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on Econometric Time Series |
| By: | Lanouar Charfeddine (OEP - Université Paris Est Marne-la-Vallée); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | Are structural breaks models true switching models or long memory processes ? The answer to this question remain ambiguous. A lot of papers, in recent years, have dealt with this problem. For instance, Diebold and Inoue (2001) and Granger and Hyung (2004) show, under specific conditions, that switching models and long memory processes can be easily confused. In this paper, using several generating models like the mean-plus-noise model, the STOchastic Permanent BREAK model, the Markov switching model, the TAR model, the sign model and the Structural CHange model (SCH) and several estimation techiques like the GPH technique, the Exact Local Whittle (ELW) and the Wavelet methods, we show that, if the answer is quite simple in some cases, it can be mitigate in other cases. Using French and American inflation rates, we show that these series cannot be characterized by the same class of models. The main result of this study suggests that estimating the long memory parameter without taking account existence of breaks in the data sets may lead to misspecification and to overestimate the true parameter. |
| Keywords: | Structural breaks models, spurious long memory behavior, inflation series. |
| Date: | 2012–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00722032&r=ets |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Philippe De Peretti (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne) |
| Abstract: | In this paper, we present a procedure that tests for the null of time-homogeneity of the first two moments of a time-series. Whereas the literature dedicated to structural breaks testing procedures often focuses on one kind of alternative, i.e. discrete shifts or smooth transition, our procedure is designed to deal with a broader alternative including i) discrete shifts, ii) smooth transition, iii) time-varying moments, iv) probability-driven breaks, v) GARCH or Stochastic Volatility Models for the variance. Our test uses the recently introduced maximum entropy bootstrap, designed to capture both time-dependency and time-heterogeneity. Running simulations, our procedure appears to be quite powerful. To some extent, our paper is an extension of Heracleous, Koutris and Spanos (2008). |
| Keywords: | Time-homogeneity; maximum entropy bootstrap |
| Date: | 2012–07–27 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00721327&r=ets |
| By: | Javier Hualde (Departamento de Economía-UPNA) |
| Abstract: | This paper proposes an estimator of the cointegrating rank of a potentially cointegrated multivariate fractional process. Our setting is very flexible, allowing the individual observable processes to have different integration orders. The proposed method is automatic and can be also employed to infer the dimensions of possible cointegrating subspaces, which are characterized by special directions in the cointegrating space which generate cointegrating errors with smaller integration orders, increasing the “achievement” of the cointegration analysis. A Monte Carlo experiment of finite sample performance and an empirical analysis are included. |
| Keywords: | fractional integration, cointegrating rank, cointegrating space and subspaces. |
| JEL: | C32 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:nav:ecupna:1205&r=ets |
| By: | Karlsson, Sune (Department of Business, Economics, Statistics and Informatics) |
| Abstract: | Prepared for the Handbook of Economic Forecasting, vol 2 <p> This chapter reviews Bayesian methods for inference and forecasting with VAR models. Bayesian inference and, by extension, forecasting depends on numerical methods for simulating from the posterior distribution of the parameters and spe- cial attention is given to the implementation of the simulation algorithm. |
| Keywords: | Markov chain Monte Carlo; Structural VAR; Cointegration; Condi- tional forecasts; Time-varying parameters; Stochastic volatility; Model selection; Large VAR |
| JEL: | C11 C32 C53 |
| Date: | 2012–08–04 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:oruesi:2012_012&r=ets |
| By: | Falk Brauning (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam) |
| Abstract: | We explore a new approach to the forecasting of macroeconomic variables based on a dynamic factor state space analysis. Key economic variables are modeled jointly with principal components from a large time series panel of macroeconomic indicators using a multivariate unobserved components time series model. When the key economic variables are observed at a low frequency and the panel of macroeconomic variables is at a high frequency, we can use our approach for both nowcasting and forecasting purposes. Given a dynamic factor model as the data generation process, we provide Monte Carlo evidence for the finite-sample justification of our parsimonious and feasible approach. We also provide empirical evidence for a U.S. macroeconomic dataset. The unbalanced panel contain quarterly and monthly variables. The forecasting accuracy is measured against a set of benchmark models. We conclude that our dynamic factor state space analysis can lead to higher forecasting precisions when panel size and time series dimensions are moderate. |
