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研究生:林季鴻
研究生(外文):Chi-Hung Lin
論文名稱:緩長記憶之虛假迴歸檢定
論文名稱(外文):Tests for the Spurious Regression with Long-memory Processes
指導教授:蔡文禎蔡文禎引用關係
指導教授(外文):Wen-Jen Tsay
學位類別:碩士
校院名稱:國立暨南國際大學
系所名稱:經濟學系
學門:社會及行為科學學門
學類:經濟學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:56
中文關鍵詞:緩長記憶分數差分時間序列虛假迴歸一階差分估計法長期變異數估計式
外文關鍵詞:Long memoryI(d) processSpurious regressionFirst differencedLong-run variance estimator
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本論文探討的主題為,當兩個同時存在緩長記憶 (long memory) 的分數差分時間序列互為迴歸時,如何修正假設檢定上可能產生之虛假迴歸現象 (spurious effect) 。由於一階差分係數估計式具有一致性與漸進於常態分配的性質,因此我們以一階差分估計法 (FD) 取代傳統之最小平方估計法 (OLS) ,在假設 FD 長期變異數估計式具一致性的前提下,對 FD 係數檢定統計量 (tFD) 的小樣本表現進行模擬分析;實驗結果顯示, FD 估計法不但可以完全改善虛假迴歸現象,同時也是個非常 powerful 的緩長記憶之虛假迴歸檢定法。此外,為了驗證FD 長期變異數估計式具一致性之假設的可靠程度,我們還模擬兩個變異數皆為 1 的白噪音時間序列 (white-noise process) 互為迴歸之FD 長期變異數估計式的實際值,透過計算其 RMSE (root-mean-squared error) 並觀察實際值的相對次數分配直方圖後發現,隨著樣本數的增加, FD 長期變異數估計式的實際值有明顯向理論值 6 集中分布的趨勢,同時其 RMSE 也如預期地越來越小。由於前述證據強力支持 FD 長期變異數估計式具一致性的假設應該成立,因此,我們可以把標準常態分配視為tFD之漸進分配,這將使得檢定統計量之臨界值的選取變得容易,實證分析上的便利性也會因而大幅提昇。

This paper considers the problem of testing for the spurious regression with long-memory processes. The first differenced (FD) coefficient estimator is studied in place of the ordinary least squares (OLS) one owing to its consistency and asymptotic normality. Given that the consistency of the long-run variance estimator holds, Monte Carlo experiments are conducted to assess the small sample performance of tFD . We find that the size of tFD test is well controlled, and its power performance is reasonably well under various combination of ARFIMA processes considered in this paper. Furthermore, in order to verify the assumption about consistency of the long-run variance estimator, two iid white-noise processes with σ = 1 are simulated to get its realized values. By observing the relative frequency histogram and calculating the RMSE for the long-run variance estimator, we find that its RMSE becomes smaller as the sample size gets larger, and its realized values are concentrated more intensively around the theoretical value of long-run variance in the same way. These results make clear that the preceding assumption should hold, and the tFD test is bound to possess a standard normal distribution accordingly. Hence, the implementation of the tFD test for empirical analyses is straightforward and can be easily accomplished by standard statistics packages.

目錄
1 前言 1
1.1 研究動機與目的. . . . . . . . . . . . . . . . . . . . . 1
1.2 論文之研究大要. . . . . . . . . . . . . . . . . . . . . 4
2 文獻回顧 5
2.1 分數差分時間序列及其性質. . . . . . . . . . . . . . . . 5
2.2 最小平方估計法與虛假迴歸現象. . . . . . . . . . . . . . 7
2.3 虛假迴歸檢定. . . . . . . . . . . . . . . . . . . . . . 8
3 研究方法 11
3.1 一階差分估計法之係數估計式性質 . . . . . . . . . . . . 11
3.2 長期變異數之漸進過程 . . . . . . . . . . . . . . . . . 15
4 模擬分析 19
4.1 資料生成過程 . . . . . . . . . . . . . . . . . . . . . 19
4.2 模擬實驗內容的設計 . . . . . . . . . . . . . . . . . . 20
4.2.1 緩長記憶之虛假迴歸檢定 . . . . . . . . . . . . . 21
4.2.2 長期變異數估計式之一致性驗證 . . . . . . . . . . 22
4.3 模擬實驗結果與分析 . . . . . . . . . . . . . . . . . . 23
4.3.1 一階差分檢定統計量之小樣本表現 . . . . . . . . . 24
4.3.2 長期變異數估計式之一致性驗證 . . . . . . . . . . 25
5 結論 52
參考文獻 53

