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Articles

Extremal Dependence-Based Specification Testing of Time Series

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References

  • Anderson, T. W. (1955), “The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and some Probability Inequalities,” Proceedings of the American Mathematical Society, 6, 170–176. DOI: 10.1090/S0002-9939-1955-0069229-1.
  • Basel Committee on Banking Supervision (2019), Basel Framework, Basel: Bank for International Settlements. Available at https://www.bis.org/basel_framework/index.htm?export=pdf.
  • Berkes, I., Horváth, L., and Kokoszka, P. (2003), “Asymptotics for GARCH Squared Residual Correlations,” Econometric Theory, 19, 515–540. DOI: 10.1017/S0266466603194017.
  • Box, G. E. P., and Pierce, D. A. (1970), “Distribution of Residual Autocorrelations in Autoregressive-Integreted Moving Average Time Series Models,” Journal of the American Statististical Association, 65, 1509–1526. DOI: 10.1080/01621459.1970.10481180.
  • Carbon, M., and Francq, C. (2011), “Portmanteau Goodness-of-Fit Test for Asymmetric Power GARCH Models,” Austrian Journal of Statistics, 40, 55–64.
  • Chan, N. H., Deng, S. J., Peng, L., and Xia, Z. (2007), “Interval Estimation of Value-at-Risk based on GARCH Models with Heavy-Tailed Innovations,” Journal of Econometrics, 137, 556–576. DOI: 10.1016/j.jeconom.2005.08.008.
  • Chavez-Demoulin, V., Embrechts, P., and Sardy, S. (2014), “Extreme-Quantile Tracking for Financial Time Series,” Journal of Econometrics, 181, 44–52. DOI: 10.1016/j.jeconom.2014.02.007.
  • Chen, B., and Hong, Y. (2014), “A Unified Approach to Validating Univariate and Multivariate Conditional Distribution Models in Time Series,” Journal of Econometrics, 178, 22–44. DOI: 10.1016/j.jeconom.2013.08.004.
  • Davis, R. A., and Mikosch, T. (2009), “The Extremogram: A Correlogram for Extreme Events,” Bernoulli, 15, 977–1009. DOI: 10.3150/09-BEJ213.
  • Davis, R. A., Mikosch, T., and Cribben, I. (2012), “Towards Estimating Extremal Serial Dependence via the Bootstrapped Extremogram,” Journal of Econometrics, 170, 142–152. DOI: 10.1016/j.jeconom.2012.04.003.
  • Davis, R. A., Mikosch, T., and Zhao, Y. (2013), “Measures of Serial Extremal Dependence and their Estimation,” Stochastic Processes and their Applications, 123, 2575–2602. DOI: 10.1016/j.spa.2013.03.014.
  • de Haan, L., and Ferreira, A. (2006), Extreme Value Theory, New York: Springer.
  • Delgado, M. A., and Velasco, C. (2011), “An Asymptotically Pivotal Transform of the Residuals Sample Autocorrelations with Application to Model Checking,” Journal of the American Statistical Association, 106, 946–958. DOI: 10.1198/jasa.2011.tm10226.
  • Du, Z., and Escanciano, J. C. (2015), “A Nonparametric Distribution-Free Test for Serial Independence of Errors,” Econometric Reviews, 34, 1011–1034. DOI: 10.1080/07474938.2014.956616.
  • Du, Z., and Escanciano, J. C. (2017), “Backtesting Expected Shortfall: Accounting for Tail Risk,” Management Science, 63, 940–958.
  • DuMouchel, W. H. (1983), “Estimating the Stable Index α in Order to Measure Tail Thickness: A Critique,” The Annals of Statistics, 11, 1019–1031. DOI: 10.1214/aos/1176346318.
  • Engle, R. F., and Manganelli, S. (2004), “CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles,” Journal of Business & Economic Statistics, 22, 367–381.
  • Escanciano, J. C. (2006), “Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models,” Journal of the American Statistical Association, 101, 531–541. DOI: 10.1198/016214505000001050.
