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on Econometric Time Series |
| By: | Eric Jondeau (University of Lausanne and Swiss Finance Institute) |
| Abstract: | It is well known that the class of strong (Generalized) AutoRegressive Conditional Heteroskedasticity (or GARCH) processes is not closed under contemporaneous aggregation. This paper provides the dynamics followed by the aggregate process when the individual persistence parameters are drawn from the same (unknown) distribution. Assuming heterogeneity across individual parameters, the dynamics of the aggregate volatility involves additional lags that reflect the moments of the distribution of the individual persistence parameters. Then the paper describes a consistent estimator of the aggregate process, based on nonlinear least squares. A simulation study reveals that this aggregation-corrected estimator performs very well under realistic sets of parameters. Last, this approach is extended to a multi-sector context. This extension is used to evaluate the importance of the aggregation bias. Using size and book-to-market portfolios, I show that the investor is willing to pay one fifth of her expected return to switch from the standard GARCH (1,1) estimator to the aggregation-corrected estimator. |
| Keywords: | Contemporaneous aggregation, Heterogeneity, Volatility, GARCH model. |
| JEL: | C13 C21 G11 |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0806&r=ets |
| By: | Banerjee, Anindya; Marcellino, Massimiliano |
| Abstract: | This paper brings together several important strands of the econometrics literature: error-correction, cointegration and dynamic factor models. It introduces the Factor-augmented Error Correction Model (FECM), where the factors estimated from a large set of variables in levels are jointly modelled with a few key economic variables of interest. With respect to the standard ECM, the FECM protects, at least in part, from omitted variable bias and the dependence of cointegration analysis on the specific limited set of variables under analysis. It may also be in some cases a refinement of the standard Dynamic Factor Model (DFM), since it allows us to include the error correction terms into the equations, and by allowing for cointegration prevent the errors from being non-invertible moving average processes. In addition, the FECM is a natural generalization of factor augmented VARs (FAVAR) considered by Bernanke, Boivin and Eliasz (2005) inter alia, which are specified in first differences and are therefore misspecified in the presence of cointegration. The FECM has a vast range of applicability. A set of Monte Carlo experiments and two detailed empirical examples highlight its merits in finite samples relative to standard ECM and FAVAR models. The analysis is conducted primarily within an in-sample framework, although the out-of-sample implications are also explored. |
| Keywords: | Cointegration; Dynamic Factor Models; Error Correction Models; Factor-augmented Error Correction Models; FAVAR; VAR |
| JEL: | C32 E17 |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6707&r=ets |
| By: | andrés M. Alonso; Carolina Garcia-Martos; Julio Rodriguez; Maria Jesus Sanchez |
| Abstract: | Year-ahead forecasting of electricity prices is an important issue in the current context of electricity markets. Nevertheless, only one-day-ahead forecasting is commonly tackled up in previous published works. Moreover, methodology developed for the short-term does not work properly for long-term forecasting. In this paper we provide a seasonal extension of the Non-Stationary Dynamic Factor Analysis, to deal with the interesting problem (both from the economic and engineering point of view) of long term forecasting of electricity prices. Seasonal Dynamic Factor Analysis (SeaDFA) allows to deal with dimensionality reduction in vectors of time series, in such a way that extracts common and specific components. Furthermore, common factors are able to capture not only regular dynamics (stationary or not) but also seasonal one, by means of common factors following a multiplicative seasonal VARIMA(p,d,q)×(P,D,Q)s model. Besides, a bootstrap procedure is proposed to be able to make inference on all the parameters involved in the model. A bootstrap scheme developed for forecasting includes uncertainty due to parameter estimation, allowing to enhance the coverage of forecast confidence intervals. Concerning the innovative and challenging application provided, bootstrap procedure developed allows to calculate not only point forecasts but also forecasting intervals for electricity prices. |
| Keywords: | Dynamic factor analysis, Bootstrap, Forecasting, Confidence intervals |
| JEL: | C32 C53 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws081406&r=ets |
| By: | Frédérique Bec (CREST-LMA, Timbre J360, 15 boulevard Gabriel Peri, 92245 Malakoff CEDEX and THEMA, University of Cergy-Pontoise, France); Anders Rahbek (Department of Economics, University of Copenhagen and Studiestraede 6, DK-1455 Copenhagen K, Denmark); Neil Shephard (Oxford-Man Institute and Economics Department, University of Oxford and Blue Boar Court, Alfred Road, Oxford OX1 4EH, United-Kingdom) |
| Abstract: | In this paper we propose and analyse the Autoregressive Conditional Root (ACR) time series mmodel. It is a multivariate dynamic mixture autoregression which allows for non-stationary epochs. It proves to be an appealing alternative to existing nonlinear models such as e.g. the threshold autoregressive or Markov switching classes of models, which are commonly used to describe non-linear dynamics as implied by arbitrage in presence of transaction costs. Simple conditions on the parameters of the ACR process and its innovations, are shown to imply geometric ergodicity, stationarity and existence of moments. Furthermore, we establish consistency and asymptotic normality of the maximum likelihood estimators in the ACR model. An application to real exchange rate data illustrates the conclusions and analysis. |
| Keywords: | Dynamic mixture vector autoregressive mmodel, autoregressive conditional root model, ACR, regime switching, stochastic unit root, threshold autoregression |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2008-11&r=ets |
| By: | Geert Dhaene; Olivier Vergote |
| Abstract: | We derive closed-form expressions for the optimal weighting matrix for GMM estimation of the stochastic volatility model with AR(1) log-volatility, and for the asymptotic covariance matrix of the resulting estimator. The moment conditions considered are generated by the absolute observations (which is the standard approach in this literature) or by the log-squared observations. We use the expressions to compare the performances of GMM and other estimators that have been proposed, and to optimally select small sets of moment conditions from very large sets. |
| Keywords: | Stochastic volatility, GMM |
| JEL: | C13 C22 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:ete:ceswps:ces0306&r=ets |
| By: | M. Hashem Pesaran; Til Schuermann; L. Vanessa Smith |
| Abstract: | This paper considers the problem of forecasting real and financial macroeconomic variables across a large number of countries in the global economy. To this end, a global vector autoregressive (GVAR) model previously estimated over the 1979:Q1-2003:Q4 period by Dees, de Mauro, Pesaran, and Smith (2007) is used to generate out-of-sample one-quarter- and four-quarters-ahead forecasts of real output, inflation, real equity prices, exchange rates, and interest rates over the period 2004:Q1-2005:Q4. Forecasts are obtained for 134 variables from twenty-six regions made up of thirty-three countries and covering about 90 percent of world output. The forecasts are compared to typical benchmarks: univariate autoregressive and random walk models. Building on the forecast combination literature, the paper examines the effects of model and estimation uncertainty on forecast outcomes by pooling forecasts obtained from different GVAR models estimated over alternative sample periods. Given the size of the modeling problem and the heterogeneity of the economies considered, industrialized, emerging, and less developed countries, as well as the very real likelihood of multiple structural breaks, averaging forecasts across both models and windows makes a significant difference. Indeed, the double-averaged GVAR forecasts performed better than the benchmark forecasts, especially for output, inflation, and real equity prices. |
| Keywords: | Economic forecasting ; Time-series analysis ; Econometric models ; Vector autoregression |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fednsr:317&r=ets |