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14
Fitting an error distribution in some heteroscedastic time series models
- Ann. Statist
, 2006
"... This paper addresses the problem of fitting a known distribution to the innovation distribution in a class of stationary and ergodic time series models. The asymptotic null distribution of the usual Kolmogorov–Smirnov test based on the residuals generally depends on the underlying model parameters a ..."
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Cited by 8 (2 self)
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This paper addresses the problem of fitting a known distribution to the innovation distribution in a class of stationary and ergodic time series models. The asymptotic null distribution of the usual Kolmogorov–Smirnov test based on the residuals generally depends on the underlying model parameters and the error distribution. To overcome the dependence on the underlying model parameters, we propose that tests be based on a vector of certain weighted residual empirical processes. Under the null hypothesis and under minimal moment conditions, this vector of processes is shown to converge weakly to a vector of independent copies of a Gaussian process whose covariance function depends only on the fitted distribution and not on the model. Under certain local alternatives, the proposed test is shown to have nontrivial asymp-totic power. The Monte Carlo critical values of this test are tabulated when fitting standard normal and double exponential distributions. The results ob-tained are shown to be applicable to GARCH and ARMA–GARCH models, the often used models in econometrics and finance. A simulation study shows that the test has satisfactory size and power for finite samples at these models. The paper also contains an asymptotic uniform expansion result for a general weighted residual empirical process useful in heteroscedastic models under minimal moment conditions, a result of independent interest. 1. Introduction. Let {yi
Mean shift testing in correlated data.
- Journal of Time Series Analysis,
, 2011
"... Several tests for detecting mean shifts at an unknown time in stationary time series have been proposed, including cumulative sum (CUSUM), Gaussian likelihood ratio (LR), maximum of F(F max ) and extreme value statistics. This article reviews these tests, connects them with theoretical results, and ..."
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Cited by 6 (2 self)
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Several tests for detecting mean shifts at an unknown time in stationary time series have been proposed, including cumulative sum (CUSUM), Gaussian likelihood ratio (LR), maximum of F(F max ) and extreme value statistics. This article reviews these tests, connects them with theoretical results, and compares their finite sample performance via simulation. We propose an adjusted CUSUM statistic which is closely related to the LR test and which links all tests. We find that tests based on CUSUMing estimated one-step-ahead prediction residuals from a fitted autoregressive moving average perform well in general and that the LR and F max tests (which induce substantial computational complexities) offer only a slight increase in power over the adjusted CUSUM test. We also conclude that CUSUM procedures work slightly better when the changepoint time is located near the centre of the data, but the adjusted CUSUM methods are preferable when the changepoint lies closer to the beginning or end of the data record. Finally, an application is presented to demonstrate the importance of the choice of method.
Estimating the innovation distribution in nonparametric autoregression
, 2008
"... We prove a Bahadur representation for a residual-based estimator of the innovation distribution function in a nonparametric autoregres-sive model. The residuals are based on a local linear smoother for the autoregression function. Our result implies a functional central limit theorem for the residua ..."
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Cited by 5 (1 self)
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We prove a Bahadur representation for a residual-based estimator of the innovation distribution function in a nonparametric autoregres-sive model. The residuals are based on a local linear smoother for the autoregression function. Our result implies a functional central limit theorem for the residual-based estimator. 1. Introduction. Regression
Specification tests for the error distribution in GARCH models
- Comput. Statist. Data Anal
"... Abstract Goodness-of-fit and symmetry tests are proposed for the innovation distribution in generalized autoregressive conditionally heteroscedastic models. The tests utilize an integrated distance involving the empirical characteristic function (or the empirical Laplace transform) computed from pr ..."
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Cited by 4 (0 self)
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Abstract Goodness-of-fit and symmetry tests are proposed for the innovation distribution in generalized autoregressive conditionally heteroscedastic models. The tests utilize an integrated distance involving the empirical characteristic function (or the empirical Laplace transform) computed from properly standardized observations. A bootstrap version of the tests serves the purpose of studying the small sample behaviour of the proclaimed procedures in comparison with more classical approaches. Finally, all tests are applied to some financial data sets.
Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown∗
, 2013
"... Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when addi ..."
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Cited by 3 (3 self)
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Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when additional exogenous or predetermined variables (“X”) are included in the volatility spec-ification. Here, we propose estimation and inference methods for univariate and multivariate Generalised log-ARCH-X (i.e. log-GARCH-X) models when the conditional density is not known via (V)ARMA-X representations. The multivariate specification allows for volatility feedback across equations, and time-varying correlations can be fitted in a subsequent step. Finally, our empirical applications on electricity prices show that the model-class is par-
Jarque-Bera normality test for the driving Lévy process of a discretely observed univariate SDE
- Stat. Inference Stoch. Process
, 2008
"... We study the validity of the Jarque-Bera test for a class of univariate parametric stochastic differential equations (SDE) dXt = b(Xt, α)dt+ dZt observed at discrete time points t n i = ihn, i = 1, 2,..., n, where Z is a nondegenerate Lévy process with finite moments, and nhn → ∞ and nh2n → 0 as n ..."
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Cited by 2 (2 self)
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We study the validity of the Jarque-Bera test for a class of univariate parametric stochastic differential equations (SDE) dXt = b(Xt, α)dt+ dZt observed at discrete time points t n i = ihn, i = 1, 2,..., n, where Z is a nondegenerate Lévy process with finite moments, and nhn → ∞ and nh2n → 0 as n → ∞. Under appropriate conditions it is shown that Jarque-Bera type statistics based on the Euler residuals can be used to test the normality of the unobserved Z, and moreover, that the proposed test is consistent against presence of any nontrivial jump component. Our result therefore provides a very easy and asymptotically distribution-free test procedure without any fine-tuning parameter. Some illustrative simulation results are given to reveal good performance of our test statistics.
SFB 823 Reaction times of monitoring schemes for ARMA time series Discussion Paper Reaction times of monitoring schemes for ARMA time series *
"... Abstract This paper is concerned with deriving the limit distributions of stopping times devised to sequentially uncover structural breaks in the parameters of an autoregressive moving average, ARMA, time series. The stopping rules are defined as the first time lag for which detectors, based on CUS ..."
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Abstract This paper is concerned with deriving the limit distributions of stopping times devised to sequentially uncover structural breaks in the parameters of an autoregressive moving average, ARMA, time series. The stopping rules are defined as the first time lag for which detectors, based on CUSUMs and Page's CUSUMs for residuals, exceed the value of a prescribed threshold function. It is shown that the limit distributions crucially depend on a drift term induced by the underlying ARMA parameters. The precise form of the asymptotic is determined by an interplay between the location of the break point and the size of the change implied by the drift. The theoretical results are accompanied by a simulation study and applications to electroencephalography, EEG, and IBM data. The empirical results indicate a satisfactory behavior in finite samples.
Econometric Analysis for Volatility Component Models
, 2011
"... The volatility component models have received much attention recently, not only because of their ability to capture complex dynamics via a parsimonious parameter structure, but also because it is believed that they can handle well structural breaks or non-stationarities in asset price volatility. Th ..."
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The volatility component models have received much attention recently, not only because of their ability to capture complex dynamics via a parsimonious parameter structure, but also because it is believed that they can handle well structural breaks or non-stationarities in asset price volatility. This paper revisits the component models fromastatistical perspective and attempts to explore the stationarity of the underlying processes. There is a clear need for such an analysis, since any discussion about non-stationarity presumes we know when component models are stationary. As it turns out, this is not the case and the purpose of the paper is to rectify this. We also look into the sampling behavior of the maximum likelihood estimates of recently proposed volatility component models and establish their consistency and asymptotic normality.
discretely observed stochastic processes
, 2013
"... Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes ..."
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Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes
