Skip to main content
Top

2011 | OriginalPaper | Chapter

Nonparametric Tests for Independence

Author : Cees Diks

Published in: Complex Systems in Finance and Econometrics

Publisher: Springer New York

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Article Outline

Glossary
Definition of the Subject
Introduction
Invariant Tests
Tests Based on Divergence Measures
Tests Based on Other Measures of Dependence
Bootstrap and Permutation Tests
Future Directions
Bibliography

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Footnotes
1
It is exactly degenerate for i.i.d. data from the uniform distribution on the circle, i. e. the interval \({[0,a]}\) with the endpoints identified [16]. Theiler [102] simulated variance of \( S=C_{m,n}(\varepsilon)-(C_{i,n}(\varepsilon))^m \) in the degenerate case, and found that it converges to 0 at the rate \({n^{-2}}\) instead of the usual rate \({n^{-1}}\).
 
Literature
1.
go back to reference Aparicio FM, Escribano A (1998) Information‐theoretic analysis of serial dependence and cointegration. Stud nonlinear dyn econ 3:119–140CrossRef Aparicio FM, Escribano A (1998) Information‐theoretic analysis of serial dependence and cointegration. Stud nonlinear dyn econ 3:119–140CrossRef
2.
go back to reference Ashley RA, Patterson DM (1986) A nonparametric, distribution‐free test for serial independence in stock returns. J Financial Quant Anal 21:221–227CrossRef Ashley RA, Patterson DM (1986) A nonparametric, distribution‐free test for serial independence in stock returns. J Financial Quant Anal 21:221–227CrossRef
3.
go back to reference Ashley RA, Patterson DM (1989) Linear versus nonlinear macroeconomics: A statistical test. Int Econ Rev 30:165–187CrossRef Ashley RA, Patterson DM (1989) Linear versus nonlinear macroeconomics: A statistical test. Int Econ Rev 30:165–187CrossRef
4.
go back to reference Ashley RA, Patterson DM, Hinich MN (1986) A diagnostic check for nonlinear serial dependence in time series fitting errors. J Time Ser Anal 7:165–187CrossRef Ashley RA, Patterson DM, Hinich MN (1986) A diagnostic check for nonlinear serial dependence in time series fitting errors. J Time Ser Anal 7:165–187CrossRef
5.
go back to reference Barnard GA (1963) Discussion of Professor Bartlett's paper. J Royal Stat Soc Ser B 25:294 Barnard GA (1963) Discussion of Professor Bartlett's paper. J Royal Stat Soc Ser B 25:294
6.
go back to reference Bartels R (1982) The rank version of von Neumann's ratio test for randomness. J Am Stat Assoc 77:40–46CrossRef Bartels R (1982) The rank version of von Neumann's ratio test for randomness. J Am Stat Assoc 77:40–46CrossRef
7.
go back to reference Benghabrit Y, Hallin M (1992) Optimal rank‐based tests against 1st‐order superdiagonal bilinear dependence. J Stat Plan Inference 32:45–61CrossRef Benghabrit Y, Hallin M (1992) Optimal rank‐based tests against 1st‐order superdiagonal bilinear dependence. J Stat Plan Inference 32:45–61CrossRef
8.
go back to reference Bera AK, Robinson PM (1989) Tests for serial dependence and other specification analysis in models of markets in equilibrium. J Bus Econ Stat 7:343–352CrossRef Bera AK, Robinson PM (1989) Tests for serial dependence and other specification analysis in models of markets in equilibrium. J Bus Econ Stat 7:343–352CrossRef
9.
go back to reference Beran J (1992) A goodness‐of‐fit test for time‐series with long‐range dependence. J Royal Stat Soc Ser B 54:749–760 Beran J (1992) A goodness‐of‐fit test for time‐series with long‐range dependence. J Royal Stat Soc Ser B 54:749–760
10.
go back to reference Blum JR, Kiefer J, Rosenblatt M (1961) Distribution free tests of independence based on sample distribution functions. Ann Math Stat 32:485–498CrossRef Blum JR, Kiefer J, Rosenblatt M (1961) Distribution free tests of independence based on sample distribution functions. Ann Math Stat 32:485–498CrossRef
11.
go back to reference Bollerslev T (1986) Generalized autoregressive heteroskedasticity. J Econometrics 31:307–327CrossRef Bollerslev T (1986) Generalized autoregressive heteroskedasticity. J Econometrics 31:307–327CrossRef
12.
go back to reference Booth GG, Martikainen T (1994) Nonlinear dependence in Finnish stock returns. Eur J Oper Res 74:273–283CrossRef Booth GG, Martikainen T (1994) Nonlinear dependence in Finnish stock returns. Eur J Oper Res 74:273–283CrossRef
13.
go back to reference Box GEP, Pierce DA (1970) Distribution of residual autocorrelations in autoregressive‐integrated moving average time series models. J Am Stat Assoc 332:1509–1526CrossRef Box GEP, Pierce DA (1970) Distribution of residual autocorrelations in autoregressive‐integrated moving average time series models. J Am Stat Assoc 332:1509–1526CrossRef
14.
go back to reference Bradley R (1986) Basic properties of strong mixing conditions. In: Eberlein E, Taqqu MS (eds) Dependence in Probability and Statistics. Birkäuser, Basel Bradley R (1986) Basic properties of strong mixing conditions. In: Eberlein E, Taqqu MS (eds) Dependence in Probability and Statistics. Birkäuser, Basel
15.
go back to reference Brock WA, Dechert WD, Scheinkman JA (1987) A test for independence based on the correlation dimension. Working paper 8702. University of Wisconsin, Madison Brock WA, Dechert WD, Scheinkman JA (1987) A test for independence based on the correlation dimension. Working paper 8702. University of Wisconsin, Madison
16.
go back to reference Brock WA, Dechert WD, Scheinkman JA, LeBaron B (1996) A test for independence based on the correlation dimension. Econometric Rev 15:197–235CrossRef Brock WA, Dechert WD, Scheinkman JA, LeBaron B (1996) A test for independence based on the correlation dimension. Econometric Rev 15:197–235CrossRef
17.
go back to reference Brockett PL, Hinich MD, Patterson D (1988) Bispectral based tests for the detection of Gaussianity and linearity in time series. J Am Stat Assoc 83:657–664CrossRef Brockett PL, Hinich MD, Patterson D (1988) Bispectral based tests for the detection of Gaussianity and linearity in time series. J Am Stat Assoc 83:657–664CrossRef
18.
go back to reference Brooks C, Heravi SM (1999) The effect of (mis‐specified) GARCH filters on the filite sample distribution of the BDS test. Comput Econ 13:147–162CrossRef Brooks C, Heravi SM (1999) The effect of (mis‐specified) GARCH filters on the filite sample distribution of the BDS test. Comput Econ 13:147–162CrossRef
19.
go back to reference Brooks C, Hinich MJ (1999) Cross‐correlations and cross‐bicorrelations in Sterling exchange rates. J Empir Finance 6:385–404CrossRef Brooks C, Hinich MJ (1999) Cross‐correlations and cross‐bicorrelations in Sterling exchange rates. J Empir Finance 6:385–404CrossRef
20.
go back to reference Brooks C, Hinich MJ (2001) Bicorrelations and cross‐bicorrelations as non‐linearity tests and tools for exchange rate forecasting. J Forecast 20:181–196CrossRef Brooks C, Hinich MJ (2001) Bicorrelations and cross‐bicorrelations as non‐linearity tests and tools for exchange rate forecasting. J Forecast 20:181–196CrossRef
21.
go back to reference Caporale GM, Ntantamis C, Pantelidis T, Pittis N (2005) The BDS test as a test for the adequacy of a GARCH(1,1) specification: A Monte Carlo study. J Financial Econometric 3:282–309CrossRef Caporale GM, Ntantamis C, Pantelidis T, Pittis N (2005) The BDS test as a test for the adequacy of a GARCH(1,1) specification: A Monte Carlo study. J Financial Econometric 3:282–309CrossRef
22.
