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on Econometrics |
| By: | Victor Chernozhukov (Massachusetts Institute of Technology); Patrick Gagliardini (University of Lugano and Swiss Finance Institute); Olivier Scaillet (University of Geneva and Swiss Finance Institute) |
| Abstract: | We study Tikhonov Regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a mini- mum distance principle. We show that the minimumdistance problem without regularization is locally ill-posed, and consider penalization by the norms of the parameter and its deriva- tive. We derive the asymptotic Mean Integrated Square Error, the rate of convergence and the pointwise asymptotic normality under a regularization parameter depending on sample size. We illustrate our theoretical findings and the small sample properties with simulation results in two numerical examples. We also discuss a data driven selection procedure of the regularization parameter via a spectral representation of the MISE. Finally, we provide an empirical application to estimation of Engel curves. |
| Keywords: | Quantile Regression, Nonparametric Estimation, Instrumental Variable, Ill-Posed Inverse Problems, Tikhonov Regularization, Engel Curve. |
| JEL: | C13 C14 D12 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0803&r=ecm |
| 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=ecm |
| By: | Jose Antonio Carnicero; Michael P. Wiper |
| Abstract: | This paper introduces a new, semi-parametric model for circular data, based on mixtures of shifted, scaled, beta (SSB) densities. This model is more general than the Bernstein polynomial density model which is well known to provide good approximations to any density with finite support and it is shown that, as for the Bernstein polynomial model, the trigonometric moments of the SSB mixture model can all be derived. Two methods of fitting the SSB mixture model are considered. Firstly, a classical, maximum likelihood approach for fitting mixtures of a given number of SSB components is introduced. The Bayesian information criterion is then used for model selection. Secondly, a Bayesian approach using Gibbs sampling is considered. In this case, the number of mixture components is selected via an appropriate deviance information criterion. Both approaches are illustrated with real data sets and the results are compared with those obtained using Bernstein polynomials and mixtures of von Mises distributions. |
| Keywords: | Circular data, Shifted, scaled, beta distribution; Mixture models, Bernstein polynomials |
| JEL: | C14 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws081305&r=ecm |
| By: | Giacomini, Raffaella; Rossi, Barbara |
| Abstract: | We propose new methods for comparing the relative out-of-sample forecasting performance of two competing models in the presence of possible instabilities. The main idea is to develop a measure of the relative “local forecasting performance” for the two models, and to investigate its stability over time by means of statistical tests. We propose two tests (the “Fluctuation test” and the test against a “One-time Reversal”) that analyze the evolution of the models’ relative performance over historical samples. In contrast to previous approaches to forecast comparison, which are based on measures of “global performance”, we focus on the entire time path of the models’ relative performance, which may contain useful information that is lost when looking for the model that forecasts best on average. We apply our tests to the analysis of the time variation in the out-of-sample forecasting performance of monetary models of exchange rate determination relative to the random walk. |
| Keywords: | Predictive Ability Testing, Instability, Structural Change, Forecast Evaluation |
| JEL: | C22 C52 C53 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:duk:dukeec:08-4&r=ecm |
| 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=ecm |
| By: | Banerjee, Anindya; Marcellino, Massimiliano; Masten, Igor |
| Abstract: | We conduct a detailed simulation study of the forecasting performance of diffusion index-based methods in short samples with structural change. We consider several data generation processes, to mimic different types of structural change, and compare the relative forecasting performance of factor models and more traditional time series methods. We find that changes in the loading structure of the factors into the variables of interest are extremely important in determining the performance of factor models. We complement the analysis with an empirical evaluation of forecasts for the key macroeconomic variables of the Euro area and Slovenia, for which relatively short samples are officially available and structural changes are likely. The results are coherent with the findings of the simulation exercise, and confirm the relatively good performance of factor-based forecasts in short samples with structural change. |
| Keywords: | Factor models; forecasts; parameter uncertainty; short samples; structural change; time series models |
| JEL: | C32 C53 E37 |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6706&r=ecm |
| By: | Marcellino, Massimiliano; Schumacher, Christian |
| Abstract: | This paper compares different ways to estimate the current state of the economy using factor models that can handle unbalanced datasets. Due to the different release lags of business cycle indicators, data unbalancedness often emerges at the end of multivariate samples, which is sometimes referred to as the `ragged edge' of the data. Using a large monthly dataset of the German economy, we compare the performance of different factor models in the presence of the ragged edge: static and dynamic principal components based on realigned data, the Expectation-Maximisation (EM) algorithm and the Kalman smoother in a state-space model context. The monthly factors are used to estimate current quarter GDP, called the `nowcast', using different versions of what we call factor-based mixed-data sampling (Factor-MIDAS) approaches. We compare all possible combinations of factor estimation methods and Factor-MIDAS projections with respect to nowcast performance. Additionally, we compare the performance of the nowcast factor models with the performance of quarterly factor models based on time-aggregated and thus balanced data, which neglect the most timely observations of business cycle indicators at the end of the sample. Our empirical findings show that the factor estimation methods don't differ much with respect to nowcasting accuracy. Concerning the projections, the most parsimonious MIDAS projection performs best overall. Finally, quarterly models are in general outperformed by the nowcast factor models that can exploit ragged-edge data |
| Keywords: | business cycle; large factor models; MIDAS; missing values; mixed-frequency data; nowcasting |
| JEL: | C53 E37 |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6708&r=ecm |
| 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=ecm |
| By: | Jeremy J. Nalewaik |
| Abstract: | This paper proposes a simple generalization of the classical measurement error model, introducing new measurement errors that subtract signal from the true variable of interest, in addition to the usual classical measurement errors (CME) that add noise. The effect on OLS regression of these lack of signal errors (LoSE) is opposite the conventional wisdom about CME: while CME in the explanatory variables causes attenuation bias, LoSE in the dependent variable, not the explanatory variables, causes a similar bias under some conditions. In addition, LoSE in the dependent variable shrinks the variance of the regression residuals, making inference potentially misleading. The paper provides evidence that LoSE is an important source of error in US macroeconomic quantity data such as GDP growth, illustrates downward bias in regressions of GDP growth on asset prices, and provides recommendations for econometric practice. |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2008-15&r=ecm |
| By: | Angelini, Elena; Camba-Mendez, Gonzalo; Giannone, Domenico; Reichlin, Lucrezia; Rünstler, Gerhard |
| Abstract: | This paper evaluates models that exploit timely monthly releases to compute early estimates of current quarter GDP (now-casting) in the euro area. We compare traditional methods used at institutions with a new method proposed by Giannone, Reichlin and Small, 2005. The method consists in bridging quarterly GDP with monthly data via a regression on factors extracted from a large panel of monthly series with different publication lags. We show that bridging via factors produces more accurate estimates than traditional bridge equations. We also show that survey data and other `soft' information are valuable for now-casting. |
| Keywords: | Factor Model; Forecasting; Large data-sets; Monetary Policy; News; Real Time Data |
| JEL: | C33 C53 E52 |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6746&r=ecm |
| By: | Raymond Kan; Cesare Robotti |
| Abstract: | Under the assumption of multivariate normality of asset returns, this paper presents a geometrical interpretation and the finite-sample distributions of the sample Hansen-Jagannathan (1991) bounds on the variance of admissible stochastic discount factors, with and without the nonnegativity constraint on the stochastic discount factors. In addition, since the sample Hansen-Jagannathan bounds can be very volatile, we propose a simple method to construct confidence intervals for the population Hansen-Jagannathan bounds. Finally, we show that the analytical results in the paper are robust to departures from the normality assumption. |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedawp:2008-09&r=ecm |
| 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=ecm |
| 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=ecm |