模型参数的简单（两步）估计器。