臺灣博碩士論文加值系統

本論文重新檢視當檢定兩整合階次不相等之時間序列(y_(t,i) and y_(t,j))間相關性時，傳統皮爾森樣本橫斷面相關係數(ρ ˆ_ij)之極限漸進分配。
我們首先證明當兩時間序列之整合階次不相等時，√T ρ ˆ_ij→N(0,1)之假設將不再成立，以及，由Breusch and Pagan (1980)提出，以此統計推論為基石，所衍生建構之拉氏乘數(LM)相關性檢定統計量亦因而不再適用。而後，本文提出以經過自我相關漸進法濾過之殘差項，重新建構適用於檢定兩整合階次不相等時間序列間相關性之 ρ ˆ_ij以及衍生之LM檢定量。經數理推論證實，重新建構之皮爾森樣本相關係數將服從標準常態分配，亦即，√T ρ ˆ_(ij,AR)→N(0,1)，並且，與其相對應之LM統計量亦將服從自由度為N(N-1)/2之卡方分配。此外，本文考慮Hong(1996)之橫斷面相關性檢定，並利用自我相關漸進法，提出兩個實行上相當簡易之檢定統計量，以用於檢測兩整合階次不相等時間序列，其落後期間之相關性。
我們的蒙地卡羅模擬結果顯示，若所考慮之兩個時間序列出現整合階次不相等的情形，與過去所熟知ρ ˆ_ij之表現相異，傳統ρ ˆ_ij之極限分配將不再服從標準常態分配。此外，根據模擬實驗結果更顯示，在有限樣本下，應用新建構之皮爾森樣本相關係數所進行之相關性檢定，其容忍度(size)可被有效控制，且其檢定力(power)亦相當可信，較傳統方法有十分顯著的進步，
更甚者，利用本文所提出之新統計量進行相關性檢定，亦可避免掉過去文獻中被分析討論的，因整合階次不等所導致之假性相關，以及結果出現偏誤的問題。
最後，以此新建構之估計方法，本文除提供一得準確捕捉金融危機之偵測指標，亦應用至風險報酬抵換議題上，以玆證明此方法之實用性。

This paper re-examines the limiting distribution of the conventional Pearson sample cross- correlation coefficients (

List of Tables..........................................................................................................................................4 1.Introduction ......................................................................................................................................... 5
2. Asymptotic properties of Pearson sample correlation coefficients .................................................... 9
2.1 The inconsistency of Pearson sample correlation coefficient...................................................... 9 2.2. Approximating a time series by an AR Model .......................................................................... 12 2.3 The AR-filtering version of Pearson sample correlation coefficient..........................................14
3. Breusch and Pagan's Lagrange multiplier (LM) test ........................................................................ 15
4. Asymptotic properties of the Hong statistics....................................................................................17
5. Monte Carlo Simulations.................................................................................................................. 21
5.1. Finite sample Properties of Pearson Sample correlation coefficient and the LM test ............... 21
5.2. Finite sample Properties of Hong's Statistics When DGP are two order-imbalanced Processes .......................................................................................................................................................... 25
6. Empirical applications ...................................................................................................................... 27 6.1. Market Contagion and Crisis Detecting Index .......................................................................... 27 6.2. The risk-return trade-offs .......................................................................................................... 30
7. Concluding remark ........................................................................................................................... 31
REFERENCES ..................................................................................................................................... 33