go back to reference Carlstein E (1984) The use of sub‐series methods for estimating the variance of a general statistic from a stationary time series. Ann Stat 14:1171–1179CrossRef Carlstein E (1984) The use of sub‐series methods for estimating the variance of a general statistic from a stationary time series. Ann Stat 14:1171–1179CrossRef
23.
go back to reference Carlstein E (1988) Degenerate U‑statistics based on non‐independent observations. Calcutta Stat Assoc Bull 37:55–65 Carlstein E (1988) Degenerate U‑statistics based on non‐independent observations. Calcutta Stat Assoc Bull 37:55–65
24.
go back to reference Chan NH, Tran LT (1992) Nonparametric tests for serial independence. J Time Ser Anal 13:19–28CrossRef Chan NH, Tran LT (1992) Nonparametric tests for serial independence. J Time Ser Anal 13:19–28CrossRef
25.
go back to reference Corrado CJ, Schatzberg J (1990) A nonparametric, distribution‐free test for serial independence in stock returns: A correction. J Financial Quant Anal 25:411–415CrossRef Corrado CJ, Schatzberg J (1990) A nonparametric, distribution‐free test for serial independence in stock returns: A correction. J Financial Quant Anal 25:411–415CrossRef
26.
go back to reference Csörgő S (1985) Testing for independence by the empirical characteristic function. J Multivar Anal 16:290–299 Csörgő S (1985) Testing for independence by the empirical characteristic function. J Multivar Anal 16:290–299
27.
go back to reference Debnath L, Mikusiński P (2005) Introduction to Hilbert Spaces With Applications, 3rd edn. Elsevier Academic Press, Burlington Debnath L, Mikusiński P (2005) Introduction to Hilbert Spaces With Applications, 3rd edn. Elsevier Academic Press, Burlington
28.
go back to reference Delgado M, Mora J (2000) A nonparametric test for serial independence of regression errors. Biometrika 87:228–234CrossRef Delgado M, Mora J (2000) A nonparametric test for serial independence of regression errors. Biometrika 87:228–234CrossRef
29.
go back to reference Delgado MA (1996) Testing serial independence using the sample distribution function. J Time Ser Anal 11:271–285CrossRef Delgado MA (1996) Testing serial independence using the sample distribution function. J Time Ser Anal 11:271–285CrossRef
30.
go back to reference Denker M, Keller G (1983) On U‐statistics and v. Mises' statistics for weakly dependent processes. Z Wahrscheinlichkeitstheorie verwandte Geb 64:505–522 Denker M, Keller G (1983) On U‐statistics and v. Mises' statistics for weakly dependent processes. Z Wahrscheinlichkeitstheorie verwandte Geb 64:505–522
31.
go back to reference Denker M, Keller G (1986) Rigorous statistical procedures for data from dynamical systems. J Stat Phys 44:67–93CrossRef Denker M, Keller G (1986) Rigorous statistical procedures for data from dynamical systems. J Stat Phys 44:67–93CrossRef
32.
go back to reference Diks C, Panchenko V (2007) Nonparametric tests for serial independence based on quadratic forms. Statistica Sin 17:81–97 Diks C, Panchenko V (2007) Nonparametric tests for serial independence based on quadratic forms. Statistica Sin 17:81–97
33.
go back to reference Diks C, Panchenko V (2008) Rank‐based entropy tests for serial independence. Stud Nonlinear Dyn Econom 12(1)art.2:0–19 Diks C, Panchenko V (2008) Rank‐based entropy tests for serial independence. Stud Nonlinear Dyn Econom 12(1)art.2:0–19
34.
go back to reference Diks C, Tong H (1999) A test for symmetries of multivariate probability distributions. Biometrika 86:605–614CrossRef Diks C, Tong H (1999) A test for symmetries of multivariate probability distributions. Biometrika 86:605–614CrossRef
35.
go back to reference Dionísio A, Menezes R, Mendes DA (2006) Entropy‐based independence test. Nonlinear Dyn 44:351–357 Dionísio A, Menezes R, Mendes DA (2006) Entropy‐based independence test. Nonlinear Dyn 44:351–357
36.
go back to reference Dufour JM (1981) Rank tests for serial dependence. J Time Ser Anal 2:117–128CrossRef Dufour JM (1981) Rank tests for serial dependence. J Time Ser Anal 2:117–128CrossRef
37.
go back to reference Dufour JM (2006) Monte Carlo tests with nuisance parameters: A general approach to finite‐sample inference and nonstandard asymptotics. J Econom 133:443–477CrossRef Dufour JM (2006) Monte Carlo tests with nuisance parameters: A general approach to finite‐sample inference and nonstandard asymptotics. J Econom 133:443–477CrossRef
38.
go back to reference Durbin J, Watson GS (1950) Testing for serial correlation in least‐squares regression, I. Biometrika 37:409–428 Durbin J, Watson GS (1950) Testing for serial correlation in least‐squares regression, I. Biometrika 37:409–428
39.
go back to reference Durbin J, Watson GS (1951) Testing for serial correlation in least‐squares regression, II. Biometrika 38:159–177 Durbin J, Watson GS (1951) Testing for serial correlation in least‐squares regression, II. Biometrika 38:159–177
40.
go back to reference Durbin J, Watson GS (1971) Testing for serial correlation in least‐squares regression, III. Biometrika 58:1–19 Durbin J, Watson GS (1971) Testing for serial correlation in least‐squares regression, III. Biometrika 58:1–19
41.
go back to reference Durlauf S (1991) Spectral based testing of the martingale hypothesis. J Econometrics 50:355–376CrossRef Durlauf S (1991) Spectral based testing of the martingale hypothesis. J Econometrics 50:355–376CrossRef
42.
go back to reference Engle R (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50:987–1007CrossRef Engle R (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50:987–1007CrossRef
43.
go back to reference Ferguson TS, Genest C, Hallin M (2000) Kendall's tau for serial dependence. Can J Stat 28:587–604CrossRef Ferguson TS, Genest C, Hallin M (2000) Kendall's tau for serial dependence. Can J Stat 28:587–604CrossRef
44.
go back to reference Fernandes M, Neri B (2008) Nonparametric entropy‐based tests of independence between stochastic processes. Econometric Reviews; Forthcoming Fernandes M, Neri B (2008) Nonparametric entropy‐based tests of independence between stochastic processes. Econometric Reviews; Forthcoming
45.
go back to reference Genest C, Quessy JF, Rémillard B (2002) Tests of serial independence based on Kendall's process. Can J Stat 30:1–21 Genest C, Quessy JF, Rémillard B (2002) Tests of serial independence based on Kendall's process. Can J Stat 30:1–21
46.
go back to reference Genest C, Rémillard B (2004) Tests of independence and randomness based on the empirical copula process. Test 13:335–369 Genest C, Rémillard B (2004) Tests of independence and randomness based on the empirical copula process. Test 13:335–369
47.
go back to reference Genest C, Verret F (2005) Locally most powerful rank tests of independence for copula models. Nonparametric Stat 17:521–539CrossRef Genest C, Verret F (2005) Locally most powerful rank tests of independence for copula models. Nonparametric Stat 17:521–539CrossRef
48.
go back to reference Genest C, Ghoudi K, Rémillard B (2007) Rank‐based extensions of the Brock, Dechert, and Scheinkman test. J Am Stat Assoc 102:1363–1376 Genest C, Ghoudi K, Rémillard B (2007) Rank‐based extensions of the Brock, Dechert, and Scheinkman test. J Am Stat Assoc 102:1363–1376
49.
go back to reference Ghoudi K, Kulperger RJ, Rémillard B (2001) A nonparametric test of serial independence for time series and residuals. J Multivar Anal 79:191–218 Ghoudi K, Kulperger RJ, Rémillard B (2001) A nonparametric test of serial independence for time series and residuals. J Multivar Anal 79:191–218
50.
