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on Econometric Time Series |
| By: | Douglas Steigerwald (University of California, Santa Barbara); Jack Erb (University of California, Santa Barbara) |
| Abstract: | We study the problem of obtaining accurately sized test statistics in finite samples for linear regression models where the error dependence is of unknown form. With an unknown dependence structure there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the decision to introduce conditional heteroskedasticity. In consequence, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags we study test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. To improve the accuracy of the test statistics, we employ the second-order asymptotic refinement in Rothenberg (1988) to determine critical values. We find substantial size improvements resulting from the second-order theory across a wide range of specifications, including substantial conditional heteroskedasticity. We also find that the size gains result in only moderate increases in the length of the associated confidence interval, which yields an increase in size-adjusted power. Finally, we note that the proposed test statistics do not require that the researcher specify the bandwidth or the kernel. |
| Keywords: | test size, confidence interval estimation, heteroskedasticity, autocorrelation, |
| Date: | 2007–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsbec:09-07&r=ets |
| By: | Ivana Komunjer (University of California - San Diego); MICHAEL OWYANG (Federal Reserve Bank of Saint Louis) |
| Abstract: | In this paper, we propose a new family of multivariate loss functions that can be used to test the rationality of vector forecasts without assuming independence across individual variables. When only one variable is of interest, the loss function reduces to the flexible asymmetric family recently proposed by Elliott, Komunjer, and Timmermann (2005). Following their methodology, we derive a GMM test for multivaariate forecast rationality that allows the forecast errors to be dependent, and takes into account forecast estimation ucertainty. We use our test to study the rationality of macroeconomic vector forecasts in the growth rate in nominal output, the CPI inflation rate, and a short-term interest rate. |
| Keywords: | multivariate forecast rationality, multivariate loss, asymmetries, Fed Transparency, |
| Date: | 2007–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:ucsdec:2007-08&r=ets |
| By: | Markus Haas (University of Munich, Institute of Statistics); Stefan Mittnik (Department of Statistics, University of Munich, Center for Financial Studies, Frankfurt, and Ifo Institute for Economic Research, Munich) |
| Abstract: | We develop a multivariate generalization of the Markov–switching GARCH model introduced by Haas, Mittnik, and Paolella (2004b) and derive its fourth–moment structure. An application to international stock markets illustrates the relevance of accounting for volatility regimes from both a statistical and economic perspective, including out–of–sample portfolio selection and computation of Value–at–Risk. |
| Keywords: | Conditional Volatility, Markov–Switching, Multivariate GARCH |
| JEL: | C32 C51 G10 G11 |
| Date: | 2008–01 |
| URL: | http://d.repec.org/n?u=RePEc:cfs:cfswop:wp200808&r=ets |
| By: | Laurent Ferrara (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, DGEI-DAMEP - Banque de France); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Ecole d'économie de Paris - Paris School of Economics - Université Panthéon-Sorbonne - Paris I); Zhiping Lu (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, ECNU - East China Normal University) |
| Abstract: | Testing the fractionally integrated order of seasonal and non-seasonal unit roots is quite important for the economic and financial time series modelling. In this paper, Robinson test (1994) is applied to various well-known long memory models. Via Monte Carlo experiments, we study and compare the performances of this test using several sample sizes. |
| Keywords: | Long memory processes, test, Monte Carlo simulations. |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00259193_v1&r=ets |
| By: | Abdou Kâ Diongue (UFR SAT - Université Gaston Berger - Université Gaston Berger de Saint-Louis, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, School of Economics and Finance - Queensland University of Technology); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Ecole d'économie de Paris - Paris School of Economics - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | Electricity spot prices exhibit a number of typical features that are not found in most financial time series, such as complex seasonality patterns, persistence (hyperbolic decay of the autocorrelation function), mean reversion, spikes, asymmetric behavior and leptokurtosis. Efforts have been made worldwide to model the behaviour of the electricity's market price. In this paper, we propose a new approach dealing with the