| Keywords: | Kalman filter; Mixed frequency; Nowcasting; Principal components; State space model; Unobserved Components Time Series Model |
| JEL: | C33 C53 E17 |
| Date: | 2012–04–20 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120042&r=ets |
| By: | Francisco Blasques (VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam); Andre Lucas (VU University Amsterdam) |
| Abstract: | We characterize the dynamic properties of Generalized Autoregressive Score (GAS) processes by identifying regions of the parameter space that imply stationarity and ergodicity. We show how these regions are affected by the choice of parameterization and scaling, which are key features of GAS models compared to other observation driven models. The Dudley entropy integral is used to ensure the non-degeneracy of such regions. Furthermore, we show how to obtain bounds for these regions in models for time-varying means, variances, or higher-order moments. |
| Keywords: | Dudley integral; Durations; Higher-order models; Nonlinear dynamics; Time-varying parameters; Volatility |
| JEL: | C13 C22 C58 |
| Date: | 2012–06–22 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120059&r=ets |
| By: | Siem Jan Koopman (VU University Amsterdam); Thuy Minh Nguyen (Deutsche Bank, London) |
| Abstract: | We show that efficient importance sampling for nonlinear non-Gaussian state space models can be implemented by computationally efficient Kalman filter and smoothing methods. The result provides some new insights but it primarily leads to a simple and fast method for efficient importance sampling. A simulation study and empirical illustration provide some evidence of the computational gains. |
| Keywords: | Kalman filter; Monte Carlo maximum likelihood; Simulation smoothing |
| JEL: | C32 C51 |
| Date: | 2012–01–12 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120008&r=ets |
| By: | Geert Mesters (Netherlands Institute for the Study of Crime and Law Enforcement, and VU University Amsterdam); Siem Jan Koopman (VU University Amsterdam) |
| Abstract: | An exact maximum likelihood method is developed for the estimation of parameters in a nonlinear non-Gaussian dynamic panel data model with unobserved random individual-specific and time-varying effects. We propose an estimation procedure based on the importance sampling technique. In particular, a sequence of conditional importance densities is derived which integrates out all random effects from the joint distribution of endogenous variables. We disentangle the integration over both the cross-section and the time series dimensions. The estimation method facilitates the flexible modeling of large panels in both dimensions. We evaluate the method in a Monte Carlo study for dynamic panel data models with observations from the Student's <i>t</i> distribution. We finally present an extensive empirical study into the interrelationships between the economic growth figures of countries listed in the Penn World Tables. It is shown that our dynamic panel data model can provide an insightful analysis of common and heterogeneous features in world-wide economic growth. |
| Keywords: | Panel data; Non-Gaussian; Importance sampling; Random effects; Student's t; Economic growth |
| JEL: | C33 C51 F44 |
| Date: | 2012–02–06 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120009&r=ets |
| By: | Yves Dominicy (Université libre de Bruxelles); Siegfried Hörmann (Université libre de Bruxelles); David Veredas (Université libre de Bruxelles); Hiroaki Ogata (Waseda University) |
| Abstract: | We establish the asymptotic normality of marginal sample quantiles for S-mixing vector stationary processes. S-mixing is a recently introduced and widely applicable notion of dependence. Results of some Monte Carlo simulations are given |
| Keywords: | Quantiles, S-mixing |
| JEL: | C01 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:1228&r=ets |
| By: | Lorenzo Ricci (ECARES); David Veredas (ECARES) |
| Abstract: | We introduce TailCoR, a new measure for tail correlation that is a function of linear and non-linear correlations, the latter characterized by the tail index. TailCoR can be exploited in a number of financial applications, such as portfolio selection where the investor faces risks of a linear and tail nature. Moreover, it has the following advantages: i) it is exact for any probability level as it is not based on tail asymptotic arguments (contrary to tail dependence coefficients), ii) it can be used in all tail scenarios (fatter, equal to or thinner than those of the Gaussian distribution), iii), it is distribution free, and iv) it is simple and no optimizations are needed. Monte Carlo simulations and calibrations reveal its goodness in finite samples. An empirical illustration using a panel of Euro area sovereign bonds shows that prior to 2009 linear correlations were in the vicinity of one and non-linear correlations were inexistent. Since the beginning of the crisis the linear correlations have decreased sharply, and non-linear correlations appeared and increased significantly in 2010-2011 |
| Keywords: | Tail correlation, quantile, ellipticity, risk |
| JEL: | C32 C51 G01 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:1227&r=ets |
| By: | Julieta Fuentes; Pilar Poncela; Julio Rodríguez |
