617
Views
69
CrossRef citations to date
0
Altmetric
Original Articles

Testing the Martingale Difference Hypothesis

&
Pages 351-377 | Published online: 19 Aug 2006

References

  • An , H.‐Z. and Bing , C. 1991 . A Kolmogorov–Smirnov type statistic with application to test for nonlinearity in time series . Int. Stat. Rev. , 59 : 287 – 307 .
  • Anderson , T. W. 1993 . Goodness of fit tests for spectral distributions . Ann. Stat. , 21 : 830 – 847 .
  • Andrews , D. W. K. 1997 . A conditional Kolmogorov test . Econometrica , 65 : 1097 – 1128 .
  • Andrews , D. W. K. and Pollard , D. 1994 . An introduction to functional central limit theorems for dependent stochastic processes . Int. Stat. Rev. , 62 : 119 – 132 .
  • Bera , A. K. and Higgins , M. L. 1997 . Arch and bilinearity as competing models for nonlinear dependence . J. Bus. Econ. Stat. , 15 : 43 – 51 .
  • Bickel , P. J. and Wichura , M. J. 1971 . Convergence criteria for multiparameter stochastic processes and some applications . Ann. Math. Stat. , 42 : 1656 – 1670 .
  • Bierens , H. 1984 . Model specification testing of time series regressions . J. Econometrics , 26 : 323 – 353 .
  • Bierens , H. 1990 . A consistent conditional moment test of functional form . Econometrica , 58 : 1443 – 1458 .
  • Bierens , H. and Ploberger , W. 1997 . Asymptotic theory of integrated conditional moment test . Econometrica , 65 : 1129 – 1151 .
  • Box , G. E. P. and Pierce , D. A. 1970 . Distribution of residual autocorrelations in autoregressive integrated moving average time series models . J. Am. Stat. Assoc. , 65 : 1509 – 1526 .
  • Brunk , H. D. 1970 . “ Estimation for isotonic regression ” . In Nonparametric Techniques in Statistical Inference Edited by: Puri , M. L. 177 – 197 . Cambridge : Cambridge University Press .
  • Chentsov , N. N. 1956 . Weak convergence of stochastic processes whose trajectories have no discontinuities of the second kind and the “heuristic” approach to the Kolmogorov–Smirnov tests . Theor. Probab. Appl. , 1 : 140 – 144 .
  • De Jong , R. M. 1996 . The Bierens test under data dependence . J. Econometrics , 72 : 1 – 32 .
  • Delgado , M. 1993 . Testing the equality of nonparametric regression curves . Stat. Probabil. Lett. , 17 : 199 – 204 .
  • Delgado , M. , Dominguez , M. and Lavergne , P. 1998 . “ Asymptotic and bootstrap specification test of nonlinear in variables econometric models ” . Universidad Carlos III . Preprint
  • Deo , R. S. 2000 . Spectral tests of the martingale hypothesis under conditional heteroscedasticity . J. Econometrics , 99 : 291 – 315 .
  • Dominguez , M. 2000 . “ Consistent specification testing of quantile regression models ” . Instituto Tecnológico Autónomo De México . Preprint
  • Durbin , J. Distribution theory for tests based on the sample distribution function . Regional Conference Series in Applied Mathematics . Vol. 9 , Philadelphia : Siam. .
  • Durlauf , S. N. 1991 . Spectral based testing of the martingale hypothesis . J. Econometrics , 50 : 355 – 376 .
  • El Babsiri , M. and Zakoian , J.‐M. 2001 . Contemporaneous asymmetry in GARCH processes . J. Econometrics , 101 : 257 – 294 .
  • Goldberger , A. 1991 . A Course in Econometrics Harvard University Press .
  • Guerre , E. and Lavergne , P. 2000 . Minimax rates for nonparametric specification testing in regression models . Econometric Theory , 18 ( 5 ) : 1139 – 1171 .
  • Hall , P. and Heyde , C. C. Martingale Limit Theory and its Applications New York : Academic Press .
  • Hall , R. E. 1978 . Stochastic implications of the life cycle—permanent income hypothesis: theory and evidence . J. Polit. Econ. , 86 : 971 – 987 .
  • Härdle , W. and Mammen , E. 1993 . Comparing nonparametric versus parametric regression fits . Ann. Stat. , 21 : 1926 – 1947 .
