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題名：ARCH族模型估計與檢定的問題
書刊名：經濟論文叢刊
作者：林建甫 引用關係／張焯然 引用關係
作者(外文)：Lin, Jeff Chien-fu／Chang, Jor-ran
出版日期：1996
卷期：24:3
頁次：頁339-355
主題關鍵詞：人造輔迴歸式；斜率外積；LM檢定；BHHH演算法；ARCH parameters；Auxiliary regression；Lagrange multiplier test；Outer-product-of-the-gradient；BHHH algorithm
原始連結：連回原系統網址new window
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  • 被引用次數被引用次數:期刊(10) 博士論文(1) 專書(0) 專書論文(0)
  • 排除自我引用排除自我引用:9
  • 共同引用共同引用:0
  • 點閱點閱:64
　　　　　本文探討人造輔迴歸式(artificial regression)與ARCH族模型估計、檢定的 關係及檢定引出的問題，我們先把Scoring及BHHH演算法中估計參數時遞迴更新 的方向同量(direction vector)化成人造輔迴歸式並且指出LM(Lagrange multiplier)檢 定的統計量與這人造輔迴歸式的關係。我們進而說明三種ARCH模型的LM檢定; 一是由一階微分的score函數出發的測驗;二是由Breusch和Pagan(1979)及 Koenker(1981)的推導，簡化的TR2(丁為樣本點個數)檢定統量;三是Bollerslev(1986) 提出用BHHH演算法以斜率外積(outer product of the gradient;OPG)作為訊息矩陣的 基礎，經由第一次OLS輔迴歸造出的TR2的統計量;其極限分配是一樣的。我們也 發現最常用的第三種檢定統計量，在小樣本下會有高估的情形。這與文獻上使用 OPG的檢定在平均數上有過度拒絕虛無假設的問題相同。這將建議一般對ARCH 族模型估計與檢定使用BHHH演算法的學者，要小心的使用BHHH演算法的檢定 結果。
　　　　　We express the direction vectors as auxiliary regressions and pointout how to take advantage of these auxiliary regressions to generate LM (Lagrange multiplier) test statistics. We test three LMtests which are asymptoticly equivalent but with different behaviors in small samples. The three LM tests are, the one with scorefunction and an information matrix; the TR@ version of Breuschand Pagan (1979) and Koenker (1981) and the TR@ version usingouter-product-of-the-gradient (OPG) in the first BHHH iterationin Bollerslev (1987). We find the third test rejects too often underthe null hypothesis. The reason is that when using the OPG toapproximate the Hessian, it produces a larger test statistic. This issimilar to the problem of applying OPG to a mean equation, butthis has not been noted in the variance equation. This suggests awarning for those who use the BHHH algorithm to generate LMtest statistics and find significant ARCH effects.
期刊論文
1.Berndt, E. K.、Hall, B. H.、Hall, R. E.、Hausman, J. A.(1974)。Estimation Inference in Nonlinear Structural Models。Annals of Economic and Social Measurement，4，653-665。  new window
2.Bera, A. K.、McKenzie, C. R.(1986)。Alternative forms and properties of the score test。Journal of Applied Statistics，13，13-25。  new window
3.Davidson, R.、MacKinnon, J. G.(1983)。Small sample properties of alternative forms of Lagrange multiplier test。Economics Letters，12，269-275。  new window
4.Davidson, R.、MacKinnon, J. G.(1984)。Model specification tests based on artificial linear regressions。International Economic Review，25，485-502。  new window
5.Davidson, R.、MacKinnon, J. G.(1985)。Testing linear and loglinear regressions against Box-Cox alternatives。Canadian Journal of Economics，18(3)，499-517。  new window
6.Davidson, R.、MacKinnon, J. G.(1990)。Specification tests based on artificial regression。Journal of the American Statistical Associatio，85，220-227。  new window
7.Efron, B.、Hinkley, D. V.(1978)。Assessing the accuracy of maximum likelihood estimator: observed verse expected Fisher information。Biometrika，65，457-487。  new window
8.Godfrey, L. G.、McAleer, M.、McKenzie, C. R.(1988)。Variable addition and Lagrange multiplier tests for linear and logarithmic regression model。Review of Economics and Statistics，70，492-503。  new window
9.Godfrey, L. G.、Wickens, M. R.(1981)。Testing linear and loglinear regressions for functional form。Review of Economic Studies，48，487-496。  new window
10.Goldfeld, S.、Quandt, R.、Trotter, H.(1966)。Maximization by quadratic hill-climbing。Econometrica，541-551。  new window
11.Koenker, R.(1981)。A note on Studentizing a test for heteroscedas ticity。Journal of Econometrics，17，107-112。  new window
12.Weiss, A. A.(1986)。Asymptotic theory for ARCH models: estimation and testing。Econometric Theory，2，107-131。  new window
13.Engle, R. F.、Lilien, D. M.、Robins, R. P.(1987)。Estimating time varying risk premia in the term structure: The ARCH-M model。Econometrica，55(2)，391-407。  new window
14.Breusch, T. S.、Pagan, A. R.(1979)。A Simple Test for Heteroscedasticity and Random Coefficient Variation。Econometrica，47(5)，1287-1294。  new window
15.Bollerslev, Tim(1986)。Generalized Autoregressive Conditional Heteroskedasticity。Journal of Econometrics，31(3)，307-327。  new window
16.Bollerslev, Tim、Chou, Ray Y.、Kroner, Kenneth F.(1992)。ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence。Journal of Econometrics，52(1/2)，5-59。  new window
17.Engle, Robert F.(1982)。Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation。Econometrica，50(4)，987-1008。  new window
18.Nelson, Daniel B.(1991)。Conditional Heteroskedasticity in Asset Returns: A New Approach。Econometrica: Journal of the Econometric Society，59(2)，347-370。  new window
圖書
1.White, H.(1984)。Asymptotic theory for Econometricians。Academic Press。  new window
2.Davidson, R.、MacKinnon, J. G.(1993)。Estimation and Inference in Econometerics。Oxford University press。  new window
3.Greene, W. H.(1993)。Econometric Analysis。New York：Maxwell Macmillan International Pub. Group。  new window
4.Box, G. E. P.、Jenkins, G. M.、Reinsel, G. C.(1976)。Time Series Analysis: Forecasting and Control。San Francisco：Holden-Day。  new window
圖書論文
1.Bollerslev, T.、Engle, R.、Nelson, D. B.(1995)。ARCH models。Handbook of Econometrics。Amsterdam：North Holland。  new window
2.Engle, R. F.、Kraft, D.(1983)。Multiperiod forecast error variances of inflation estimated from ARCH models。Applied Time Series Analysis of Economic Data。Washington, DC：Bureau of the Census。  new window
 
 
 
 
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