stationary k-factor Gegenbauer process with asymmetric Power GARCH noise under conditional Student-t distribution, which can take into account the previous features. We derive the stationary and invertible conditions as well as the δth-order moment of this model that we called GGk-APARCH model. Then we focus on the estimation parameters and provide the analytical from of the likelihood which permits to obtain consitent estimates. In order to characterize the properties of these estimates we perform a Monte Carlo experiment. Finally the previous approach is used to the model electricity spot prices coming from the Leipzig Power Exchange (LPX) in Germany, Powernext in France, Operadora del Mercado Espagñol de Electricidad (OMEL) in Spain and the Pennsylvania-New Jersey-Maryland (PJM) interconnection in United States. In terms of forecasting criteria we obtain very good results comparing with models using hederoscedastic asymmetric errors. |
| Keywords: | Asymmetric distribution function, electricity spot prices, Leptokurtosis, persistence, seasonality, GARMA, A-PARCH. |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00259225_v1&r=ets |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Ecole d'économie de Paris - Paris School of Economics - Université Panthéon-Sorbonne - Paris I); Justin Leroux (Institute for Applied Economics - HEC MONTRÉAL, CIRPEE - Centre Interuniversitaire sur le Risque, les Politiques Economiques et l'Emploi) |
| Abstract: | We propose a novel methodology for forecasting chaotic systems which is based on the nearest-neighbor predictor and improves upon it by incorporating local Lyapunov exponents to correct for its inevitable bias. Using simulated data, we show that gains in prediction accuracy can be substantial. The general intuition behind the proposed method can readily be applied to other non-parametric predictors. |
| Keywords: | Chaos theory, Lyapunov exponent, logistic map, Monte Carlo simulations. |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00259238_v1&r=ets |
| By: | Mohammed Bouaddi; Jeroen V.K. Rombouts (IEA, HEC Montréal) |
| Abstract: | To match the stylized facts of high frequency financial time series precisely and parsimoniously, this paper presents a finite mixture of conditional exponential power distributions where each component exhibits asymmetric conditional heteroskedasticity. We provide stationarity conditions and unconditional moments to the fourth order. We apply this new class to Dow Jones index returns. We find that a two-component mixed exponential power distribution dominates mixed normal distributions with more components, and more parameters, both in-sample and out-of-sample. In contrast to mixed normal distributions, all the conditional variance processes become stationary. This happens because the mixed exponential power distribution allows for component-specific shape parameters so that it can better capture the tail behaviour. Therefore, the more general new class has attractive features over mixed normal distributions in our application: Less components are necessary and the conditional variances in the components are stationary processes. Results on NASDAQ index returns are similar. |
| Keywords: | Finite mixtures, exponential power distributions, conditional heteroskedasticity, asymmetry, heavy tails, value at risk. |
| JEL: | C11 C22 C52 |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:iea:carech:0715&r=ets |
| By: | Cristina Amado (Department of Economic Statistics, Stockholm School of Economics and University of Minho and NIPE); Timo Teräsvirta (CREATES, School of Economics and Management, University of Aarhus) |
| Abstract: | In this paper, we propose two parametric alternatives to the standard GARCH model. They allow the conditional variance to have a smooth time-varying structure of either additive or multiplicative type. The suggested parameterizations describe both nonlinearity and structural change in the conditional and unconditional variances where the transition between regimes over time is smooth. A modelling strategy for these new time-varying parameter GARCH models is developed. It relies on a sequence of Lagrange multiplier tests, and the adequacy of the estimated models is investigated by Lagrange multiplier type misspecification tests. Finite-sample properties of these procedures and tests are examined by simulation. An empirical application to daily stock returns and another one to daily exchange rate returns illustrate the functioning and properties of our modelling strategy in practice. The results show that the long memory type behaviour of the sample autocorrelation functions of the absolute returns can also be explained by deterministic changes in the unconditional variance. |
| Keywords: | Conditional heteroskedasticity; Structural change; Lagrange multiplier test; Misspecification test; Nonlinear time series; Time-varying parameter model. |
| JEL: | C12 C22 C51 C52 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:nip:nipewp:03/2008&r=ets |