This paper provides a simple technique of carrying out inference robust to serial correlation, heteroskedasticity and spatial correlation on the estimators which follow an asymptotic normal distribution. The idea is based on the fact that the estimates from a larger sample tend to have a smaller variance which can be expressed as a function of the variance of the estimator from smaller subsamples. The major advantage of the technique other than the ease of application and simplicity is its finite sample performance both in terms of the empirical null rejection probability as well as the power of the test. It does not restrict the data in terms of structure in any way and works pretty well for any kind of heteroskedasticity, autocorrelation and spatial correlation in a finite sample. Furthermore, unlike theoretical HAC robust techniques available in the existing literature, it does not require any kernel estimation and hence eliminates the discretion of the analyst to choose a specific kernel and bandwidth. The technique outperforms the Ibragimov and Müller (2010) approach in terms of null rejection probability as well as the local asymptotic power of the test.
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Table 14 is prepared as per suggestions of anonymous referees.
Alan Bester, C., Conley, T. G., Hansen, C. B. and Vogelsang, T. J. 2009. Fixed-b asymptotics for spatially dependent robust nonparametric covariance matrix estimators, Econometric Theory pp. 1–33.
Andrews, D.W.K. 1991. Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59: 817–854.
Andrews, D.W.K., and J.C. Monahan. 1992. An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60: 953–966.
Berkowitz, J., and L. Kilian. 2000. Recent developments in bootstrapping time series. Econometric Reviews 19 (1): 1–48.
Bühlmann, P. 2002. Bootstraps for time series, Statistical Science pp. 52–72.
Cameron, A. C. and Miller, D. L. 2010. Robust inference with clustered data, Technical report, Working Papers, University of California, Department of Economics.
Dale, M.R., and M.-J. Fortin. 2009. Spatial autocorrelation and statistical tests: Some solutions. Journal of Agricultural, Biological, and Environmental Statistics 14 (2): 188–206.
de Jong, R.M., and J. Davidson. 2000. Consistency of kernel estimators of heteroskedastic and autocorrelated covariance matrices. Econometrica 68: 407–424.
Driscoll, J., and A. Kraay. 1998. Consistent covariance matrix estimation with spatially dependent panel data. Review of Economics and Statistics 80 (4): 549–560.
Gallant, A. 1987. Nonlinear Statistical Models. New York: Wiley.
Härdle, W., J. Horowitz, and J.-P. Kreiss. 2003. Bootstrap methods for time series. International Statistical Review 71 (2): 435–459.
Hongyi, G., and L. Maddala, 1996. Bootstrapping time series models. Econometric Reviews 15 (2): 115–158.
Ibragimov, R., and U. Müller. 2010. \(t\)-statistic based correlation and heterogeneity robust inference. Journal of Business and Economic Statistics 28 (4): 453–468.
Jansson, M. 2002. Consistent covariance estimation for linear processes. Econometric Theory 18: 1449–1459.
Kelejian, H.H., and I.R. Prucha. 2001. On the asymptotic distribution of the moran i test statistic with applications. Journal of Econometrics 104 (2): 219–257.
Kiefer, N.M., and T.J. Vogelsang. 2005. A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21: 1130–1164.
Newey, W.K., and K.D. West. 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703–708.
Paparoditis, E., and D.N. Politis. 2009. Resampling and Subsampling for Financial Time Series, 983–999., Handbook of Financial Time Series Berlin: Springer.
Robinson, P. 1998. Inference-without smoothing in the presence of nonparametric autocorrelation. Econometrica 66: 1163–1182.
Ruiz, E., and L. Pascual. 2002. Bootstrapping financial time series. Journal of Economic Surveys 16 (3): 271–300.
Vogelsang, T.J. 2012. Heteroskedasticity, autocorrelation, and spatial correlation robust inference in linear panel models with fixed-effects. Journal of Econometrics 166 (2): 303–319.
White, H. 1984. Asymptotic Theory for Econometricians. New York: Academic Press.
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Nawaz, N. Robust Inference by Sub-sampling. J. Quant. Econ. (2020). https://doi.org/10.1007/s40953-020-00207-x
- Spatial correlation