Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models

Balázs Csanád Csáji
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:296-304, 2016.

Abstract

A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions about moments are made. ScoPe is inspired by the recently developed Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH case. ScoPe works by perturbing the score function using randomly permuted residuals. This produces alternative samples which lead to exact confidence regions. Experiments on simulated and stock market data are also presented, and ScoPe is compared with the asymptotic theory and bootstrap approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v51-csaji16, title = {Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models}, author = {Csáji, Balázs Csanád}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {296--304}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/csaji16.pdf}, url = {https://proceedings.mlr.press/v51/csaji16.html}, abstract = {A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions about moments are made. ScoPe is inspired by the recently developed Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH case. ScoPe works by perturbing the score function using randomly permuted residuals. This produces alternative samples which lead to exact confidence regions. Experiments on simulated and stock market data are also presented, and ScoPe is compared with the asymptotic theory and bootstrap approaches.} }
Endnote
%0 Conference Paper %T Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models %A Balázs Csanád Csáji %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-csaji16 %I PMLR %P 296--304 %U https://proceedings.mlr.press/v51/csaji16.html %V 51 %X A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions about moments are made. ScoPe is inspired by the recently developed Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH case. ScoPe works by perturbing the score function using randomly permuted residuals. This produces alternative samples which lead to exact confidence regions. Experiments on simulated and stock market data are also presented, and ScoPe is compared with the asymptotic theory and bootstrap approaches.
RIS
TY - CPAPER TI - Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models AU - Balázs Csanád Csáji BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-csaji16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 296 EP - 304 L1 - http://proceedings.mlr.press/v51/csaji16.pdf UR - https://proceedings.mlr.press/v51/csaji16.html AB - A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum Likelihood (QML) method, which works under mild statistical assumptions. Here, we suggest a finite sample approach, called ScoPe, to construct distribution-free confidence regions around the QML estimate, which have exact coverage probabilities, despite no additional assumptions about moments are made. ScoPe is inspired by the recently developed Sign-Perturbed Sums (SPS) method, which however cannot be applied in the GARCH case. ScoPe works by perturbing the score function using randomly permuted residuals. This produces alternative samples which lead to exact confidence regions. Experiments on simulated and stock market data are also presented, and ScoPe is compared with the asymptotic theory and bootstrap approaches. ER -
APA
Csáji, B.C.. (2016). Score Permutation Based Finite Sample Inference for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) Models. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:296-304 Available from https://proceedings.mlr.press/v51/csaji16.html.

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