| Abstract: | Factor models have been applied extensively for forecasting when high dimensional datasets are available. In this case, the number of variables can be very large. For instance, usual dynamic factor models in central banks handle over 100 variables. However, there is a growing body of the literature that indicates that more variables do not necessarily lead to estimated factors with lower uncertainty or better forecasting results. This paper investigates the usefulness of partial least squares techniques, that take into account the variable to be forecasted when reducing the dimension of the problem from a large number of variables to a smaller number of factors. We propose different approaches of dynamic sparse partial least squares as a means of improving forecast efficiency by simultaneously taking into account the variable forecasted while forming an informative subset of predictors, instead of using all the available ones to extract the factors. We use the well-known Stock and Watson database to check the forecasting performance of our approach. The proposed dynamic sparse models show a good performance in improving the efficiency compared to widely used factor methods in macroeconomic forecasting. |
| Keywords: | Factor Models, Forecasting, Large Datasets, Partial Least Squares, Sparsity, Variable Selection |
| Date: | 2012–08 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws122216&r=ets |
| By: | Delgado, Miguel A.; Velasco, Carlos |
| Abstract: | We propose an asymptotically distribution-free transform of the sample autocorrelations of residuals in general parametric time series models, possibly nonlinear in variables. The residuals autocorrelation function is the basic model checking tool in time series analysis, but it is not useful when its distribution is incorrectly approximated because the effects of parameter estimation and/or higher-order serial dependence have not been taken into account. The limiting distribution of the residuals sample autocorrelations may be difficult to derive, particularly when the underlying innovations are uncorrelated but not independent. In contrast, our proposal is easily implemented in fairly general contexts and the resulting transformed sample autocorrelations are asymptotically distributed as independent standard normals when innovations are uncorrelated, providing an useful and intuitive device for time series model checking in the presence of estimated parameters. We also discuss in detail alternatives to the classical Box–Pierce test, showing that our transform entails no efficiency loss under Gaussianity in the direction of MA and AR departures from the white noise hypothesis, as well as alternatives to Bartlett’s Tp-process test. The finite-sample performance of the procedures is examined in the context of a Monte Carlo experiment for the new goodness-of-fit tests discussed in the article. The proposed methodology is applied to modeling the autocovariance structure of the well-known chemical process temperature reading data already used for the illustration of other statistical procedures. Additional technical details are included in a supplemental material online. |
| Keywords: | Higher-order serial dependence; Local alternatives; Long memory; Model checking; Nonlinear in variables models; Recursive residuals; |
| Date: | 2012–01–24 |
| URL: | http://d.repec.org/n?u=RePEc:ner:carlos:info:hdl:10016/15032&r=ets |
| By: | Taeyoung Doh; Michael Connolly |
| Abstract: | To capture the evolving relationship between multiple economic variables, time variation in either coefficients or volatility is often incorporated into vector autoregressions (VARs). However, allowing time variation in coefficients or volatility without restrictions on their dynamic behavior can increase the number of parameters too much, making the estimation of such a model practically infeasible. For this reason, researchers typically assume that time-varying coefficients or volatility are not directly observed but follow random processes which can be characterized by a few parameters. The state space representation that links the transition of possibly unobserved state variables with observed variables is a useful tool to estimate VARs with time-varying coefficients or stochastic volatility. ; In this paper, we discuss how to estimate VARs with time-varying coefficients or stochastic volatility using the state space representation. We focus on Bayesian estimation methods which have become popular in the literature. As an illustration of the estimation methodology, we estimate a time-varying parameter VAR with stochastic volatility with the three U.S. macroeconomic variables including inflation, unemployment, and the long-term interest rate. Our empirical analysis suggests that the recession of 2007-2009 was driven by a particularly bad shock to the unemployment rate which increased its trend and volatility substantially. In contrast, the impacts of the recession on the trend and volatility of nominal variables such as the core PCE inflation rate and the ten-year Treasury bond yield are less noticeable. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedkrw:rwp12-04&r=ets |
| By: | Mark J. Jensen; John M. Maheu |
