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on Econometric Time Series |
| By: | Marco Aiolfi (Goldman Sachs Asset Management); Carlos Capistrán (Banco de México); Allan Timmermann (University of California, San Diego and CREATES) |
| Abstract: | We consider combinations of subjective survey forecasts and model-based forecasts from linear and non-linear univariate specifications as well as multivariate factor-augmented models. Empirical results suggest that a simple equal-weighted average of survey forecasts outperform the best model-based forecasts for a majority of macroeconomic variables and forecast horizons. Additional improvements can in some cases be gained by using a simple equal-weighted average of survey and model-based forecasts. We also provide an analysis of the importance of model instability for explaining gains from forecast combination. Analytical and simulation results uncover break scenarios where forecast combinations outperform the best individual forecasting model. |
| Keywords: | Time-series forecasts, survey forecasts, model instability |
| JEL: | C22 C53 |
| Date: | 2010–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-21&r=ets |
| By: | Keith Ord; Ralph Snyder; Adrian Beaumont |
| Abstract: | Organizations with large-scale inventory systems typically have a large proportion of items for which demand is intermittent and low volume. We examine different approaches to forecasting for such products, paying particular attention to the need for inventory planning over a multi-period lead-time when the underlying process may be non-stationary. We develop a forecasting framework based upon the zero-inflated Poisson distribution (ZIP), which enables the explicit evaluation of the multi-period lead-time demand distribution in special cases and an effective simulation scheme more generally. We also develop performance measures related to the entire predictive distribution, rather than focusing exclusively upon point predictions. The ZIP model is compared to a number of existing methods using data on the monthly demand for 1,046 automobile parts, provided by a US automobile manufacturer. We conclude that the ZIP scheme compares favorably to other approaches, including variations of Croston's method as well as providing a straightforward basis for inventory planning. |
| Keywords: | Croston's method; Exponential smoothing; Intermittent demand; Inventory control; Prediction likelihood; State space models; Zero-inflated Poisson distribution |
| JEL: | C22 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2010-12&r=ets |
| By: | Alysha M De Livera |
| Abstract: | A new automatic forecasting procedure is proposed based on a recent exponential smoothing framework which incorporates a Box-Cox transformation and ARMA residual corrections. The procedure is complete with well-defined methods for initialization, estimation, likelihood evaluation, and analytical derivation of point and interval predictions under a Gaussian error assumption. The algorithm is examined extensively by applying it to single seasonal and non-seasonal time series from the M and the M3 competitions, and is shown to provide competitive out-of-sample forecast accuracy compared to the best methods in these competitions and to the traditional exponential smoothing framework. The proposed algorithm can be used as an alternative to existing automatic forecasting procedures in modeling single seasonal and non-seasonal time series. In addition, it provides the new option of automatic modeling of multiple seasonal time series which cannot be handled using any of the existing automatic forecasting procedures. The proposed automatic procedure is further illustrated by applying it to two multiple seasonal time series involving call center data and electricity demand data. |
| Keywords: | Exponential smoothing, state space models, automatic forecasting, Box-Cox transformation, residual adjustment, multiple seasonality, time series |
| JEL: | C22 C53 |
| Date: | 2010–04–28 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2010-10&r=ets |
| By: | Cecilia Mancini (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze) |
| Abstract: | In this paper we consider a semimartingale model for the evolution of the price of a financial asset, driven by a Brownian motion (plus drift) and possibly infinite activity jumps. Given discrete observations, the threshold estimator is able to separate the integrated variance from the sum of the squared jumps. This has importance in measuring and forecasting the asset risks. The exact convergence speed was found in the literature only when the jumps are of finite variation. Here we give the speed even in presence of infinite variation jumps, as they appear e.g. in some cgmy plus diffusion models. |
| Keywords: | Integrated variance, threshold estimator, convergence speed, infinite activity stable Le'vy jumps. |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2010-03&r=ets |
| By: | Cecilia Mancini (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze); Fabio Gobbi (Department of Mathematical Economics, University of Bologna) |
| Abstract: | In this paper we consider two semimartingales driven by Wiener processes and (possibly infinite activity) jumps. Given discrete observations we separately estimate the integrated covariation IC from the sum of the co-jumps. The Realized Covariation (RC) approaches the sum of IC with the co-jumps as the number of observations increases to infinity. Our threshold (or truncated) estimator \hat{IC}_n excludes from RC all the terms containing jumps in the finite activity case and the terms containing jumps over the threshold in the infinite activity case, and is consistent. To further measure the dependence between the two processes also the betas, \beta^{(1,2)} and \beta^{(2,1)}, and the correlation coefficient \rho^{(1,2)} among the Brownian semimartingale parts are consistently estimated. In presence of only finite activity jumps: 1) we reach CLTs for \hat{IC}_n, \hat\beta^{(i,j)} and \hat \rho^{(1,2)}; 2) combining thresholding with the observations selection proposed in Hayashi and Yoshida (2005) we reach an estimate of IC which is robust to asynchronous data. We report the results of an illustrative application, made in a web appendix (on www.dmd.unifi.it/upload/sub/persone/mancini/WebAppendix3.pdf), to two very different simulated realistic asset price models and we see that the finite sample performances of \hat{IC}_n and of the sum of the co-jumps estimator are good for values of the observation step large enough to avoid the typical problems arising in presence of microstructure noises in the data. However we find that the co-jumps estimators are more sensible than \hat{IC}_n to the choice of the threshold. Finding criteria for optimal threshold selection is object of further research. |
