Current Perspectives on Long Memory Processes

Clive W.J. Granger

《經濟論文》 28卷1期 (2000/03) Pp. 1-16

摘要

在研究金融性資產如股票的日報酬率時，經常發現日報酬率的絕對值在高達2000期時，自我相關函數仍然呈現顯著的正相關。如果對日報酬率的絕對值配適部分差分模型，I(d)，往往發現用全樣本的d估計值小於1/2，但用部分樣本時，則d的估計值會隨樣本的選擇而有明顯的變動。這些實証結果頻頻出現，已被認定為“典型事實”。
縱然I(d)模型是這類研究最熱門的模型，但它卻不見得有正確的性質，尤其是該模型隱含實際上無法觀察的線性趨勢。結構變動模型是另外一個可行的選擇。

關鍵字

變異性 ； 報酬率的絕對值 ； 長記憶 ； 趨勢 ； 結構變動

並列摘要

When daily absolute returns from speculative markets, such as stocks and commodities, are analyzed, they are found to have autocorrelations that remain positive and significant for very long lags (perhaps over 2000). If a fractional integrated I(d) model is fitted, then d is just under 1/2 for the full sample, but varies significantly over sub-samples, and the original distribution of the absolute returns, after removal of a few outliers, is approximately exponential. As such observations are usually found, they have been called “stylized facts.” The I(d) model is the obvious one to fit to absolute daily returns, but it does not have all the correct properties. In particular, it suggests a linear trend in mean for a positive series, which is not observed in practice. A model with occasional structural breaks will provide an adequate alternative explanation.

並列關鍵字

Volatility ； Absolute returns ； Long memory ； Trends ； Structural breaks

參考文獻

Ashley, R., Granger, W. J.(1979).Time Series Analysis of Residuals from the St. Louis Model.Journal of Macroeconomics.1

Baillie, R. T.(1996).Long Memory Processes and Fractional Integration in Econometrics.Journal of Econometrics.73

Beran, J.(1994).Statistics for long-memory processes.London:Chapman and Hall.

Box, G. E. P., Jenkins, G. M.(1970).Time Series Analysis: Forecasting and Control.San Francisco, CA:Holden-Day.

Clapham, J. H.(1922).Of Empty Economic Boxes.Economic Journal.32