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on Econometric Time Series |
| By: | Konstantinos Fokianos (Department of Mathematics & Statistics, University of Cyprus); Anders Rahbek (Department of Economics, University of Copenhagen and CREATES); Dag Tjøstheim (Department of Mathematics, University of Bergen) |
| Abstract: | This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric ergodicity proceeds via Markov theory and irreducibility. Finding transparent conditions for proving ergodicity turns out to be a delicate problem in the original model formulation. This problem is circumvented by allowing a perturbation of the model. We show that as the perturbations can be chosen to be arbitrarily small, the differences between the perturbed and non-perturbed versions vanish as far as the asymptotic distribution of the parameter estimates is concerned. |
| Keywords: | asymptotic theory, count data, generalized linear models, geometric ergodicity, integer GARCH, likelihood, noncanonical link function, observation driven models, Poisson regression, ø-irreducibility. |
| JEL: | C51 C22 |
| Date: | 2009–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-12&r=ets |
| By: | Peter Reinhard Hansen (Stanford University and CREATES); Guillaume Horel (Merrill Lynch, New York) |
| Abstract: | We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti- cal results. The proposed estimator is consistent with a Gaussian limit distribution and we study its properties in simulations and an empirical application. |
| Keywords: | Markov chain, Filtering Contaminated Semimartingale, Quadratic Variation, Integrated Variance, Realized Variance, High Frequency Data |
| JEL: | C10 C22 C80 |
| Date: | 2009–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2009-13&r=ets |
| By: | John Beirne; Guglielmo Maria Caporale; Marianne Schulze-Ghattas; Nicola Spagnolo |
| Abstract: | This paper examines volatility spillovers from mature to emerging stock markets and tests for changes in the transmission mechanism-contagion-during turbulences in mature markets. Tri-variate GARCH-BEKK models of returns in global (mature), regional, and local markets are estimated for 41 emerging market economies (EMEs), with a dummy capturing parameter shifts during turbulent episodes. LR tests suggest that mature markets influence conditional variances in many emerging markets. Moreover, spillover parameters change during turbulent episodes. Conditional variances in most EMEs rise during these episodes, but there is only limited evidence of shifts in conditional correlations between mature and emerging markets. |
| Keywords: | Volatility spillovers, contagion, stock markets, emerging markets |
| JEL: | F30 G15 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp873&r=ets |
| By: | Mc CRORIE, J. Roderick |
| Abstract: | This paper discusses the fundamental role played by Skorokhod space, through its underpinning of functional central limit theory, in the development of the paradigm of unit roots and co-integration. This paradigm has fundamentally affected the way economists approach economic time series as was recognized by the award of the Nobel Memorial Prize in Economic Sciences to Robert F. Engle and Clive W.J. Granger in 2003. Here, we focus on how P.C.B. Phillips and others used the Skorokhod topology to establish a limiting distribution theory that underpinned and facilitated the development of methods of estimation and testing of single equations and systems of equations with possibly integrated regressors. This approach has spawned a large body of work that can be traced back to Skorokhod's conception of fifty years ago. Much of this work is surprisingly confined to the econometrics literature. |
| Keywords: | Skorokhod space, functional central limit theorems, non-stationary time series, unit roots and co-integration, Wiener functionals, econometrics. |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2008059&r=ets |
| By: | Wang, Shin-Huei (UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)); Hafner, Christian (UniversitŽ catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE); ---) |
| Abstract: | This paper considers the impact of ordinary least squares (OLS) detrending and the first difference (FD) detrending on autocorrelation estimation in the presence of long memory and deterministic trends. We show that the FD detrending results in inconsistent autocorrelation estimates when the error term is stationary. Thus, the FD detrending should not be employed for autocorrelation estimation of the detrended series when constructing e.g. portmanteau-type tests. In an empirical application of volume in Dow Jones stocks, we show that for some stocks, OLS and FD detrending result in substantial differences in ACF estimates. |
| Keywords: | autocorrelations, OLS, first difference detrending, long memory. |
| JEL: | C22 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2008073&r=ets |
| By: | Les Oxley (University of Canterbury); Marco Reale; Carl Scarrott; Xin Zhao |
| Abstract: | Extreme value theory is widely used financial applications such as risk analysis, forecasting and pricing models. One of the major difficulties in the applications to finance and economics is that the assumption of independence of time series observations is generally not satisfied, so that the dependent extremes may not necessarily be in the domain of attraction of the classical generalised extreme value distribution. This study examines a conditional extreme value distribution with the added specification that the extreme values (maxima or minima) follows a conditional autoregressive heteroscedasticity process. The dependence has been modelled by allowing the location and scale parameters of the extreme distribution to vary with time. The resulting combined model, GEV-GARCH, is developed by implementing the GARCH volatility mechanism in these extreme value model parameters. Bayesian inference is used for the estimation of parameters and posterior inference is available through the Markov Chain Monte Carlo (MCMC) method. The model is firstly applied to relevant simulated data to verify model stability and reliability of the parameter estimation method. Then real stock returns are used to consider evidence for the appropriate application of the model. A comparison is made between the GEV-GARCH and traditional GARCH models. Both the GEV-GARCH and GARCH show similarity in the resulting conditional volatility estimates, however the GEV-GARCH model differs from GARCH in that it can capture and explain extreme quantiles better than the GARCH model because of more reliable extrapolation of the tail behaviour. |
| Keywords: | Extreme value distribution, dependency, Bayesian, MCMC, Return quantile |
| JEL: | C11 G12 |
| Date: | 2009–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:09/05&r=ets |
| By: | Xiaohong Chen (Institute for Fiscal Studies and Yale); Roger Koenker (Institute for Fiscal Studies and University of Illinois); Zhijie Xiao |
| Abstract: | <p>Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data.</p> |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:27/08&r=ets |