非分数记忆：过滤、反持久性和预测

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摘要翻译：
分数差分算子由于其模拟和预测的有效算法的存在，仍然是最流行的产生长记忆的机制。然而，没有理论上的论点将分数差分算子与实际数据中的长记忆性联系起来。在这方面，对长记忆存在的最主要的理论解释之一是持久微单元的横截面聚集。然而，通过横截面聚集得到的过程类型不同于由于分数差异而得到的过程类型。因此，本文提出了基于横截面聚合的长内存生成和预测的快速算法。此外，还表明分数差分文献中负记忆度引起的反持续现象并不存在于横截面聚集过程中。有针对性地，虽然分数差分算子的自相关对于构造的负记忆度是负的，但这种限制不适用于横截面聚合格式。我们表明，这对频域中的长记忆测试有影响，对于具有负记忆度的横截面聚集过程，长记忆测试将被错误地指定。最后，我们评估了高阶$AR$和$ARFIMA$模型在用横截面聚合生成长记忆序列时的预测性能。我们的结果对开发长记忆变量预测的从业者很感兴趣，如通货膨胀、波动性和气候数据，在这些变量中，聚合可能是长记忆的来源。
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英文标题：
《Nonfractional Memory: Filtering, Antipersistence, and Forecasting》
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作者：
J. Eduardo Vera-Vald\'es
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最新提交年份：
2018
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
--
一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
--

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英文摘要：
  The fractional difference operator remains to be the most popular mechanism to generate long memory due to the existence of efficient algorithms for their simulation and forecasting. Nonetheless, there is no theoretical argument linking the fractional difference operator with the presence of long memory in real data. In this regard, one of the most predominant theoretical explanations for the presence of long memory is cross-sectional aggregation of persistent micro units. Yet, the type of processes obtained by cross-sectional aggregation differs from the one due to fractional differencing. Thus, this paper develops fast algorithms to generate and forecast long memory by cross-sectional aggregation. Moreover, it is shown that the antipersistent phenomenon that arises for negative degrees of memory in the fractional difference literature is not present for cross-sectionally aggregated processes. Pointedly, while the autocorrelations for the fractional difference operator are negative for negative degrees of memory by construction, this restriction does not apply to the cross-sectional aggregated scheme. We show that this has implications for long memory tests in the frequency domain, which will be misspecified for cross-sectionally aggregated processes with negative degrees of memory. Finally, we assess the forecast performance of high-order $AR$ and $ARFIMA$ models when the long memory series are generated by cross-sectional aggregation. Our results are of interest to practitioners developing forecasts of long memory variables like inflation, volatility, and climate data, where aggregation may be the source of long memory.
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PDF链接：
https://arxiv.org/pdf/1801.06677

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关键词：持久性 数据 差分 cross 算子 negative