论长记忆的起源与预测视界
On Long Memory Origins and Forecast Horizons
摘要：
大多数长记忆预测研究假设记忆是由分数差分算子产生的。我们认为，最被引用的理论参数的存在长记忆并不意味着分数差分算子，并评估的自回归分数积分移动平均$(ARFIMA)$模型的性能时，预测序列与长记忆产生的非分数过程。我们发现高阶自回归$(AR)$模型在短期内产生类似或优于$ARFIMA$模型的预测性能。尽管如此，随着预测范围的增加，$ARFIMA$模型往往在预测性能上占主导地位。因此，$ARFIMA$模型非常适合于长记忆过程的预测，无论长记忆的产生机制，特别是中期和长期的预测范围。此外，我们分析了异质自回归（$HAR$）模型的预测性能，它对高阶$AR$模型施加了限制。我们发现，结构强加的$HAR$模型产生更好的长期预测比$AR$模型相同的顺序，在价格低劣的短期预测在某些情况下。我们的研究结果有影响，除其他外，气候计量经济学和金融计量经济学模型处理长记忆系列在不同的预测范围。我们在一个例子中表明，虽然短记忆自回归移动平均$(ARMA)$模型在预测标准普尔500指数的已实现方差时给出了最佳性能，但在未来一个月内，$ARFIMA$模型在较长的预测范围内给出了最佳性能。
英文摘要：
Most long memory forecasting studies assume that the memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator, and assess the performance of the autoregressive fractionally integrated moving average $(ARFIMA)$ model when forecasting series with long memory generated by nonfractional processes. We find that high-order autoregressive $(AR)$ models produce similar or superior forecast performance than $ARFIMA$ models at short horizons. Nonetheless, as the forecast horizon increases, the $ARFIMA$ models tend to dominate in forecast performance. Hence, $ARFIMA$ models are well suited for forecasts of long memory processes regardless of the long memory generating mechanism, particularly for medium and long forecast horizons. Additionally, we analyse the forecasting performance of the heterogeneous autoregressive ($HAR$) model which imposes restrictions on high-order $AR$ models. We find that the structure imposed by the $HAR$ model produces better long horizon forecasts than $AR$ models of the same order, at the price of inferior short horizon forecasts in some cases. Our results have implications for, among others, Climate Econometrics and Financial Econometrics models dealing with long memory series at different forecast horizons. We show in an example that while a short memory autoregressive moving average $(ARMA)$ model gives the best performance when forecasting the Realized Variance of the S\&P 500 up to a month ahead, the $ARFIMA$ model gives the best performance for longer forecast horizons.
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