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on Econometric Time Series |
| By: | Christian Bach (Aarhus University, School of Economics and Management and CREATES); Bent Jesper Christensen (Aarhus University, School of Economics and Management and CREATES) |
| Abstract: | We include simultaneously both realized volatility measures based on high-frequency asset returns and implied volatilities backed out of individual traded at the money option prices in a state space approach to the analysis of true underlying volatility. We model integrated volatility as a latent fi?rst order Markov process and show that our model is closely related to the CEV and Barndorff-Nielsen & Shephard (2001) models for local volatility. We show that if measurement noise in the observable volatility proxies is not accounted for, then the estimated autoregressive parameter in the latent process is downward biased. Implied volatility performs better than any of the alternative realized measures when forecasting future integrated volatility. The results are largely similar across the stock market (S&P 500), bond market (30-year U.S. T-bond), and foreign currency exchange market ($/£ ). |
| Keywords: | Autoregression, bipower variation, high-frequency data, implied volatility, integrated volatility, Kalman fi?lter, moving average, option prices, realized volatility, state space model, stochastic volatility. |
| JEL: | C32 G13 G14 |
| Date: | 2011–02–11 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-61&r=ets |
| By: | Marine Carrasco; Rachidi Kotchoni |
| Abstract: | A shrinkage estimator of the integrated volatility is derived within a semiparametric moving average microstructure noise model specified at the highest frequency. The order the moving average is allowed to increase with the sampling frequency, which implies that the first order autocorrelation of the noise converges to one as the sampling frequency goes to infinity. Estimators are derived for the identifiable parameters of the model and their good properties are confirmed in simulation. The results of an empirical application with stocks listed in the DJI suggest that the order of the moving average model postulated for the noise typically increases slower than the square root of the sampling frequency. <P>Nous construisons un estimateur de volatilité intégrée qui se présente sous la forme d’une combinaison linéaire optimale d’autres estimateurs, dans le cadre d’un modèle semi-paramétrique de type moyenne mobile postulé pour le bruit de microstructure. L’ordre de ce processus moyen mobile est une fonction croissante de la fréquence des observations, ce qui implique que l’autocorrélation d’ordre 1 du bruit de microstructure tend vers l’unité lorsque la fréquence tend vers l’infini. Des estimateurs sont proposés pour les paramètres identifiables du modèle et leurs bonnes propriétés sont confirmées par simulation. Les résultats d’une application empirique basée sur des actifs du DJI suggèrent qu’en général, l’ordre du processus moyen mobile postulé pour le bruit de microstructure augmente moins vite que la racine carrée de la fréquence des observations |
| Keywords: | Integrated Volatility, method of moment, microstructure noise, realized kernel, shrinkage. , Volatilité intégrée, méthode des moments, bruit de microstructure, estimateur à noyaux réalisés, combinaison linéaire optimale d’estimateurs |
| Date: | 2011–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2011s-29&r=ets |
| By: | Hyungsik Roger Moon; Benoit Perron |
| Abstract: | Most panel unit root tests are designed to test the joint null hypothesis of a unit root for each individual series in a panel. After a rejection, it will often be of interest to identify which series can be deemed to be stationary and which series can be deemed nonstationary. Researchers will sometimes carry out this classi.cation on the basis of n individual (univariate) unit root tests based on some ad hoc significance level. In this paper, we suggest and demonstrate how to use the false discovery rate (FDR) in evaluating I (1) = I (0) classifications <P> |
| Keywords: | False discovery rate, multiple testing, unit root tests, panel data., |
| JEL: | C32 C33 C44 |
| Date: | 2011–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2011s-17&r=ets |
| By: | Pesaran, Hashem (University of Cambridge); Chudik, Alexander (University of Cambridge) |
