Appendix 1 - A brief guide to asymptotic theory

Summary

As we mentioned in the introduction we omitted completely asymptotic theory in our discussion saying that it can be found in the respective papers cited. However, the following references give the basics of asymptotic theory needed in most cases. For more specialized results, the respective papers have to be consulted.

The papers by Chan and Wei (1987), Phillips (1987a), and Chan (1988) are on local to unity asymptotics.

Andrews, D.W.K. (1993), “An Introduction to Econometric Applications of Empirical Process Theory for Dependent Random Variables,” Econometric Reviews, 12, 183–216.

Billingsley, P. (1968), Convergence of Probability Measures, Wiley and Sons, New York.

Chan, N.H. (1988), “On the Parameter Inference for Nearly Nonstationary Time Series,” Journal of the American Statistical Association, 83, 857–862.

(1989), “Asymptotic Inference for Unstable Autoregressive Time Series with Drifts,” Journal of Statistical Planning and Inference, 23, 301–312.

Chan, N.H. and C.Z. Wei (1987), “Asymptotic Inference for Nearly Nonstationary AR(1) Processes,” The Annals of Statistics, 15, 1050–1063.

(1988), “Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes,” The Annals of Statistics, 16, 367–401.

Johansen, S. (1995), Likelihood Based Inference in Cointegrated Vector Autoregressive Models, Oxford University Press, Oxford.

Park, J.Y. and P.C.B. Phillips (1988), “Statistical Inference in Regressions with Integrated Processes I,” Econometric Theory, 4, 468–497.

(1989), “Statistical Inference in Regressions with Integrated Processes II,” Econometric Theory, 5, 95–131.

Phillips, P.C.B. (1986), “Understanding Spurious Regressions in Econometrics,” Journal of Econometrics, 33, 311–340.