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on Econometric Time Series |
| By: | Ciuiu, Daniel |
| Abstract: | In this paper we will study the influence of qualitative variables on the unit root tests for stationarity. For the linear regressions involved the implied assumption is that they are not influenced by such qualitative variables. For this reason, after we have introduced such variables, we check ï¬rst if we can remove some of them from the model. The considered qualitative variables are according the corresponding coefï¬cient (the intercept, the coefï¬cient of Xt −1 and the coefï¬cient of t ), and on the different groups built tacking into account the characteristics of the time moments. |
| Keywords: | Qualitative variables, Dickey-Fuller, ARIMA, GDP, homogeneity. |
| JEL: | C52 C58 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:59284&r=ets |
| By: | Francisco Blasques (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam, the Netherlands, and CREATES, Aarhus University, Denmark); Andr� Lucas (VU University Amsterdam) |
| Abstract: | We investigate the information theoretic optimality properties of the score function of the predictive likelihood as a device to update parameters in observation driven time-varying parameter models. The results provide a new theoretical justification for the class of generalized autoregressive score models, which covers the GARCH model as a special case. Our main contribution is to show that only parameter updates based on the score always reduce the local Kullback-Leibler divergence between the true conditional density and the model implied conditional density. This result holds irrespective of the severity of model misspecification. We also show that the use of the score leads to a considerably smaller global Kullback-Leibler divergence in empirically relevant settings. We illustrate the theory with an application to time-varying volatility models. We show that th e reduction in Kullback-Leibler divergence across a range of different settings can be substantial in comparison to updates based on for example squared lagged observations. |
| Keywords: | generalized autoregressive models, information theory, optimality, Kullback-Leibler distance, volatility models |
| JEL: | C12 C22 |
| Date: | 2014–04–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140046&r=ets |
| By: | Siem Jan Koopman; Geert Mesters (VU University Amsterdam) |
| Abstract: | We consider the dynamic factor model where the loading matrix, the dynamic factors and the disturbances are treated as latent stochastic processes. We present empirical Bayes methods that enable the efficient shrinkage-based estimation of the loadings and the factors. We show that our estimates have lower quadratic loss compared to the standard maximum likelihood estimates. We investigate the methods in a Monte Carlo study where we document the finite sample properties. Finally, we present and discuss the results of an empirical study concerning the forecasting of U.S. macroeconomic time series using our empirical Bayes methods. |
| Keywords: | Importance sampling, Kalman filtering, Likelihood-based analysis, Posterior modes, Rao-Blackwellization, Shrinkage |
| JEL: | C32 C43 |
| Date: | 2014–05–23 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140061&r=ets |
| By: | Michael McAleer (National Tsing Hua University Taiwan; Erasmus University Rotterdam, the Netherlands; Complutense University of Madrid, Spain) |
| Abstract: | The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstrated by Tsay (1987), and that of EGARCH was shown recently in McAleer and Hafner (2014). These models are important in estimating and forecasting volatility, as well as capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. As there seems to be some confusion in the literature between asymmetry and leverage, as well as which asymmetric models are purported to be able to capture leverage, the purpose of the paper is two-fold, namely: (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; and (2) to show that leverage is not possible in these univariate conditional volatility models. |
| Keywords: | Conditional volatility models, random coefficient autoregressive processes, random coefficient complex nonlinear moving average process, asymmetry, leverage |
| JEL: | C22 C52 C58 G32 |
| Date: | 2014–09–18 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140125&r=ets |
| By: | Istv�n Barra (VU University Amsterdam, Duisenberg School of Finance, the Netherlands); Lennart Hoogerheide (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam); Andr� Lucas (VU University Amsterdam, the Netherlands) |
| Abstract: | We propose a new methodology for designing flexible proposal densities for the joint posterior density of parameters and states in a nonlinear non-Gaussian state space model. We show that a highly efficient Bayesian procedure emerges when these proposal densities are used in an independent Metropolis-Hastings algorithm. A particular feature of our approach is that smoothed estimates of the states and the marginal likelihood are obtained directly as an output of the algorithm. Our method provides a computationally efficient alternative to several recently proposed algorithms. We present extensive simulation evidence for stochastic volatility and stochastic intensity models. For our empirical study, we analyse the performance of our method for stock returns and corporate default panel data. (This paper is an updated version of the paper that appeared earlier as Barra, I., Hoogerheide, L.F., Koopman, S.J., and Lucas, A. (2013) "Joint Independent Metropolis-Hastings Methods for Nonlinear Non-Gaussian State Space Models". TI Discussion Paper 13-050/III. Amsterdam: Tinbergen Institute.) |
| Keywords: | Bayesian inference, importance sampling, Monte Carlo estimation, Metropolis-Hastings algorithm, mixture of Student's t-distributions |
| JEL: | C11 C15 C22 C32 C58 |
| Date: | 2014–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140118&r=ets |