| Abstract: | This paper considers the problem of aggregation in the case of large linear dynamic panels, where each micro unit is potentially related to all other micro units, and where micro innovations are allowed to be cross sectionally dependent. Following Pesaran (2003), an optimal aggregate function is derived, and the limiting behavior of the aggregation error is investigated as N (the number of cross section units) increases. Certain distributional features of micro parameters are also identified from the aggregate function. The paper then establishes Granger's (1980) conjecture regarding the long memory properties of aggregate variables from 'a very large scale dynamic, econometric model', and considers the time profiles of the effects of macro and micro shocks on the aggregate and disaggregate variables. Some of these findings are illustrated in Monte Carlo experiments, where we also study the estimation of the aggregate effects of micro and macro shocks. The paper concludes with an empirical application to consumer price inflation in Germany, France and Italy, and re-examines the extent to which ‘observed’ inflation persistence at the aggregate level is due to aggregation and/or common unobserved factors. Our findings suggest that dynamic heterogeneity as well as persistent common factors are needed for explaining the observed persistence of the aggregate inflation. |
| Keywords: | aggregation, large dynamic panels, long memory, weak and strong cross section dependence, VAR models, impulse responses, factor models, inflation persistence |
| JEL: | C43 E31 |
| Date: | 2011–02 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp5478&r=ets |
| By: | Hecq Alain; Laurent Sébastien; Palm Franz (METEOR) |
| Abstract: | First, we investigate the minimal univariate representation of some well known n dimensional conditional volatility models. Simple systems (e.g. a VEC(0,1)) for the joint behaviour of several variables imply individual processes with a lot of persistence in the form of long order lags. We show that in the presence of factors, parsimonious univariate representations (e.g. GARCH(1,1)) can result from large multivariate models generating the conditional variances and conditional correlations. Second, we propose an approach to use empirical results for these univariate processes in the analysis of the underlying multivariate, possibly high-dimensional, GARCH process. We use reduced rank procedures to discriminate between a system with seemingly unrelated assets (e.g. a diagonal model) from a set of series with few common sources of volatility. Among the analyzed procedures, the cannonical correlation test statistics on logs of squared returns proposed by Engle and Marcucci (2006) has quite good properties even in the case of falsely omitted cross-moments. Out of 30 returns from the NYSE, six returns are shown to display a parsimonious GARCH(1,1) model for their conditional variance. We do not reject the hypothesis that a single common volatility factor drives these six series. |
| Keywords: | financial economics and financial management ; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011011&r=ets |
| By: | Gengenbach Christian; Hecq Alain; Urbain Jean-Pierre (METEOR) |
| Abstract: | With the development of real-time databases, N vintages are available for T observations instead of a single realization of the time series process. Although the use of panel unit root tests with the aim to gain in efficiency seems obvious, empirical and simulation results shown in this paper heavily mitigate the intuitive perspective. |
| Keywords: | macroeconomics ; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011012&r=ets |
| By: | David Ardia (aeris CAPITAL AG, and University of Fribourg, Switzerland); Lennart F. Hoogerheide (Erasmus University Rotterdam) |
| Abstract: | This paper proposes an up-to-date review of estimation strategies available for the Bayesian inference of GARCH-type models. The emphasis is put on a novel efficient procedure named AdMitIS. The methodology automatically constructs a mixture of Student-t distributions as an approximation to the posterior density of the model parameters. This density is then used in importance sampling for model estimation, model selection and model combination. The procedure is fully automatic which avoids difficult and time consuming tuning of MCMC strategies. The AdMitIS methodology is illustrated with an empirical application to S&P index log-returns. Several non-nested GARCH-type models are estimated and combined to predict the distribution of next-day ahead log-returns. |
| Keywords: | GARCH; marginal likelihood; Bayesian model averaging; adaptive mixture of Student-t distributions; importance sampling |
| JEL: | C11 C15 C22 |
| Date: | 2010–04–27 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20100046&r=ets |
| By: | Monica Billio (University Ca'Foscari di Venezia); Roberto Casarin (University Ca'Foscari di Venezia); Francesco Ravazzolo (Norges Bank); Herman K. van Dijk (Erasmus University Rotterdam) |
| Abstract: | Using a Bayesian framework this paper provides a multivariate combination approach to prediction based on a distributional state space representation of predictive densities from alternative models. In the proposed approach the model set can be incomplete. Several multivariate time-varying combination strategies are introduced. In particular, a weight dynamics driven by the past performance of the predictive densities is considered and the use of learning mechanisms. The approach is assessed using statistical and utility-based performance measures for evaluating density forecasts of US macroeconomic time series and of surveys of stock market prices. |
