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on Econometric Time Series |
| By: | Giuseppe Cavaliere; David I. Harvey; Stephen J. Leybourne; A.M. Robert Taylor (School of Economics and Management, University of Aarhus, Denmark) |
| Abstract: | In this paper we analyse the impact of non-stationary volatility on the recently devel- oped unit root tests which allow for a possible break in trend occurring at an unknown point in the sample, considered in Harris, Harvey, Leybourne and Taylor (2008) [HHLT]. HHLT's analysis hinges on a new break fraction estimator which, when a break in trend occurs, is consistent for the true break fraction at rate Op(T??1). Unlike other available estimators, however, when there is no trend break HHLT's estimator converges to zero at rate Op(T1=2). In their analysis HHLT assume the shocks to follow a linear process driven by IID innovations. Our first contribution is to show that HHLT's break fraction estimator retains the same consistency properties as demonstrated by HHLT for the IID case when the innovations display non-stationary behaviour of a quite general form, in- cluding, for example, the case of a single break in the volatility of the innovations which may or may not occur at the same time as a break in trend. However, as we subsequently demonstrate, the limiting null distribution of unit root statistics based around this es- timator are not pivotal in the presence of non-stationary volatility. Associated Monte Carlo evidence is presented to quantify the impact of various models of non-stationary volatility on both the asymptotic and finite sample behaviour of such tests. A solution to the identified inference problem is then provided by considering wild bootstrap-based implementations of the HHLT tests, using the trend break estimator from the original sample data. The proposed bootstrap method does not require the practitioner to specify a parametric model for volatility, and is shown to perform very well in practice across a range of models. |
| Keywords: | Unit root tests, quasi difference de-trending, trend break, non-stationary volatility, wild bootstrap |
| JEL: | C22 |
| Date: | 2008–12–02 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2008-62&r=ets |
| By: | Gianluca, MORETTI; Giulio, NICOLETTI |
| Abstract: | Recent literature clams that key variables such as aggregate productivity and inflation display long memory dynamics. We study the impllications of this high degree of persistence on the estimation of Dynamic Stochastic General Equilibrium (DGSE) models. We show that long memory data produce substantial bias in the deep parameter estimates when a standard Kalman Filter-MLE procedure is used. We propose a modification of the Kalman Filter procedure, we mainly augment the state space, which deals with this problem. By the means of the augmented state space we can consistently estimate the model parameters as well as produce more accurate out-of-sample forecasts compared to the standard Kalman filter. |
| Date: | 2008–12–04 |
| URL: | http://d.repec.org/n?u=RePEc:ctl:louvec:2008037&r=ets |
| By: | Kaddour Hadri; Eiji Kurozumi |
| Abstract: | This paper develops a simple test for the null hypothesis of stationarity in heterogeneous panel data with cross-sectional dependence in the form of a common factor in the disturbance. We do not estimate the common factor but mop-up its effect by employing the same method as the one proposed in Pesaran (2007) in the unit root testing context. Our test is basically the same as the KPSS test but the regression is augmented by cross-sectional average of the observations. We also develop a Lagrange multiplier (LM) test allowing for cross-sectional dependence and, under restrictive assumptions, compare our augmented KPSS test with the extended LM test under the null of stationarity, under the local alternative and under the fixed alternative, and discuss the differences between these two tests. We also extend our test to the more realistic case where the shocks are serially correlated. We use Monte Carlo simulations to examine the finite sample property of the augmented KPSS test. |
| Keywords: | Panel data, stationarity, KPSS test, cross-sectional dependence, LM test, locally best test |
| JEL: | C12 C33 |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd08-016&r=ets |
| By: | Palm Franz C.; Smeekes Stephan; Urbain Jean-Pierre (METEOR) |
| Abstract: | In this paper we consider the issue of unit root testing in cross-sectionally dependent panels. We consider panels that may be characterized by various forms of cross-sectionaldependence including (but not exclusive to) the popular common factor framework. Weconsider block bootstrap versions of the group-mean Im, Pesaran, and Shin (2003) and thepooled Levin, Lin, and Chu (2002) unit root coefficient DF-tests for panel data, originallyproposed for a setting of no cross-sectional dependence beyond a common time effect. Thetests, suited for testing for unit roots in the observed data, can be easily implemented asno specification or estimation of the dependence structure is required. Asymptotic propertiesof the tests are derived for T going to infinity and N finite. Asymptotic validity of thebootstrap tests is established in very general settings, including the presence of commonfactors and even cointegration across units. Properties under the alternative hypothesisare also considered. In a Monte Carlo simulation, the bootstrap tests are found to haverejection frequencies that are much closer to nominal size than the rejection frequenciesfor the corresponding asymptotic tests. The power properties of the bootstrap tests appearto be similar to those of the asymptotic tests. |
| Keywords: | Economics (Jel: A) |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2008048&r=ets |
| By: | Hafner Christian M.; Manner Hans (METEOR) |