go back to reference Granger C, Lin JL (2001) Using the mutual information coefficient to identify lags in nonlinear models. J Time Ser Anal 15:371–384CrossRef Granger C, Lin JL (2001) Using the mutual information coefficient to identify lags in nonlinear models. J Time Ser Anal 15:371–384CrossRef
51.
go back to reference Granger CW, Maasoumi E, Racine J (2004) A dependence metric for possibly nonlinear processes. J Time Ser Anal 25:649–669CrossRef Granger CW, Maasoumi E, Racine J (2004) A dependence metric for possibly nonlinear processes. J Time Ser Anal 25:649–669CrossRef
52.
go back to reference Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D 9:189–208CrossRef Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D 9:189–208CrossRef
53.
go back to reference Grassberger P, Schreiber T, Schaffrath C (1991) Nonlinear time sequence analysis. Int J Bifurc Chaos 1:521–547CrossRef Grassberger P, Schreiber T, Schaffrath C (1991) Nonlinear time sequence analysis. Int J Bifurc Chaos 1:521–547CrossRef
54.
go back to reference Hallin M, Ingenbleek J-F, Puri ML (1985) Linear serial rank tests for randomness against ARMA alternatives. Ann Stat 13:1156–1181CrossRef Hallin M, Ingenbleek J-F, Puri ML (1985) Linear serial rank tests for randomness against ARMA alternatives. Ann Stat 13:1156–1181CrossRef
55.
go back to reference Hallin M, Mélard G (1988) Rank-based tests for randomness against first-order serial dependence. J Am Stat Assoc 83:1117–1128 Hallin M, Mélard G (1988) Rank-based tests for randomness against first-order serial dependence. J Am Stat Assoc 83:1117–1128
56.
go back to reference Hannan EJ (1957) Testing for serial correlation in least squares regression. Biometrika 44:57–66 Hannan EJ (1957) Testing for serial correlation in least squares regression. Biometrika 44:57–66
57.
go back to reference Hinich M, Patterson D (1985) Evidence of nonlinearity in stock returns. J Bus Econ Stat 3:69–77CrossRef Hinich M, Patterson D (1985) Evidence of nonlinearity in stock returns. J Bus Econ Stat 3:69–77CrossRef
58.
go back to reference Hinich MJ (1982) Testing for Gaussianity and linearity of a stationary time series. J Time Ser Anal 3:169–176CrossRef Hinich MJ (1982) Testing for Gaussianity and linearity of a stationary time series. J Time Ser Anal 3:169–176CrossRef
59.
go back to reference Hinich MJ (1996) Testing for dependence in the input to a linear time series model. J Nonparametric Stat 8:205–221CrossRef Hinich MJ (1996) Testing for dependence in the input to a linear time series model. J Nonparametric Stat 8:205–221CrossRef
60.
go back to reference Hjellvik V, Tjøstheim D (1995) Nonparametric tests of linearity for time series. Biometrika 82:351–368 Hjellvik V, Tjøstheim D (1995) Nonparametric tests of linearity for time series. Biometrika 82:351–368
61.
go back to reference Hjellvik V, Yao Q, Tjøstheim D (1998) Linearity testing using polynomial approximation. J Stat Plan Inference 68:295–321 Hjellvik V, Yao Q, Tjøstheim D (1998) Linearity testing using polynomial approximation. J Stat Plan Inference 68:295–321
62.
go back to reference Hoeffding W (1948) A non‐parametric test of independence. Ann Math Stat 19:546–557CrossRef Hoeffding W (1948) A non‐parametric test of independence. Ann Math Stat 19:546–557CrossRef
63.
go back to reference Hong Y (1999) Hypothesis testing in time series via the empirical characteristic function: a generalized spectral density approach. J Am Stat Assoc 94:1201–1220CrossRef Hong Y (1999) Hypothesis testing in time series via the empirical characteristic function: a generalized spectral density approach. J Am Stat Assoc 94:1201–1220CrossRef
64.
go back to reference Hong Y (2000) Generalized spectral tests for serial dependence. J Royal Stat Soc Ser B 62:557–574CrossRef Hong Y (2000) Generalized spectral tests for serial dependence. J Royal Stat Soc Ser B 62:557–574CrossRef
65.
go back to reference Hong Y, White H (2005) Asymptotic distribution theory for nonparametric entropy measures of serial dependence. Econometrica 73:837–901CrossRef Hong Y, White H (2005) Asymptotic distribution theory for nonparametric entropy measures of serial dependence. Econometrica 73:837–901CrossRef
66.
go back to reference Horowitz JL (2001) The bootstrap. In: Heckman JJ, Leamer EE (eds) Handbook of Econometrics, vol 5. Elsevier, Amsterdam, pp 3159–3228 Horowitz JL (2001) The bootstrap. In: Heckman JJ, Leamer EE (eds) Handbook of Econometrics, vol 5. Elsevier, Amsterdam, pp 3159–3228
67.
go back to reference Horowitz JL, Spokoiny VG (2001) An adaptive, rate‐optimal test of a parametric mean‐regression model against a nonparametric alternative. Econometrica 69:599–631CrossRef Horowitz JL, Spokoiny VG (2001) An adaptive, rate‐optimal test of a parametric mean‐regression model against a nonparametric alternative. Econometrica 69:599–631CrossRef
68.
go back to reference Joe H (1989) Relative entropy measures of multivariate dependence. J Am Stat Assoc 84:157–164CrossRef Joe H (1989) Relative entropy measures of multivariate dependence. J Am Stat Assoc 84:157–164CrossRef
69.
70.
go back to reference Johnson D, McLelland R (1997) Nonparametric tests for the independence of regressors and disturbances as specification tests. Rev Econ Stat 79:335–340CrossRef Johnson D, McLelland R (1997) Nonparametric tests for the independence of regressors and disturbances as specification tests. Rev Econ Stat 79:335–340CrossRef
71.
go back to reference Johnson D, McLelland R (1998) A general dependence test and applications. J Appl Econometrics 13:627–644CrossRef Johnson D, McLelland R (1998) A general dependence test and applications. J Appl Econometrics 13:627–644CrossRef
72.
go back to reference Kallenberg WCM, Ledwina T (1999) Data driven rank tests for independence. J Am Stat Assoc 94:285–301CrossRef Kallenberg WCM, Ledwina T (1999) Data driven rank tests for independence. J Am Stat Assoc 94:285–301CrossRef
73.
go back to reference Kendall MG (1938) A new measure of rank correlation. Biometrika 30:81–93 Kendall MG (1938) A new measure of rank correlation. Biometrika 30:81–93
74.
go back to reference Kočenda E, Briatka Ľ (2005) Optimal range for the IID test based on integration across the correlation integral. Econometric Rev 24:265–296 Kočenda E, Briatka Ľ (2005) Optimal range for the IID test based on integration across the correlation integral. Econometric Rev 24:265–296
75.
go back to reference Kulperger RJ, Lockhart RA (1998) Tests of independence in time series. J Time Ser Anal 1998:165–185CrossRef Kulperger RJ, Lockhart RA (1998) Tests of independence in time series. J Time Ser Anal 1998:165–185CrossRef
76.
go back to reference Künsch HR (1989) The jackknife and the bootstrap for general stationary observations. Ann Stat 17:1217–1241 Künsch HR (1989) The jackknife and the bootstrap for general stationary observations. Ann Stat 17:1217–1241
77.
go back to reference Lim KP, Hinich MJ, Liew VKS (2005) Statistical inadequacy of GARCH models for Asian stock markets: Evidence and implications. J Emerg Mark Finance 4:263–279CrossRef Lim KP, Hinich MJ, Liew VKS (2005) Statistical inadequacy of GARCH models for Asian stock markets: Evidence and implications. J Emerg Mark Finance 4:263–279CrossRef
78.
go back to reference Lima P De (1996) Nuisance parameter free properties of correlation integral based statistics. Econometric Rev 15:237–259CrossRef Lima P De (1996) Nuisance parameter free properties of correlation integral based statistics. Econometric Rev 15:237–259CrossRef
79.