| Keywords: | Density Forecast Combination; Survey Forecast; Bayesian Filtering; Sequential Monte Carlo |
| JEL: | C11 C15 C53 E37 |
| Date: | 2011–01–06 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20110003&r=ets |
| By: | Drew Creal (University of Chicago, Booth School of Business); Siem Jan Koopman (VU University Amsterdam); André Lucas (VU University Amsterdam) |
| Abstract: | We propose a new class of observation-driven time-varying parameter models for dynamic volatilities and correlations to handle time series from heavy-tailed distributions. The model adopts generalized autoregressive score dynamics to obtain a time-varying covariance matrix of the multivariate Student's <I>t</I> distribution. The key novelty of our proposed model concerns the weighting of lagged squared innovations for the estimation of future correlations and volatilities. When we account for heavy tails of distributions, we obtain estimates that are more robust to large innovations. The model also admits a representation as a time-varying heavy-tailed copula which is particularly useful if the interest focuses on dependence structures. We provide an empirical illustration for a panel of daily global equity returns. |
| Keywords: | dynamic dependence; multivariate Student's t distribution; copula |
| JEL: | C10 C22 C32 C51 |
| Date: | 2010–03–16 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20100032&r=ets |
| By: | Sjoerd van den Hauwe (Erasmus University Rotterdam); Richard Paap (Erasmus University Rotterdam); Dick J.C. van Dijk (Erasmus University Rotterdam) |
| Abstract: | We propose a new approach to deal with structural breaks in time series models. The key contribution is an alternative dynamic stochastic specification for the model parameters which describes potential breaks. After a break new parameter values are generated from a so-called baseline prior distribution. Modeling boils down to the choice of a parametric likelihood specification and a baseline prior with the proper support for the parameters. The approach accounts in a natural way for potential out-of-sample breaks where the number of breaks is stochastic. Posterior inference involves simple computations that are less demanding than existing methods. The approach is illustrated on nonlinear discrete time series models and models with restrictions on the parameter space. |
| Keywords: | Structural breaks; Bayesian analysis; forecasting; MCMC methods; nonlinear time series |
| JEL: | C11 C22 C51 C53 C63 |
| Date: | 2011–02–08 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20110023&r=ets |
| By: | David Ardia (University of Fribourg, Switzerland); Lennart F. Hoogerheide (Erasmus University Rotterdam) |
| Abstract: | This note presents the R package bayesGARCH (Ardia, 2007) which provides functions for the Bayesian estimation of the parsimonious and effective GARCH(1,1) model with Student-<I>t</I> innovations. The estimation procedure is fully automatic and thus avoids the tedious task of tuning a MCMC sampling algorithm. The usage of the package is shown in an empirical application to exchange rate logreturns. |
| Keywords: | Bayesian; Markov Chain Monte Carlo; GARCH; Student-t; R software |
| JEL: | C11 C15 C22 |
| Date: | 2010–04–27 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20100045&r=ets |
| By: | Irma Hindrayanto (VU University Amsterdam); John A.D. Aston (University of Warwick, UK); Siem Jan Koopman (VU University Amsterdam); Marius Ooms (VU University Amsterdam) |
| Abstract: | The basic structural time series model has been designed for the modelling and forecasting of seasonal economic time series. In this paper we explore a generalisation of the basic structural time series model in which the time-varying trigonometric terms associated with different seasonal frequencies have different variances for their disturbances. The contribution of the paper is two-fold. The first aim is to investigate the dynamic properties of this frequency specific basic structural model. The second aim is to relate the model to a comparable generalised version of the Airline model developed at the U.S. Census Bureau. By adopting a quadratic distance metric based on the restricted reduced form moving-average representation of the models, we conclude that the generalised models have properties that are close to each other compared to their default counterparts. In some settings, the distance between the models is almost zero so that the models can be regarded as observationally equivalent. An extensive empirical study on disaggregated monthly shipment and foreign trade series illustrates the improvements of the frequency-specific extension and investigates the relations between the two classes of models. |
| Keywords: | Frequency-specific model; Kalman filter; model-based seasonal adjustment; unobserved components time series model. |
| JEL: | C22 C52 |
| Date: | 2010–02–04 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20100018&r=ets |