| Keywords: | co-jumps, integrated covariation, integrated variance, finite activity jumps, infinite activity jumps, threshold estimator |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2010-05&r=ets |
| By: | Rama Cont (IEOR Dept., Columbia University, New York, USA, and Laboratoire de Probabilites et Modeles Aleatoires, CNRS-Universite Paris VI, France); Cecilia Mancini (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze) |
| Abstract: | We propose two nonparametric tests for investigating the pathwise properties of a signal modeled as the sum of a L\'evy process and a Brownian semimartingale. Using a nonparametric threshold estimator for the continuous component of the quadratic variation, we design a test for the presence of a continuous martingale component in the process and a test for establishing whether the jumps have finite or infinite variation, based on observations on a discrete time grid. We evaluate the performance of our tests using simulations of various stochastic models and use the tests to investigate the fine structure of the DM/USD exchange rate fluctuations and SPX futures prices. In both cases, our tests reveal the presence of a non-zero Brownian component and a finite variation jump component. |
| Keywords: | Threshold estimator, central limit theorem, test for finite variation jumps, test for Brownian component. |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:flo:wpaper:2010-02&r=ets |
| By: | Bouezmarni, Taoufik; Van Bellegem, Sébastien |
| Abstract: | The paper introduces a new nonparametric estimator of the spectral density that is given in smoothing the periodogram by the probability density of Beta random variable (Beta kernel). The estimator is proved to be bounded for short memory data, and diverges at the origin for long memory data. The convergence in probability of the relative error and Monte Carlo simulations suggest that the estimator automaticaly adapts to the long- or the short-range dependency of the process. A cross-validation procedure is also studied in order to select the nuisance parameter of the estimator. Illustrations on historical as well as most recent returns and absolute returns of the S&P500 index show the reasonable performance of the estimation, and show that the data-driven estimator is a valuable tool for the detection of long-memory as well as hidden periodicities in stock returns. |
| Keywords: | spectral density, long rage dependence, nonparametric estimation |
| Date: | 2009–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:22191&r=ets |
| By: | Caporin, M. (Erasmus Econometric Institute); McAleer, M.J. (Erasmus Econometric Institute) |
| Abstract: | DAMGARCH is a new model that extends the VARMA-GARCH model of Ling and McAleer (2003) by introducing multiple thresholds and time-dependent structure in the asymmetry of the conditional variances. Analytical expressions for the news impact surface implied by the new model are also presented. DAMGARCH models the shocks affecting the conditional variances on the basis of an underlying multivariate distribution. It is possible to model explicitly asset-specific shocks and common innovations by partitioning the multivariate density support. This paper presents the model structure, describes the implementation issues, and provides the conditions for the existence of a unique stationary solution, and for consistency and asymptotic normality of the quasi-maximum likelihood estimators. The paper also presents an empirical example to highlight the usefulness of the new model. |
| Keywords: | multivariate asymmetry;conditional variance;stationarity conditions;asymptotic theory;multivariate news impact cure |
| Date: | 2010–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765019452&r=ets |
| By: | Caporin, M. (Erasmus Econometric Institute); McAleer, M.J. (Erasmus Econometric Institute) |
| Abstract: | In the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. The two most widely known and used are the Scalar BEKK model of Engle and Kroner (1995) and Ding and Engle (2001), and the DCC model of Engle (2002). Some recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. In this paper, we provide an empirical comparison of a set of MGARCH models, namely BEKK, DCC, Corrected DCC (cDCC) of Aeilli (2008), CCC of Bollerslev (1990), Exponentially Weighted Moving Average, and covariance shrinking of Ledoit and Wolf (2004), using the historical data of 89 US equities. Our methods follow some of the approach described in Patton and Sheppard (2009), and contribute to the literature in several directions. First, we consider a wide range of models, including the recent cDCC model and covariance shrinking. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Weighted Likelihood Ratio test of Amisano and Giacomini (2007). Third, we examine how the model rankings are influenced by the cross-sectional dimension of the problem. |
| Keywords: | covariance forecasting;model confidence set;model ranking;MGARCH;model comparison |
| Date: | 2010–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureir:1765019447&r=ets |