  • Escanciano, J. C. (2008), “Joint and Marginal Specification Tests for Conditional Mean and Variance Models,” Journal of Econometrics, 143, 74–87.
  • Escanciano, J. C. (2009), “Quasi-Maximum Likelihood Estimation of Semi-Strong GARCH Models,” Econometric Theory, 25, 561–570.
  • Escanciano, J. C. (2010), “Asymptotic Distribution-Free Diagnostic Tests for Heteroskedastic Time Series Models,” Econometric Theory, 26, 744–773.
  • Escanciano, J. C., and Lobato, I. N. (2009), “An Automatic Portmanteau Test for Serial Correlation,” Journal of Econometrics, 151, 140–149. DOI: 10.1016/j.jeconom.2009.03.001.
  • Escanciano, J. C., and Olmo, J. (2010), “Backtesting Parametric Value-at-Risk with Estimation Risk,” Journal of Business & Economic Statistics, 28, 36–51.
  • Fisher, T. J., and Gallagher, C. M. (2012), “New Weighted Portmanteau Statistics for Time Series Goodness of Fit Testing,” Journal of the American Statistical Association, 107, 777–787. DOI: 10.1080/01621459.2012.688465.
  • Francq, C., Roy, R., and Zakoïan, J. M. (2005), “Diagnostic Checking in ARMA Models with Uncorrelated Errors,” Journal of the American Statistical Association, 100, 532–544. DOI: 10.1198/016214504000001510.
  • Francq, C., and Thieu, L. Q. (2019), “QML Inference for Volatility Models with Covariates,” Econometric Theory, 35, 37–72. DOI: 10.1017/S0266466617000512.
  • Francq, C., and Zakoïan, J. M. (2010), GARCH Models: Structure, Statistical Inference and Financial Applications, Chichester: Wiley.
  • Ghalanos, A. (2020), rugarch: Univariate GARCH Models. R package version 1.4–2.
  • Hall, P., and Yao, Q. (2003), “Inference in ARCH and GARCH Models with Heavy-Tailed Errors,” Econometrica, 71, 285–317. DOI: 10.1111/1468-0262.00396.
  • Han, H., and Kristensen, D. (2014), “Asymptotic Theory for the QMLE in GARCH-X Models with Stationary and Nonstationary Covariates,” Journal of Business & Economic Statistics, 32, 416–429.
  • Hansen, B. E. (1994), “Autoregressive Conditional Density Estimation,” International Economic Review, 35, 705–730. DOI: 10.2307/2527081.
  • Heffernan, J. E. (2000), “A Directory of Coefficients of Tail Dependence,” Extremes, 3, 279–290.
  • Hidalgo, J., and Zaffaroni, P. (2007), “A Goodness-of-Fit Test for ARCH(∞ ) Models,” Journal of Econometrics, 141, 973–1013.
  • Hill, J. B. (2009), “On Functional Central Limit Theorems for Dependent, Heterogeneous Arrays with Applications to Tail Index and Tail Dependence Estimation,” Journal of Statistical Planning and Inference, 139, 2091–2110. DOI: 10.1016/j.jspi.2008.09.005.
  • Hill, J. B. (2011a), “Extremal Memory of Stochastic Volatility with an Application to Tail Shape Inference,” Journal of Statistical Planning and Inference, 141, 663–676.
  • Hill, J. B. (2011b), “Tail and Nontail Memory with Applications to Extreme Value and Robust Statistics,” Econometric Theory, 27, 844–884.
  • Hill, J. B. (2015a), “Robust Estimation and Inference for Heavy Tailed GARCH,” Bernoulli, 21:1629–1669.
  • Hill, J. B. (2015b), “Tail Index Estimation for a Filtered Dependent Time Series,” Statistica Sinica, 25, 609–629.
  • Hill, J. B., and Motegi, K. (2020), “A Max-Correlation White Noise Test for Weakly Dependent Time Series,” Econometric Theory, 36, 907–960. DOI: 10.1017/S0266466619000367.
  • Hoga, Y. (2019), “Confidence Intervals for Conditional Tail Risk Measures in ARMA–GARCH Models,” Journal of Business & Economic Statistics, 37, 613–624.
  • Hoga, Y., and Demetrescu, M. (in press), “Monitoring Value-at-Risk and Expected Shortfall Forecasts,” Management Science, 1–18. DOI: 10.1287/mnsc.2022.4460..
  • Hong, Y. (1999), “Hypothesis Testing in Time Series via the Empirical Characteristic Function: A Generalized Spectral Density Approach,” Journal of the American Statistical Association, 94, 1201–1220. DOI: 10.1080/01621459.1999.10473874.
  • Hong, Y., and Lee, T. H. (2003), “Diagnostic Checking for the Adequacy of Nonlinear Time Series Models,” Econometric Theory, 19, 1065–1121. DOI: 10.1017/S0266466603196089.
  • Li, W. K., and Mak, T. K. (1994), “On the Squared Residual Autocorrelations in Non-linear Time Series with Conditional heteroskedasticity,” Journal of Time Series Analysis, 15, 627–636. DOI: 10.1111/j.1467-9892.1994.tb00217.x.
  • Ling, S., and Li, W. K. (1997), “On Fractionally Integrated Autoregressive Moving-Average Time Series Models with Conditional Heteroscedasticity,” Journal of the American Statistical Association, 92, 1184–1194. DOI: 10.1080/01621459.1997.10474076.
  • Ljung, G. M., and Box, G. E. P. (1978), “On a Measure of Lack of Fit in Time Series Models,” Biometrika, 65, 297–303. DOI: 10.1093/biomet/65.2.297.
  • McNeil, A. J., and Frey, R. (2000), “Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach,” Journal of Empirical Finance, 7, 271–300. DOI: 10.1016/S0927-5398(00)00012-8.
  • Oh, D. H., and Patton, A. J. (2018), “Time-Varying Systemic Risk: Evidence from a Dynamic Copula Model of CDS Spreads,” Journal of Business & Economic Statistics, 36, 181–195.
  • Quintos, C., Fan, Z., and Phillips, P. C. B. (2001), “Structural Change Tests in Tail Behaviour and the Asian Crisis,” Review of Economic Studies, 68, 633–663. DOI: 10.1111/1467-937X.00184.
  • R Core Team. 2021. R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
  • Resnick, S., and Stǎricǎ, C. (1997), “Smoothing the Hill Estimator,” Advances in Applied Probability, 29, 271–293. DOI: 10.2307/1427870.
  • Rothe, C., and Wied, D. (2013), “Misspecification Testing in a Class of Conditional Distributional Models,” Journal of the American Statistical Association, 108, 314–324. DOI: 10.1080/01621459.2012.736903.
  • Schmidt, R., and Stadtmüller, U. (2006), “Nonparametric Estimation of Tail Dependence,” Scandinavian Journal of Statistics, 33, 307–335. DOI: 10.1111/j.1467-9469.2005.00483.x.
  • Sibuya, M. (1960), “Bivariate Extreme Statistics,” Annals of the Institute of Statistical Mathematics, 11, 195–210. DOI: 10.1007/BF01682329.
  • Velasco, C., and Wang, X. (2015), “A Joint Portmanteau Test for Conditional Mean and Variance Time-Series Models,” Journal of Time Series Analysis, 36, 39–60. DOI: 10.1111/jtsa.12091.
  • Zheng, Y., Li, W. K., and Li, G. (2018), “A Robust Goodness-of-Fit Test for Generalized Autoregressive Conditional Heteroscedastic Models,” Biometrika, 105, 73–89. DOI: 10.1093/biomet/asx063.
  • Zhu, K., and Ling, S. (2011), “Global Self-Weighted and Local Quasi-Maximum Exponential Likelihood Estimators for ARMA–GARCH/IGARCH Models,” Annals of Statistics, 39, 2131–2163.

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