| By: | Peter Exterkate (Erasmus University Rotterdam); Patrick J.F. Groenen (Erasmus University Rotterdam); Christiaan Heij (Erasmus University Rotterdam); Dick van Dijk (Erasmus University Rotterdam) |
| Abstract: | This paper puts forward kernel ridge regression as an approach for forecasting with many predictors that are related nonlinearly to the target variable. In kernel ridge regression, the observed predictor variables are mapped nonlinearly into a high-dimensional space, where estimation of the predictive regression model is based on a shrinkage estimator to avoid overfitting. We extend the kernel ridge regression methodology to enable its use for economic time-series forecasting, by including lags of the dependent variable or other individual variables as predictors, as is typically desired in macroeconomic and financial applications. Monte Carlo simulations as well as an empirical application to various key measures of real economic activity confirm that kernel ridge regression can produce more accurate forecasts than traditional linear methods for dealing with many predictors based on principal component regression. |
| Keywords: | High dimensionality; nonlinear forecasting; ridge regression; kernel methods |
| JEL: | C53 C63 E27 |
| Date: | 2011–01–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20110007&r=ets |
| By: | Rianne Legerstee (Erasmus University Rotterdam); Philip Hans Franses (Erasmus University Rotterdam) |
| Abstract: | Forecasts from various experts are often used in macroeconomic forecasting models. Usually the focus is on the mean or median of the survey data. In the present study we adopt a different perspective on the survey data as we examine the predictive power of disagreement amongst forecasters. The premise is that this variable could signal upcoming structural or temporal changes in an economic process or in the predictive power of the survey forecasts. In our empirical work, we examine a variety of macroeconomic variables, and we use different measurements for the degree of disagreement, together with measures for location of the survey data and autoregressive components. Forecasts from simple linear models and forecasts from Markov regime-switching models with constant and with time-varying transition probabilities are constructed in real-time and compared on forecast accuracy. We find that disagreement has predictive power indeed and that this variable can be used to improve forecasts when used in Markov regime-switching models. |
| Keywords: | model forecasts; expert forecasts; survey forecasts; Markov regime-switching models; disagreement; time series |
| JEL: | C53 |
| Date: | 2010–09–03 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20100088&r=ets |
| By: | Olfa Zaafrane; Anouar Ben Mabrouk |
| Abstract: | In the present paper, a fuzzy logic based method is combined with wavelet decomposition to develop a step-by-step dynamic hybrid model for the estimation of financial time series. Empirical tests on fuzzy regression, wavelet decomposition as well as the new hybrid model are conducted on the well known $SP500$ index financial time series. The empirical tests show an efficiency of the hybrid model. |
| Date: | 2011–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1102.3702&r=ets |
| By: | Matteo Pelagatti (Department of Statistics, Università degli Studi di Milano-Bicocca); Pranab Sen (Department of Statistics and Operations Research, University of North Carolina at Chapel Hill) |
| Abstract: | We propose a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending. For the level-stationarity hypothesis, the test statistic we propose is a modified version of the popular KPSS statistic, in which ranks substitute the original observations. We prove that the rank KPSS statistic shares the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives. For the trend-stationarity hypothesis, we apply the same rank KPSS statistic to the residual of a Theil-Sen regression on a linear trend. We derive the asymptotic distribution of the Theil-Sen estimator under short memory errors and prove that the Theil-Sen detrended rank KPSS statistic shares the same weak limit as the least-squares detrended KPSS. We study the asymptotic relative efficiency of our test compared to the KPSS and prove that it may have unbounded efficiency gains under fat-tailed distributions compensated by very moderate efficiency losses under thin-tailed distributions. For this and other reasons discussed in the body of the article our rank KPSS test turns out to be an irresistible competitor of the KPSS for most real-world economic and financial applications. The weak convergence results and asymptotic representations proved in this article may have an interest on their own, as they extend to ranks analogous results widely used in unit-root econometrics. |
| Keywords: | Stationarity test, Unit roots, Robustness, Rank statistics, Theil-Sen estimator, Asymptotic eciency |
| JEL: | C12 C14 C22 |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:mis:wpaper:20110201&r=ets |