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on Econometric Time Series |
| By: | Katarzyna Lasak (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointe- gration relations, the degree of fractional cointegration, the matrix of the speed of adjustment to the equilibrium parameters and the variance-covariance matrix of the error term. We show that using ML principles to estimate jointly all parameters of the fractionally cointegrated system we obtain consistent estimates and provide their asymptotic distributions. The cointegration matrix is asymptotically mixed normal distributed, while the degree of fracional cointegration and the speed of adjustment to the equilibrium matrix have joint normal distribution, which proves the intuition that the memory of the cointegrating residuals affects the speed of conver- gence to the long-run equilibrium, but does not have any influence on the long-run relationship. The rate of convergence of the estimators of the long-run relationships depends on the coin- tegration degree but it is optimal for the strong cointegration case considered. We also prove that misspecification of the degree of fractional cointegation does not affect the consistency of the estimators of the cointegration relationships, although usual inference rules are not valid. We illustrate our results in finite samples by Monte Carlo analysis. |
| Keywords: | Error correction model, Gaussian VAR model, Maximum likelihood estimation, Fractional cointegration |
| JEL: | C13 C32 |
| Date: | 2008–09–12 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-53&r=ets |
| By: | Jouchi Nakajima (Institute for Monetary and Economic Studies, Bank of Japan (E-mail: jouchi.nakajima-1@boj.or.jp)) |
| Abstract: | This paper proposes the EGARCH model with jumps and heavy- tailed errors, and studies the empirical performance of different models including the stochastic volatility models with leverage, jumps and heavy-tailed errors for daily stock returns. In the framework of a Bayesian inference, the Markov chain Monte Carlo estimation methods for these models are illustrated with a simulation study. The model comparison based on the marginal likelihood estimation is provided with data on the U.S. stock index. |
| Keywords: | Bayesian analysis, EGARCH, Heavy-tailed error, Jumps, Marginal likelihood, Markov chain Monte Carlo, Stochastic volatility |
| JEL: | C11 C15 G12 |
| Date: | 2008–09 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:08-e-23&r=ets |
| By: | Bent Jesper Christensen; Michael Sørensen (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | By an application of the theory of optimal estimating function, optimal in- struments for dynamic models with conditional moment restrictions are derived. The general efficiency bound is provided, along with estimators attaining the bound. It is demonstrated that the optimal estimators are always at least as ef- ficient as the traditional optimal generalized method of moments estimator, and usually more efficient. The form of our optimal instruments resembles that from Newey (1990), but involves conditioning on the history of the stochastic pro- cess. In the special case of i.i.d. observations, our optimal estimator reduces to Newey’s. Specification and hypothesis testing in our framework are introduced. We derive the theory of optimal instruments and the associated asymptotic dis- tribution theory for general cases including non-martingale estimating functions and general history dependence. Examples involving time-varying conditional volatility and stochastic volatility are offered. |
| Keywords: | optimal estimating function, generalized method of moments, conditional moment restrictions, dynamic models, optimal instruments, martingale estimating function, specification test |
| JEL: | C12 C13 C22 C32 |
| Date: | 2008–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-51&r=ets |
| By: | Tim Bollerslev (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | The literature on modeling and forecasting time-varying volatility is ripe with acronyms and abbreviations used to describe the many different parametric models that have been put forth since the original linear ARCH model introduced in the seminal Nobel Prize winning paper by Engle (1982). The present paper provides an easy-to-use encyclopedic reference guide to this long list of ARCH acronyms. In addition to the acronyms associated with specific parametric models, I have also included descriptions of various abbreviations associated with more general statistical procedures and ideas that figure especially prominently in the ARCH literature. |
| Keywords: | (G)ARCH, Volatility models |
| JEL: | C22 |
| Date: | 2008–09–04 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-49&r=ets |
| By: | Katarzyna Lasak (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | We consider two likelihood ratio tests, so-called maximum eigenvalue and trace tests, for the null of no cointegration when fractional cointegration is allowed under the alternative, which is a first step to generalize the so-called Johansen's procedure to the fractional cointegration case. The standard cointegration analysis only considers the assumption that deviations from equilibrium can be integrated of order zero, which is very restrictive in many cases and may imply an important loss of power in the fractional case. We consider the alternative hypotheses with equilibrium deviations that can be mean reverting with order of integration possibly greater than zero. Moreover, the degree of fractional cointegration is not assumed to be known, and the asymptotic null distribution of both tests is found when considering an interval of possible values. The power of the proposed tests under fractional alternatives and size accuracy provided by the asymptotic distribution in finite samples are investigated. |