| Abstract: | We propose a new dynamic copula model where the parameter characterizing dependence follows an autoregressive process. As this model class includes the Gaussian copula with stochastic correlation process, it can be viewed as a generalization of multivariate stochastic volatility models. Despite the complexity of the model, the decoupling of marginals and dependence parameters facilitates estimation. We propose estimation in two steps, where first the parameters of the marginal distributions are estimated, and then those of the copula. Parameters of the latent processes (volatilities and dependence) are estimated using efficient importance sampling (EIS). We discuss goodness-of-fit tests and ways to forecast the dependence parameter. For two bivariate stock index series, we show that theproposed model outperforms standard competing models. |
| Keywords: | econometrics; |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2008043&r=ets |
| By: | Avarucci Marco; Velasco Carlos (METEOR) |
| Abstract: | This paper develops new methods for determining the cointegration rank in a nonstationary fractionally integrated system, extending univariate optimal methods for testing the degree of integration. We propose a simple Wald test based on the singular value decompositionof the unrestricted estimate of the long run multiplier matrix. When the "strength" of the cointegrating relationship is less than 1/2, the test statistic has a standard asymptotic distribution, like Lagrange Multiplier tests exploiting local properties. We consider the behavior of our test under estimation of short run parameters and local alternatives. We compare our procedure with other cointegration tests based on dierent principles and find that the new method has better properties in a range of situations by using information on the alternative obtained through a preliminary estimate of the cointegration strength. |
| Keywords: | Economics (Jel: A) |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2008049&r=ets |
| By: | Frank A.G. den Butter (VU University Amsterdam); Pieter W. Jansen (Aegon Investment Management) |
| Abstract: | This paper assesses the performance of a number of long-term interest rate forecast approaches, namely time series models, structural economic models, expert forecasts and combinations thereof. The predictive performance of these approaches is compared using out of sample forecast errors, where a random walk forecast acts as benchmark. It is found that for five major OECD countries, namely United States, Germany, United Kingdom, The Netherlands and Japan, the other forecasting approaches do not outperform the random walk, or a somewhat more sophisticated time series model, on a 3 month forecast horizon. On a 12 month forecast horizon the random walk model can be outperformed by a model that combines economic data and expert forecasts. Here several methods of combination are considered: equal weights, optimized weights and weights based on forecast error. It appears that the additional information contents of the structural models and expert knowledge is only relevant for forecasting 12 months ahead. |
| Keywords: | interest rate forecasting; expert knowledge; combining forecasts; optimizing forecast errors |
| JEL: | C53 E27 E43 E47 |
| Date: | 2008–10–28 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20080102&r=ets |
| By: | Drew Creal (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam); André Lucas (VU University Amsterdam) |
| Abstract: | We propose a new class of observation driven time series models referred to as Generalized Autoregressive Score (GAS) models. The driving mechanism of the GAS model is the scaled score of the likelihood function. This approach provides a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The GAS model encompasses other well-known models such as the generalized autoregressive conditional heteroskedasticity, the autoregressive conditional duration, the autoregressive conditional intensity, and the single source of error models. In addition, the GAS specification provides a wide range of new observation driven models. Examples include non-linear regression models with time-varying parameters, observation driven analogues of unobserved components time series models, multivariate point process models with time-varying parameters and pooling restrictions, new models for time-varying copula functions, and models for time-varying higher order moments. We study the properties of GAS models and provide several non-trivial examples of their application. |
| Keywords: | dynamic models; time-varying parameters; non-linearity; exponential family; marked point processes; copulas |
| JEL: | C10 C22 C32 C51 |
| Date: | 2008–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20080108&r=ets |
| By: | Matthieu Lemoine (Observatoire Français des Conjonctures Économiques); Gian Luigi Mazzi (Eurostat); Paola Monperrus-Veroni (Observatoire Français des Conjonctures Économiques); Frédéric Reynes (Observatoire Français des Conjonctures Économiques) |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:fce:doctra:0834&r=ets |
| By: | Ran, Tao; Zapata, Hector |
| Abstract: | Using Japanese economic data and a Monte Carlo simulation, this study analyzes the consequences of ignoring deterministic trends in mixed unit-root data for Granger noncausality tests. Results from an augmented VAR suggest over-rejection in certain empirically relevant cases at various sample sizes. |
| Keywords: | Research Methods/ Statistical Methods, |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:ags:saeaed:6745&r=ets |
| By: | Ihle, Rico; Cramon-Taubadel, Stephan von |
