Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling

References

• Andrews, B., Calder, M., and Davis, R. A. (2009), “Maximum Likelihood Estimation for α-Stable Autoregressive Processes,” The Annals of Statistics, 37, 1946–1982.
   Web of Science ®Google Scholar
• Athreya, K. B. (1987), “Bootstrap of the Mean in the Infinite Variance Case,” The Annals of Statistics, 15, 724–731.
   Web of Science ®Google Scholar
• Bickel, P. J., and Sakov, A. (2008), “On the Choice of m in the m out of n Bootstrap and Confidence Bounds for Extrema,” Statistica Sinica, 18, 967–985.
   Web of Science ®Google Scholar
• Breidt, F. J., Davis, R. A., Lii, K.-S., and Rosenblatt, M. (1991), “Maximum Likelihood Estimation for Noncausal Autoregressive Processes,” Journal of Multivariate Analysis, 36, 175–198.
   Web of Science ®Google Scholar
• Brockwell, P. J., and Davis, R. (1991), Time Series: Theory and Methods, New York: Springer.
   Google Scholar
• Cavaliere, G., Georgiev, I., and Taylor, A. M. R. (2013), “Wild Bootstrap of the Mean in the Infinite Variance Case,” Econometric Reviews, 32, 204–219.
   Web of Science ®Google Scholar
• ——— (2016), “Sieve-Based Inference for Infinite-Variance Linear Processes,” The Annals of Statistics, 44, 1467–1494 (with Supplement).
   Web of Science ®Google Scholar
• Cavaliere, G., Nielsen, H. B., and Rahbek, A. (2015), “Bootstrap Testing of Hypotheses on Co-Integration Relations in Vector Autoregressive Models,” Econometrica, 83, 813–831.
   Web of Science ®Google Scholar
• ——— (2018), Supplementary Material for “Boostrapping Non-Causal Autoregressions: with Applications to Explosive Bubble Modelling.”
   Google Scholar
• Cornea-Madeira, A., and Davidson, R. (2015), “A Parametric Bootstrap for Heavy-Tailed Distributions,” Econometric Theory, 31, 449–470.
   Web of Science ®Google Scholar
• Davidson, R., and Flachaire, E. (2008), “The Wild Bootstrap, Tamed at Last,” Journal of Econometrics, 146, 162–169.
   Web of Science ®Google Scholar
• Davidson, R., and MacKinnon, J. (2006), “The Power of Bootstrap and Asymptotic Tests,” Journal of Econometrics, 133, 421–441.
   Web of Science ®Google Scholar
• Davis, R., and Resnick, S. (1985a), “Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities,” The Annals of Probability, 13, 179–195.
   Web of Science ®Google Scholar
• ——— (1985b), “More Limit Theory for the Sample Correlation Function of Moving Averages,” Stochastic Processes and their Applications, 20, 257–279.
   Web of Science ®Google Scholar
• ——— (1986), “Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages,” The Annals of Statistics, 14, 533–558.
   Web of Science ®Google Scholar
• Gonçalves, S., and Kilian, L. (2004), “Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form,” Journal of Econometrics, 123, 89–120.
   Web of Science ®Google Scholar
• Gonçalves, S., and White, H. (2004), “Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models,” Journal of Econometrics, 119, 199–219.
   Web of Science ®Google Scholar
• Gourieroux, C., and Jasiak, J. (2016), “Filtering, Prediction and Simulation Methods for Noncausal Processes,” Journal of Time Series Analysis, 37, 405–430.
   Web of Science ®Google Scholar
• Gourieroux, C., Jasiak, J., and Monfort, A. (2016), Stationary Bubble Equilibria in Rational Expectation Models, Working Paper, 2016-31, CREST-Paris.
   Google Scholar
• Gourieroux, C., and Zakoïan, J.-M. (2017), “Local Explosion Modelling by Non-causal Process,” Journal of the Royal Statistical Society, Series B, 79, 737–756.
   Google Scholar
• Hecq, A., Lieb, L., and Telg, S. (2016), “Identification of Mixed Causal-Noncausal Models in Finite Samples,” Annals of Economics & Statistics, 123/124, 307–331.
   Google Scholar
• Hencic, A., and Gourieroux, C. C. (2015), “Noncausal Autoregressive Modelling in Application to Bitcoin/USD Exchange Rates,” in Econometrics of Risk, eds. V.-N. Huynh, V. Kreinovich, S. Sriboonchitta, and K. Suriya, Cham: Springer, pp. 17–40.
   Google Scholar
• Knight, K. (1989), “On the Bootstrap of the Sample Mean in the Infinite Variance Case,” The Annals of Statistics, 17, 1168–1175.
   Web of Science ®Google Scholar
• Lanne, M., and Luoto, J. (2013), “Autoregression-Based Estimation of the New Keynesian Phillips Curve,” Journal of Economic Dynamics and Control, 37, 561–570.
   Web of Science ®Google Scholar
• ——— (2017), “A New Time-Varying Parameter Autoregressive Model or U.S. Inflation Expectations,” Journal of Money, Credit and Banking, 49, 969–995.
   Web of Science ®Google Scholar
• Lanne, M., Meitz, M., and Saikkonen, P. (2013), “Testing for Linear and Nonlinear Predictability of Stock Returns,” Journal of Financial Econometrics, 11, 682–705.
   Web of Science ®Google Scholar
• Lanne, M., and Saikkonen, P. (2011), “Noncausal Autoregressions for Economic Time Series,” Journal of Time Series Econometrics, 3, Article 2.
   Google Scholar
• LePage, R. (1992), “Bootstrapping Signs,” in Exploring the Limits of the Bootstrap, eds. R. LePage and L. Billard L., New York: Wiley, pp. 215–224.
   Google Scholar
• LePage, R., and Podgorski, K. (1996), “Resampling Permutations in Regressions without a Second Moment,” Journal of Multivariate Analysis, 57, 119–141.
   Web of Science ®Google Scholar
• LePage, R., Woodroofe, M., and Zinn, J. (1981), “Convergence to a Stable Distribution via Order Statistics,” Annals of Probability, 9, 624–632.
   Web of Science ®Google Scholar
• Ling, S. (2004), “Estimation and Testing of Stationarity for Double-Autoregressive Models,” Journal of the Royal Statistical Society, Series B, 66, 63–78.
   Google Scholar
• ——— (2007), “A Double AR(p) Model: Structure and Estimation,” Statistica Sinica, 17, 161–175.
   Web of Science ®Google Scholar
• Ling, S., and Li, D. (2008), “Asymptotic Inference for a Nonstationary Double AR(1) Model,” Biometrika, 95, 257–263.
   Web of Science ®Google Scholar
• Moran, P. A. P. (1950), “Recent Developments in Ranking Theory,” Journal of the Royal Statistical Society, Series B, 12, 153–162.
   Google Scholar
• Nielsen, H. B., and Rahbek, A. (2014), “Unit Root Vector Autoregression with Volatility Induced Stationarity,” Journal of Empirical Finance, 29, 144–167.
   Web of Science ®Google Scholar
• Nolan, J. P. (2018), Stable Distributions - Models for Heavy Tailed Data (Chapter 1), Boston: MA: Birkhauser.
   Google Scholar
• Yang, Y., and Ling, S. (2017), “Inference for Heavy-Tailed and Multiple-Threshold Double Autoregressive Models,” Journal of Business & Economic Statistics, 35, 318–333.
   Web of Science ®Google Scholar