| Keywords: | Error correction model, Gaussian VAR model, Maximum likelihood estimation, Fractional cointegration, Likelihood ratio tests, fractional Brownian motion |
| JEL: | C12 C15 C32 |
| Date: | 2008–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-52&r=ets |
| By: | Catherine Kyrtsou (Department of Economics, University of Macedonia); Michel Terraza (Department of Economics, LAMETA) |
| Abstract: | The aim of this article is the study of complex structures which are behind the short-term predictability of stock returns series. In this regard, we employ a seasonal version of the Mackey-Glass-GARCH(p,q) model, initially proposed by Kyrtsou and Terraza (2003) and generalized by Kyrtsou (2005, 2006). It has either negligible or significant autocorrelations in the conditional mean, and a rich structure in the conditional variance. To reveal short or long memory components and non-linear structures in the French Stock Exchange (CAC40) returns series, we apply the test of Geweke and Porter-Hudak (1983), the Brock et al. (1996) and Dechert (1995) tests, the correlation-dimension method of Grassberger and Procaccia (1983), the Lyapunov exponents method of Gencay and Dechert (1992), and the Recurrence Quantification Analysis introduced by Webber and Zbilut (1994). As a confirmation procedure of the dynamics generating future movements in CAC40, we forecast the return series using a seasonal Mackey-Glass-GARCH(1,1) model. The interest of the forecasting exercise is found in the inclusion of high-dimensional non-linearities in the mean equation of returns. |
| Keywords: | Noisy chaos, short-term dynamics, correlation dimension, Lyapunov exponents, recurrence quantifications, forecasting. |
| JEL: | C49 C51 C52 C53 D84 G12 G14 |
| Date: | 2008–09 |
| URL: | http://d.repec.org/n?u=RePEc:mcd:mcddps:2008_09&r=ets |
| By: | Giuseppe Cavaliere; Anders Rahbek; A.M.Robert Taylor (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | Many key macro-economic and financial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in Johansen (1988,1991) are potentially unreliable. In particular, their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co-integration tests, as we demonstrate numerically. A solution to the identified inference problem is provided by considering wild bootstrap-based implementations of the rank tests. These do not require the practitioner to specify a parametric model for volatility, nor to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. The bootstrap is shown to perform very well in practice. |
| Keywords: | Co-integration, non-stationary volatility, trace and maximum eigenvalue tests, wild bootstrap |
| JEL: | C30 C32 |
| Date: | 2008–09–08 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-50&r=ets |
| By: | Zhongfang He; John M Maheu |
| Abstract: | This paper proposes a sequential Monte Carlo method for estimating GARCH models subject to an unknown number of structural breaks. We use particle filtering techniques that allow for fast and efficient updates of posterior quantities and forecasts in real-time. The method conveniently deals with the path dependence problem that arises in these type of models. The performance of the method is shown to work well using simulated data. Applied to daily NASDAQ returns, the evidence favors a partial structural break specification in which only the intercept of the conditional variance equation has breaks compared to the full structural break specification in which all parameters are subject to change. Our empirical application underscores the importance of model assumptions when investigating breaks. A model with normal return innovations result in strong evidence of breaks; while more flexible return distributions such as t-innovations or adding jumps to the model still favor breaks but indicate much more uncertainty regarding the time and impact of them. |
| Keywords: | particle filter, GARCH model, change point, sequential Monte Carlo |
| JEL: | C11 C22 C53 G10 |
| Date: | 2008–09–19 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-336&r=ets |
| By: | Alexander Kriwoluzky |
| Abstract: | This paper shows how to identify the structural shocks of a Vector Autore- gression (VAR) while at the same time estimating a dynamic stochastic general equilibrium (DSGE) model that is not assumed to replicate the data generating process. It proposes a framework to estimate the parameters of the VAR model and the DSGE model jointly: the VAR model is identified by sign restrictions derived from the DSGE model; the DSGE model is estimated by matching the corresponding impulse response functions. |
| Keywords: | Bayesian Model Estimation, Vector Autoregression, Identification. |
| JEL: | C51 |
| Date: | 2008–09 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2008-060&r=ets |