标题： 非分数记忆：滤波、反持续性和预测 显示英文标题

标题： Nonfractional Memory: Filtering, Antipersistence, and Forecasting

摘要： 分数差分算子由于存在有效的模拟和预测算法，仍然是生成长记忆的最流行机制。然而，没有理论依据将分数差分算子与真实数据中的长记忆现象联系起来。 在这方面，长记忆现象最普遍的理论解释之一是持久微观单位的横截面聚合。 然而，通过横截面聚合得到的过程类型与通过分数差分得到的过程类型不同。 因此，本文开发了快速算法来通过横截面聚合生成和预测长记忆。 此外，我们证明了在分数差分文献中对于负记忆度数出现的反持续现象在横截面聚合过程中不存在。 明确地说，虽然分数差分算子的自相关系数在负记忆度数下构造时为负，但这种限制不适用于横截面聚合方案。 我们表明这对频率域中的长记忆检验有影响，在负记忆度数的情况下，对于横截面聚合过程，这些检验将是错误指定的。 最后，我们评估了高阶 $AR$ 和 $ARFIMA$ 模型在长记忆序列由横截面聚合生成时的预测性能。 我们的结果对开发长记忆变量（如通货膨胀、波动性和气候数据）预测的从业者感兴趣，因为在这些情况下，聚合可能是长记忆的来源。 显示英文摘要

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.