| Abstract: | This paper proposes a Bayesian nonparametric modeling approach for the return distribution in multivariate GARCH models. In contrast to the parametric literature, the return distribution can display general forms of asymmetry and thick tails. An infinite mixture of multivariate normals is given a flexible Dirichlet process prior. The GARCH functional form enters into each of the components of this mixture. We discuss conjugate methods that allow for scale mixtures and nonconjugate methods, which provide mixing over both the location and scale of the normal components. MCMC methods are introduced for posterior simulation and computation of the predictive density. Bayes factors and density forecasts with comparisons to GARCH models with Student-t innovations demonstrate the gains from our flexible modeling approach. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedawp:2012-09&r=ets |
| By: | Rosen Azad Chowdhury; Bill Russell |
| Abstract: | The effects of structural breaks in dynamic panels are more complicated than in time series models as the bias can be either negative or positive. This paper focuses on the effects of mean shifts in otherwise stationary processes within an instrumental variable panel estimation framework. We show the sources of the bias and a Monte Carlo analysis calibrated on United States bank lending data demonstrates the size of the bias for a range of auto-regressive parameters. We also propose additional moment conditions that can be used to reduce the biases caused by shifts in the mean of the data. |
| Keywords: | Dynamic panel estimators, mean shifts/structural breaks, Monte Carlo Simulation |
| JEL: | C23 C22 C26 |
| Date: | 2012–06 |
| URL: | http://d.repec.org/n?u=RePEc:dun:dpaper:268&r=ets |
| By: | Zhu, Ke |
| Abstract: | This paper investigates the joint limiting distribution of the residual autocorrelation functions and the absolute residual autocorrelation functions of ARMA-GARCH model. This leads a mixed portmanteau test for diagnostic checking of the ARMA-GARCH model fitted by using the quasi-maximum exponential likelihood estimation approach in Zhu and Ling (2011). Simulation studies are carried out to examine our asymptotic theory, and assess the performance of this mixed test and other two portmanteau tests in Li and Li (2008). A real example is given. |
| Keywords: | ARMA-GARCH model; LAD estimator; mixed portmanteau test; model diagnostics; quasi-maximum exponential likelihood estimator |
| JEL: | C10 C52 |
| Date: | 2012–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:40382&r=ets |
| By: | Galimberti, Jaqueson K. |
| Abstract: | Assuming an ARIMA(p,I,q) model represents the data, I show how optimal forecasts can be computed and derive general expressions for its main properties of interest. Namely, I present stepwise derivations of expressions for the variances of forecast errors, and the covariances between them at arbitrary forecasting horizons. Matricial forms for these expressions are also presented to facilitate computational implementation. |
| Keywords: | optimal forecasts; forecasts properties; ARIMA |
| JEL: | C53 |
| Date: | 2012–01–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:40303&r=ets |
| By: | Bildirici, Melike; Ersin, Özgür |
| Abstract: | Recently, Donaldson and Kamstra (1997) proposed a class of NN-GARCH models which are extended to a class of NN-GARCH family by Bildirici and Ersin (2009). The study aims to analyze the nonlinear behavior and leptokurtic distribution in petrol prices by utilizing a newly developed family of econometric models that deal with these concepts by benefiting from both LSTAR type and ANN based nonlinearity. With this purpose, the study proposed several LSTAR-GARCH-NN family models. It is noted that the multilayer perceptron (MLP) neural network and LSTAR models have significant architectural similarities. Accordingly, linear GARCH, fractionally integrated FI-GARCH, asymmetric power APGARCH and fractionally integrated asymmetric power APGARCH models are augmented with a family of Neural Network models. The study has following contributions: i. STAR-GARCH and LSTAR-GARCH are extended to their fractionally integrated asymmetric power versions and STAR-ST-FIGARCH and STAR-ST-APGARCH, STAR-ST-FIAPGARCH models are developed and evaluated. ii. By extending these models with neural networks, LSTAR-LST-GARCH-MLP family models are developed and investigated. These models benefit from LSTAR type nonlinearity and NN based nonlinear NN-GARCH models to capture time varying volatility and nonlinearity in petrol prices. ANN augmented versions of LSTAR-LST-GARCH models are as follows: LSTAR-LST-GARCH-MLP, LSTAR-LST-FIGARCH-MLP, LSTAR-LST-APGARCH-MLP and LSTAR-LST-FIAPGARCH-MLP. Empirical findings are collected as follows. i. To model petrol prices, fractionally integrated and asymmetric power versions provided improvements among the GARCH family models in terms of forecasting. ii. LSTAR-LST-GARCH model family is promising and show significant gains in out-of-sample forecasting. iii. MLP-GARCH family provided similar results with the LSTAR-LST-GARCH family models, except for the MLP-FIGARCH and MLP-FIAPGARCH models. iv. Volatility clustering, asymmetry and nonlinearity characteristics of petrol prices are captured most efficiently with the LSTAR-LST-GARCH-MLP models benefiting from forecasting capabilities of neural network techniques, whereas, among the newly developed models, LSTAR-LST-APGARCH-MLP model provided the best performance overall. |
| Keywords: | Volatility; Stock Returns; ARCH; Fractional Integration; MLP; Neural Networks |
| JEL: | F30 C45 C01 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:40330&r=ets |