[1] Andrews, D.W.K. (1991) : Heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica, 59, 817-858.
[2] Baillie, R.T. (1996) : Long memory processes and fractional integration in econometrics, Econometrica, 73, 5-59.
[3] Bartlett, M.S. (1935) : Some aspects of the time-correlation problem in regard to tests of signicance, Journal of the Royal Statistical Society, 98, 536-543.
[4] Chipman, J.S. (1979) : Efficiency of least squares estimation of linear trend when residuals are autocorrelated, Econometrica, 47, 115-128.
[5] Diebold, F.X., S. Husted & M. Rush (1991) : Real exchange rates under the gold standard, Journal of Political Economy, 99, 1252-1271.
[6] Granger, C.W.J. (1980) : Long memory relationships and aggregation of dynamic models, Journal of Econometrics, 14, 227-238.
[7] Granger, C.W.J. (1981) : Some properties of time series data and their use in econometric model specication, Journal of Econometrics, 16, 121-130.
[8] Granger, C.W.J. & R. Joyeux (1980) : An introduction to long-memory time series models and fractionally differencing, Journal of Time Series Analysis, 1, 15-29.
[9] Granger, C.W.J. & P. Newbold (1974) : Spurious regression in econometrics, Journal of Econometrics, 2, 111-120.
[10] Greene, W.H. (2000) : Econometric Analysis, 4th ed. Upper Sadde River, NJ, USA: Prentice Hall Press.
[11] Hamilton, J.D. (1994) : Time series analysis. Princeton, NJ, USA: Princeton University Press.
[12] Hansen, B.E. (1992) : Efcient estimation and testing of cointegrating vectorsin the presence of deterministic trends, Journal of Econometrics, 53, 87-121.
[13] Haugh, L.D. (1976) : Checking thr independence of two covariance stationary time series: A univariate residual cross-correlation approach, Journal of the American Statistical Association, 71, 378-385.
[14] Hong, H. (1996) : Testing for independence between two covariance stationary time series, Biometrica, 83, 615-625.
[15] Hosking, J.R.M. (1981) : Fractional differencing, Biometrica, 68, 165-176.
[16] Hosking, J.P.M. (1984) : Modeling persistence in hydrological time series using fractional differencing, Water Resources Research, 20, 1898-1908.
[17] Kr®amer, W. (1982) : Note on estimating linear trend when residuals are autocorrelated, Econometrica, 50, 1065-1067.
[18] Maddala, G.S. & I.-M. Kim (1998) : Unit roots, cointegration, and structural change. Cambridge, UK: Cambridge University Press.
[19] Maeshiro, A.I. (1976) : Autoregressive transformation, trended independent variables and autocorrelated disturbance term, Review of Economics and Statistics, 58, 497-500.
[20] McLeod, A.I. & K.W. Hipel (1978) : Preservation of the rescaled adjusted range, 1: A reassessment of the Hurst phenomenon, Water Resources Research, 14, 491-508.
[21] Newney, W.K. & K.D. West (1987) : A simple, positive semi-denite, heteroskedasticity and autocorrelationconsistent covariance matrix estimation, Econometrica, 55, 703-708.
[22] Parzen, E. (1957) : On consistent estimates of the spectrum of a stationary time series, Annals of Mathematical Statistics, 28, 329-348.
[23] Phillips, P.C.B. (1986) : Understanding spurious regressions in econometrics, Journal of Econometrics, 33, 311-340.
[24] Robinson, P.M. (1993) : Highly insignicant F-ratio, Econometrica, 61, 687-696.
[25] Robinson, P.M. (1994) : Semiparametric analysis of long-memory time series, The Annals of Statistics, 22, 515-539.
[26] Robinson, P.M. (1997) : Large-sample inference for nonparametric regression with dependent errors, The Annals of Statistics, 25, 2054-2083.
[27] Robinson, P.M. (1998) : Inference-without-smoothing in the presence of nonparametric autocorrelation, Econometrica, 66, 1163-1182.
[28] Schwert, G.W. (1989) : Tests for unit roots: a Monte Carlo investigation, Journal of Business and Economic Statistics, 7, 147-159.
[29] Tsay, W.J. (2000) : Estimating trending variables in the presence of fractionally integrated errors, Econometric Theory, 16, 324-346.
[30] Tsay,W.J. (2002) : Robust inference when regressors and errors are long memory processes, workingpaper, Institute of Economics Academia Sinica, Taipei.
[31] Tsay, W.J. & C.-F. Chung (2000) : The spurious regression of fractionally integrated processes, Journal of Econometrics, 96, 155-182.
[32] White, H. (2001) : Asymptotic Theory for Econometricans, Revised ed. San Diego, CA, USA: Academic Press.
[33] Yule, G.U. (1926) : Why do we sometimes get nonsense correlation between time series? A study in sampling and the nature of time series, Journal of the Royal Statistical Society, 89, 1-64.

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