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# Robust inference in conditionally heteroskedastic autoregressions

## Author

Listed:
• Pedersen, Rasmus Søndergaard

## Abstract

We consider robust inference for an autoregressive parameter in a stationary autoregressive model with GARCH innovations when estimation is based on least squares estimation. As the innovations exhibit GARCH, they are by construction heavy-tailed with some tail index $\kappa$. The rate of consistency as well as the limiting distribution of the least squares estimator depend on $\kappa$. In the spirit of Ibragimov and Müller (“t-statistic based correlation and heterogeneity robust inference”, Journal of Business & Economic Statistics, 2010, vol. 28, pp. 453-468), we consider testing a hypothesis about a parameter based on a Student’s t-statistic for a fixed number of subsamples of the original sample. The merit of this approach is that no knowledge about the value of $\kappa$ nor about the rate of consistency and the limiting distribution of the least squares estimator is required. We verify that the one-sided t-test is asymptotically a level $\alpha$ test whenever $\alpha \le$ 5% uniformly over $\kappa \ge 2$, which includes cases where the innovations have infinite variance. A simulation experiment suggests that the finite-sample properties of the test are quite good.

## Suggested Citation

• Pedersen, Rasmus Søndergaard, 2017. "Robust inference in conditionally heteroskedastic autoregressions," MPRA Paper 81979, University Library of Munich, Germany.
• Handle: RePEc:pra:mprapa:81979
as

File URL: https://mpra.ub.uni-muenchen.de/81979/1/MPRA_paper_81979.pdf
File Function: original version

## References listed on IDEAS

as
1. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR-GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
2. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
3. Zhang, Rongmao & Ling, Shiqing, 2015. "Asymptotic Inference For Ar Models With Heavy-Tailed G-Garch Noises," Econometric Theory, Cambridge University Press, vol. 31(04), pages 880-890, August.
Full references (including those not matched with items on IDEAS)

### Keywords

t-test; AR-GARCH; regular variation; least squares estimation;

### JEL classification:

• C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
• C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
• C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
• C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

### NEP fields

This paper has been announced in the following NEP Reports:

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