| Abstract: | We compare two regime-dependent econometric models for price transmission analysis, namely the threshold vector error correction model and Markov-switching vector error correction model. We first provide a detailed characterization of each of the models which is followed by a comprehensive comparison. We find that the assumptions regarding the nature of their regime-switching mechanisms are fundamentally different so that each model is suitable for a certain type of nonlinear price transmission. Furthermore, we conduct a Monte Carlo experiment in order to study the performance of the estimation techniques of both models for simulated data. We find that both models are adequate for studying price transmission since their characteristics match the underlying economic theory and allow hence for an easy interpretation. Nevertheless, the results of the corresponding estimation techniques do not reproduce the true parameters and are not robust against nuisance parameters. The comparison is supplemented by a review of empirical studies in price transmission analysis in which mostly the threshold vector error correction model is applied. |
| Keywords: | price transmission, market integration, threshold vector error correction model, Markov-switching vector error correction model, comparison, nonlinear time series analysis, Agricultural Finance, |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:ags:nccest:37603&r=ets |
| By: | Jean-François Goux (GATE, University of Lyon, CNRS, ENS-LSH, Centre Léon Bérard, France) |
| Abstract: | The taking into account of a period of break (thick break) makes it possible to correctly analyze the time series of the euro-dollar exchange rate. By retaining the posterior period with the Louvre agreements, but by eliminating the first years from existence of the euro, and until today, one can affirm that this rate is stationary and after trend stationary and thus that there is a mechanism of return towards a level (a trend) of equilibrium. This point is shown using a new procedure of test based on the elimination of thick breaks. That makes it possible to propose a forecast based on this deterministic trend |
| Keywords: | euro-dollar exchange rate, stationarity, breaks, outliers |
| JEL: | C F F32 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:0826&r=ets |
| By: | Di Iorio, Francesca; Fachin, Stefano |
| Abstract: | We address the issue of estimation and inference in dependent nonstationary panels of small cross-section dimensions. The main conclusion is that the best results are obtained applying bootstrap inference to single-equation estimators. SUR estimators perform badly, or are even unfeasible, when the time dimension is not very large compared to the cross-section dimension. |
| Keywords: | Panel cointegration; FM-OLS; FM-SUR. |
| JEL: | C13 C15 C33 |
| Date: | 2008–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:12053&r=ets |
| By: | Hanck, Christoph |
| Abstract: | This paper proposes a new testing approach for panel unit roots that is, unlike previously suggested tests, robust to nonstationarity in the volatility process of the innovations of the time series in the panel. Nonstationarity volatility arises for instance when there are structural breaks in the innovation variances. A prominent example is the reduction in GDP growth variances enjoyed by many industrialized countries, known as the `Great Moderation.' The panel test is based on Simes' [Biometrika 1986, "An Improved Bonferroni Procedure for Multiple Tests of Signicance"] classical multiple test, which combines evidence from time series unit root tests of the series in the panel. As time series unit root tests, we employ recently proposed tests of Cavaliere and Taylor [Journal of Time Series Analysis, "Time-Transformed Unit Root Tests for Models with Non-Stationary Volatility"]. The panel test is robust to general patterns of cross-sectional dependence and yet straightforward to implement, only requiring valid p-values of time series unit root tests, and no resampling. Monte Carlo experiments show that other panel unit root tests suer from sometimes severe size distortions in the presence of nonstationary volatility, and that this defect can be remedied using the test proposed here. The new test is applied to test for a unit root in an OECD panel of gross domestic products, yielding inference robust to the `Great Moderation.' We nd little evidence of trend stationarity. |
| Keywords: | Nonstationary Volatility; Multiple Testing; Panel Unit Root Test; Cross-Sectional Dependence |
| JEL: | C12 C23 |
| Date: | 2008–11–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:11988&r=ets |
| By: | Xu, Zhiwei |
| Abstract: | In this note, we revisit the univariate unobserved-component (UC) model of US GDP by relaxing the traditional random-walk assumption of the permanent component. Since our general UC model is unidentified, we investigate the upper bound of the contribution of the transitory component, and find it is dominated by the permanent component. |
| Keywords: | Unobserved-Component Model; Random Walk Assumption; Permanent and Transitory Shocks |
| JEL: | E32 C22 C49 |
| Date: | 2008–11–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:12038&r=ets |
| By: | Kleppe, Tore Selland; Skaug, Hans J. |
| Abstract: | Maximum likelihood has proved to be a valuable tool for fitting the log-normal stochastic volatility model to financial returns time series. Using a sequential change of variable framework, we are able to cast more general stochastic volatility models into a form appropriate for importance samplers based on the Laplace approximation. We apply the methodology to two example models, showing that efficient importance samplers can be constructed even for highly non-Gaussian latent processes such as square-root diffusions. |
| Keywords: | Change of Variable; Heston Model; Laplace Importance Sampler; Simulated Maximum Likelihood; Stochastic Volatility |
| JEL: | C13 C22 |
| Date: | 2008–07–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:12022&r=ets |