  • Hong , Y. and White , H. 1995 . Consistent specification testing via nonparametric series regressions . Econometrica , 63 : 1133 – 1160 .
  • Hong , Y. 1996 . Consistent testing for serial correlation of unknown form . Econometrica , 64 : 837 – 864 .
  • Hong , Y. 1999 . Hypothesis testing in time series via the empirical characteristic function: a generalized spectral density approach . J. Am. Stat. Assoc. , 94 : 1201 – 1220 .
  • Horowitz , J. L. 2001 . “ The bootstrap ” . In Handbook of Econometrics Edited by: Heckamn , J. J. and Leamer , E. E. Vol. 5 , 3159 – 3228 . Elsevier Science B.V. . Ch. 52
  • Horowitz , J. L. and Spokoiny , V. G. 2001 . An adaptive, rate‐optimal test of a parametric mean‐regression model against a nonparametric alternative . Econometrica , 69 : 599 – 631 .
  • Koul , H. L. and Stute , W. 1999 . Nonparametric model checks for time series . Ann. Stat. , 27 : 204 – 236 .
  • Li , Q. 1999 . Consistent model specification tests for time series econometric models . J. Econometrics , 92 : 101 – 147 .
  • Lobato , I. N. , Nankervis , J. and Savin , N. E. 2001 . Testing for autocorrelation using a modified box‐pierce Q test . Int. Econ. Rev. , 42 : 187 – 205 .
  • Lobato , I. N. , Nankervis , J. and Savin , N. E. 2002 . Testing for zero autocorrelation in the presence of statistical dependence . Economet. Theor. , 18 : 730 – 743 .
  • Mammen , E. 1993 . Bootstrap and wild bootstrap for high dimensional linear models . Ann. Stat. , 21 : 255 – 285 .
  • Marron , S. J. 1988 . Automatic smoothing parameter selection: a survey . Empirical Economics , 13 : 187 – 208 .
  • Ming , X. 1999 . One–one transformation of multidimensional general distribution to multidimensional uniform distribution . Economet. Theor. , 15 : 429 – 430 .
  • Neuhaus , G. 1971 . On weak convergence of stochastic processes with multidimensional time parameter . Ann. Math. Stat. , 42 : 1285 – 1295 .
  • Park , J. and Whang , Y.‐J. 1999 . “ Testing for the martingale hypothesis ” . Ewha University . Preprint
  • Robinson , P. M. 1991 . Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression . J. Econometrics , 47 : 67 – 84 .
  • Rosenblatt , M. 1975 . A quadratic measure of deviation of two‐dimensional density estimates and a test of independence . Ann. Stat. , 3 : 1 – 14 .
  • Shorack , G. R. and Wellner , J. A. 1986 . Empirical Processes with Applications to Statistics New York : Wiley .
  • Stinchcombe , M. and White , H. 1998 . Consistent specification testing with nuisance parameters present only under the alternative . Economet. Theor. , 14 : 295 – 325 .
  • Straf , M. L. 1970 . Weak convergence of stochastic processes with several parameters . Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability . 1970 . pp. 187 – 221 .
  • Stute , W. 1997 . Nonparametric model checks for regression . Ann. Stat. , 25 : 613 – 641 .
  • Stute , W. , Gonzalez‐Manteiga , W. G. and Presedo‐Quindmil , M. 1998 . Bootstrap approximations in model checks for regression . J. Am. Stat. Assoc. , 83 : 141 – 149 .
  • Stute , W. , Thies , S. and Zhu , L. X. 1998 . Model checks for regression: an innovation process approach . Ann. Stat. , 26 : 1916 – 1934 .
  • Su , J. Q. and Wei , L. J. 1991 . A lack of fit test for the mean function in a generalized linear model . J. Am. Stat. Assoc. , 86 : 420 – 426 .
  • Terdik , G. 1999 . Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis New York : Springer Verlag .
  • Wu , C. F. J. 1986 . Jacknife, bootstrap and other resampling methods in regression analysis . Ann. Stat. , 14 : 1261 – 1350 . (with discussion)
  • Whang , Y.‐J. 2000 . Consistent bootstrap tests of parametric regression functions . J. Econometrics , 98 : 27 – 46 .
  • Zheng , X. 1996 . A consistent test of functional form via nonparametric estimation technique . J. Econometrics , 75 : 263 – 289 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.