go back to reference Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65:297–202CrossRef Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65:297–202CrossRef
80.
go back to reference Lo AW (2000) Finance: A selective survey. J Am Stat Assoc 95:629–635CrossRef Lo AW (2000) Finance: A selective survey. J Am Stat Assoc 95:629–635CrossRef
81.
go back to reference Maasoumi E (2002) Entropy and predictability of stock market returns. J Econometrics 107:291–312CrossRef Maasoumi E (2002) Entropy and predictability of stock market returns. J Econometrics 107:291–312CrossRef
82.
go back to reference McLeod AI, Li WK (1983) Diagnostic checking ARMA time series models using squared‐residual autocorrelations. J Time Ser Anal 4:269–273CrossRef McLeod AI, Li WK (1983) Diagnostic checking ARMA time series models using squared‐residual autocorrelations. J Time Ser Anal 4:269–273CrossRef
83.
go back to reference Von Neumann J (1941) Distribution of the ratio of the mean square successive difference to the variance. Ann Math Stat 12:367–395CrossRef Von Neumann J (1941) Distribution of the ratio of the mean square successive difference to the variance. Ann Math Stat 12:367–395CrossRef
84.
go back to reference Pinkse J (1998) A consistent nonparametric test for serial independence. J Econometrics 84:205–231CrossRef Pinkse J (1998) A consistent nonparametric test for serial independence. J Econometrics 84:205–231CrossRef
85.
go back to reference Politis DN, Romano JP (1994) The stationary bootstrap. J Am Stat Assoc 89:1303–1313CrossRef Politis DN, Romano JP (1994) The stationary bootstrap. J Am Stat Assoc 89:1303–1313CrossRef
86.
go back to reference Racine J, Maasoumi E (2007) A versatile and robust metric entropy test for time‐irreversibility, and other hypotheses. J Econometrics 138:547–567CrossRef Racine J, Maasoumi E (2007) A versatile and robust metric entropy test for time‐irreversibility, and other hypotheses. J Econometrics 138:547–567CrossRef
87.
go back to reference Ramsey JB, Rothman P (1990) Time irreversibility of stationary time series: estimators and test statistics. Unpublished manuscript, Department of Economics, New York University and University of Delaware Ramsey JB, Rothman P (1990) Time irreversibility of stationary time series: estimators and test statistics. Unpublished manuscript, Department of Economics, New York University and University of Delaware
88.
go back to reference Robinson PM (1991) Consistent nonparametric entropy‐based testing. Rev Econ Stud 58:437–453CrossRef Robinson PM (1991) Consistent nonparametric entropy‐based testing. Rev Econ Stud 58:437–453CrossRef
89.
go back to reference Rosenblatt M (1975) A quadratic measure of deviation of two‐dimensional density estimates and a test of independence. Ann Stat 3:1–14CrossRef Rosenblatt M (1975) A quadratic measure of deviation of two‐dimensional density estimates and a test of independence. Ann Stat 3:1–14CrossRef
90.
go back to reference Rosenblatt M, Wahlen BE (1992) A nonparametric measure of independence under a hypothesis of independent components. Stat Probab Lett 15:245–252CrossRef Rosenblatt M, Wahlen BE (1992) A nonparametric measure of independence under a hypothesis of independent components. Stat Probab Lett 15:245–252CrossRef
91.
go back to reference Rothman P (1992) The comparative power of the TR test against simple threshold models. J Appl Econometrics 7:S187–S195CrossRef Rothman P (1992) The comparative power of the TR test against simple threshold models. J Appl Econometrics 7:S187–S195CrossRef
92.
go back to reference Scaillet O (2005) A Kolmogorov–Smirnov type test for positive quadrant dependence. Can J Stat 33:415–427CrossRef Scaillet O (2005) A Kolmogorov–Smirnov type test for positive quadrant dependence. Can J Stat 33:415–427CrossRef
93.