| By: | Costantini, Mauro (Department of Economics, University of Vienna, Vienna, Austria); Gunter, Ulrich (Department of Economics, University of Vienna, Vienna, Austria); Kunst, Robert M. (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and Department of Economics, University of Vienna, Vienna, Austria) |
| Abstract: | We use data generated by a macroeconomic DSGE model to study the relative benefits of forecast combinations based on forecast-encompassing tests relative to simple uniformly weighted forecast averages across rival models. Assumed rival models are four linear autoregressive specifications, one of them a more sophisticated factor-augmented vector autoregression (FAVAR). The forecaster is assumed not to know the true data-generating DSGE model. The results critically depend on the prediction horizon. While one-step prediction hardly supports test-based combinations, the test-based procedure attains a clear lead at prediction horizons greater than two. |
| Keywords: | Combining forecasts, encompassing tests, model selection, time series, DSGE model |
| JEL: | C15 C32 C53 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihsesp:251&r=ets |
| By: | Bertrand B. Maillet (ABN AMRO Advisors, Variances and University of Paris-1 (CES/CNRS and EIF)); Jean-Philippe R. Médecin (Paris School of Economics, University of Paris-1 and Variances) |
| Abstract: | Following Bali and Weinbaum (2005) and Maillet et al. (2010), we present several estimates of volatilities computed with high- and low frequency data and complement their results using additional measures of risk and several alternative methods for Tail-index estimation. The aim here is to confirm previous results regarding the slope of the tail of various risk measure distributions, in order to define the high watermarks of market risks. We also produce synthetic general results concerning the method of estimation of the Tail-indexes related to expressions of the L-moments. Based on estimates of Tail-indexes, retrieved from the high frequency 30’ sampled CAC40 French stock Index series from the period 1997-2009, using Non-parametric Generalized Hill, Maximum Likelihood and various kinds of L-moment Methods for the estimation of both a Generalized Extreme Value density and a Generalized Pareto Distribution, we confirm that a heavy-tail density specification of the Log-volatility is not necessary. |
| Keywords: | Financial Crisis, Realized Volatility, Range-based Volatility, Extreme Value Distributions, Tail-index, L-moments, High Frequency Data. |
| JEL: | G10 G14 |
| URL: | http://d.repec.org/n?u=RePEc:ven:wpaper:2010_10&r=ets |
| By: | Massimiliano Caporin (Department of Economics and Management "Marco Fanno", University of Padova); Michael McAleer (Erasmus School of Economics, Erasmus University Rotterdam, Tinbergen Institute and Department of Economics and Finance, University of Canterbury) |
| Abstract: | In the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. The two most widely known and used are the Scalar BEKK model of Engle and Kroner (1995) and Ding and Engle (2001), and the DCC model of Engle (2002). Some recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. In this paper, we provide an empirical comparison of a set of MGARCH models, namely BEKK, DCC, Corrected DCC (cDCC) of Aeilli (2008), CCC of Bollerslev (1990), Exponentially Weighted Moving Average, and covariance shrinking of Ledoit and Wolf (2004), using the historical data of 89 US equities. Our methods follow some of the approach described in Patton and Sheppard (2009), and contribute to the literature in several directions. First, we consider a wide range of models, including the recent cDCC model and covariance shrinking. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Weighted Likelihood Ratio test of Amisano and Giacomini (2007). Third, we examine how the model rankings are influenced by the cross-sectional dimension of the problem. |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2010cf742&r=ets |
| By: | Massimiliano Caporin (Department of Economic Sciences, University of Padova); Michael McAleer (Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute) |
| Abstract: | DAMGARCH is a new model that extends the VARMA-GARCH model of Ling and McAleer (2003) by introducing multiple thresholds and time-dependent structure in the asymmetry of the conditional variances. Analytical expressions for the news impact surface implied by the new model are also presented. DAMGARCH models the shocks affecting the conditional variances on the basis of an underlying multivariate distribution. It is possible to model explicitly asset-specific shocks and common innovations by partitioning the multivariate density support. This paper presents the model structure, describes the implementation issues, and provides the conditions for the existence of a unique stationary solution, and for consistency and asymptotic normality of the quasimaximum likelihood estimators. The paper also presents an empirical example to highlight the usefulness of the new model. |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2010cf740&r=ets |
| By: | Regnard, Nazim; Zakoian, Jean-Michel |
| Abstract: | A novel GARCH(1,1) model, with coefficients function of the realizations of an exogenous process, is considered for the volatility of daily gas prices. A distinctive feature of the model is that it produces non-stationary solutions. The probability properties, and the convergence and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) have been derived by Regnard and Zakoian (2009). The prediction properties of the model are considered. We derive a strongly consistent estimator of the asymptotic variance of the QMLE. An application to daily gas spot prices from the Zeebruge market is presented. Apart from conditional heteroskedasticity, an empirical finding is the existence of distinct volatility regimes depending on the temperature level. |
| Keywords: | GARCH; Gas prices; Nonstationary models; Periodic models; Quasi-maximum likelihood estimation; Time-varying coefficients |
| JEL: | C53 C22 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22642&r=ets |