Akaike, H., 1969. Power spectrum estimation through autoregressive model fitting. Annals of Institute of Statistics Mathematics 21, 407-419.
Allen, F., Gale, D. M., 2000. Financial Contagion. Journal of Political Economy 108(1), 1-33.
Baillie, R. T., 1996. Long Memory Processes and Fractional Integration in Econometrics. Journal of Econometrics 73, 5-59.
Baillie, R. T., Bollerslev, T., 2000. The forward premium anomaly is not as bad as you think. Journal of International Money and Finance 19(4), 471-488.
Bekaert, G., Harvey, C. R., Ng, A., 2005. Market Integration and Contagion. The Journal of Business 78(1), 39-70.
Berk, K. N. 1974. Consistent Autoregressive Spectral Estimates. The Annals of Statistics 2, 489-502.
Bollerslev, T., 1990. Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model. The Review of Economics and Statistics 72(3), 498- 505.
Bollerslev, T., Wright, J.H., 2000. Semiparametrics estimation of long-memory volatility dependencies: the role of high-frequency Data. Journal of Econometrics 98, 81-106.
Bordo, M., Eichengreen B., Klingebiel D., MartinezPeria M. S., Rose A. K., 2001. Is the Crisis Problem Growing More Severe. Economic Policy 16(32), 53-82.
Breusch, T.S., Pagan, A.R., 1980. The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics. The Review of Economic Studies 47(1),239-253.
Brockwell, P. J. and R. A. Davis (1991), Time Series: Theory and Methods, 2nd Edn. New York: Springer-Verlag.
Caramazza, F., Ricci, L., Salgado, R., 2004. International financial contagion in currency crises. Journal of International Money and Finance 23(1), 51-70.
Christensen, B.J., Nielsen, M.∅., 2006. Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting. Journal of Econometrics 133, 343-371.
Choi, K., Yu, W.C., Zivot, E., 2010. Long memory versus structural breaks in modeling and forecasting realized volatility. Journal of International Money and Finance 29, 857-875.
Deb, S., 2005. Trade First and Trade Fast: A Duration Analysis of Recovery from Currency Crisis. Departmental Working Papers from Rutgers University, Department of Economics.
Engle, R. F., 2002. Dynamic Conditional Correlation. Journal of Business & Economic Statistics 20(3), 339-350.
Forbes, K., Rigobon, R., 2001. No contagion, only interpendence: measuring stock market co- movements. The Journal of Finance 57(5), 2223-2261.
Granger, C.W.J., 1980. Long memory relationships and the aggregation of dynamic models. Journal of Econometrics 14(2), 227-238.
Hansen, P.R., Timmermann, A., 2015. Equivalence between out-of-sample forecast comparisons and Wald statistics. Econometrica 83(6). 2485-2505.
Haugh, L.D., 1976. Checking the independence of two covariance stationary time series: a univariate residual cross-correlation approach. Journal of American Statistical Association 71, 378-385.
Hosking, J.R.M., 1981. Fractional differencing. Biometrika 68, 165–176.
Hosking, J. R. M., 1996. Asymptotic Distributions of the Sample Mean, Autocovariances, and Autocorrelations of Long-Memory Time Series. Journal of Econometrics 73, 261-284.
Hong, Y., 1996 a. Testing for independence between two covariance stationary time series. Biometrika 83, 615-625.
Hong, Y., 1996 b. Consistent Testing for Serial Correlation of Unknown Form. Econometrica 64, 837-864.
Hong, Y.M., 2000. Generalized spectral tests for serial dependence. Journal of the Royal Statistical Society, Series B (Statistical Methodology) 62 (2000), 557-574.
Hong, Y., 2001. A Test for Volatility Spillover with application to exchange rate. Journal of Economterics 103, 183-224.
Hsiao, C., Pesaran, M.H., Pick, A., 2012. Diagnostic Tests of Cross‐section Independence for Limited Dependent Variable Panel Data Models. Oxford Bulletin of Economics and Statistics 74(2), 253-277.
Karolyi, A. G., 2003. Does International Financial Contagion Really Exist?. Journal of International Finance 6(2), 179–199.
Liu, W., Maynard, A., 2005. Testing forward rate unbiasedness allowing for persistent regressors," Journal of Empirical Finance 12(5). 613-628.
Lobato, I.N., Savin, N.E., 1998. Real and spurious long-memory properties of stock-market data. Journal of Business and Economic Statistics 16, 261–268.
Longin, F., Solnik, B., 2001. Extreme Correlation of International Equity Markets. Journal of Finance 56(2), 649–676.
Maynard, A., Phillips, P. C. B., 2001. Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly. Journal of Applied Econometrics 16(6), 671-708.
McLeod, A.I., Hipel, K.W., 1978. Preservation of the Rescaled Adjusted Range 1: A Reassessment of the Hurst Phenomenon. Water Resources Research 14, 491-508.
Merton, R. C., 1973. Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science 4(1), 141-183.
Merton, R. C., 1980. On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics 8(4), 323–361.
Nabeya S., Perron, P., 1994. Local asymptotic distribution related to the AR(1) model with dependent errors. Journal of Econometrics 62(2), 229–264.
Perron, P., Ng, S., 1996. Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties. Review of Economic Studies 63(3), 435-463.
Perron, P., Ng, S., 1998. An Autoregressive Spectral Density Estimator At Frequency Zero For Nonstationarity Tests. Econometric Theory 14, 560-603.
Poskitt, D.S., 2007. Autoregressive approximation in nonstandard situations; the Fractional Integrated and Non-Invertible Cases. Annals of Institute of Statistical Mathematics 59, 697- 725.
Priestley, M.B., 1981. '' Spectral Analysis and Time Series.'' London: Academic Press.
Pukthuanthong, K., Roll, R., 2009. Global market integration: An alternative measure and its application. Journal of Financial Economics 94, 214–232.