go back to reference Serfling RJ (1980) Approximation Theorems of Mathematical Statistics. Wiley, New YorkCrossRef Serfling RJ (1980) Approximation Theorems of Mathematical Statistics. Wiley, New YorkCrossRef
94.
go back to reference Silverman BW (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall, New York Silverman BW (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall, New York
95.
go back to reference Skaug HJ, Tjøstheim D (1993a) A nonparametric test for serial independence based on the empirical distribution function. Biometrika 80:591–602 Skaug HJ, Tjøstheim D (1993a) A nonparametric test for serial independence based on the empirical distribution function. Biometrika 80:591–602
96.
go back to reference Skaug HJ, Tjøstheim D (1993b) Nonparametric tests of serial independence. In: Subba Rao T (ed) Developments in Time Series Analysis: the M. B. Priestley Birthday Volume. Wiley, New York Skaug HJ, Tjøstheim D (1993b) Nonparametric tests of serial independence. In: Subba Rao T (ed) Developments in Time Series Analysis: the M. B. Priestley Birthday Volume. Wiley, New York
97.
go back to reference Spearman C (1904) The proof and measurement of association between two things. Am J Psychol 15:72–101CrossRef Spearman C (1904) The proof and measurement of association between two things. Am J Psychol 15:72–101CrossRef
98.
go back to reference Subba Rao T, Gabr MM (1980) A test for linearity of stationary time series. J Time Ser Anal 1:145–158CrossRef Subba Rao T, Gabr MM (1980) A test for linearity of stationary time series. J Time Ser Anal 1:145–158CrossRef
99.
go back to reference Takens F (1981) Detecting strange attractors in turbulence. In: Rand DA, Young LS (eds) Dynamical Systems and Turbulence, Warwick 1980. (Lecture Notes in Mathematics), vol 898. Springer, Berlin, pp 366–381CrossRef Takens F (1981) Detecting strange attractors in turbulence. In: Rand DA, Young LS (eds) Dynamical Systems and Turbulence, Warwick 1980. (Lecture Notes in Mathematics), vol 898. Springer, Berlin, pp 366–381CrossRef
100.
go back to reference Terdik G, Máth J (1998) A new test of linearity of time series based on the bispectrum. J Time Ser Anal 19:737–753 Terdik G, Máth J (1998) A new test of linearity of time series based on the bispectrum. J Time Ser Anal 19:737–753
101.
go back to reference Theil H, Nagar AL (1961) Testing the independence of regression disturbances. J Am Stat Assoc 56:793–806CrossRef Theil H, Nagar AL (1961) Testing the independence of regression disturbances. J Am Stat Assoc 56:793–806CrossRef
102.
go back to reference Theiler J (1990) Statistical precision of dimension estimators. Phys Rev A 41:3038–3051CrossRef Theiler J (1990) Statistical precision of dimension estimators. Phys Rev A 41:3038–3051CrossRef
103.
go back to reference Tjøstheim D (1996) Measures of dependence and tests of independence. Statistics 28:249–284 Tjøstheim D (1996) Measures of dependence and tests of independence. Statistics 28:249–284
104.
go back to reference Tong H (1990) Non‐linear Time Series: A Dynamical Systems Approach. Clarendon Press, Oxford Tong H (1990) Non‐linear Time Series: A Dynamical Systems Approach. Clarendon Press, Oxford
105.
go back to reference Tsallis C (1998) Generalized entropy‐based criterion for consistent testing. Phys Rev E 58:1442–1445CrossRef Tsallis C (1998) Generalized entropy‐based criterion for consistent testing. Phys Rev E 58:1442–1445CrossRef
106.
go back to reference Wolff RC (1994) Independence in time series: another look at the BDS test. Philos Trans Royal Soc Ser A 348:383–395CrossRef Wolff RC (1994) Independence in time series: another look at the BDS test. Philos Trans Royal Soc Ser A 348:383–395CrossRef
Metadata
Title
Nonparametric Tests for Independence
Author
Cees Diks
Copyright Year
2011
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4419-7701-4_35