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on Econometric Time Series |
| By: | Nicolas Debarsy (CERPE - Centre de Recherches en Economie Régionale et Politique Economique - Université de Namur); Vincenzo Verardi (European Centre for Advanced Research in Economics and Statistics (ECARES) - Université Libre de Bruxelles, CRED - Centre de Recherche en Economie du Développement - Université de Namur) |
| Abstract: | In spatial autoregressive models, the functional form of autocorrelation is assumed to be linear. In this paper, we propose a simple semiparametric procedure, based on Yatchew's (1998) partial linear least squares, that relaxes this restriction. Simple simulations show that this model outperforms traditional SAR estimation when nonlinearities are present. We then apply the methodology on real data to test for the spatial pattern of voting for independent candidates in US presidential elections. We find that in some counties, votes for “third candidates” are non-linearly related to votes for “third candidates” in neighboring counties, which pleads for strategic behavior. |
| Keywords: | Spatial econometrics; semiparametric estimations |
| Date: | 2010–01–13 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00446574_v1&r=ets |
| By: | Gabriele Fiorentini (Università di Firenze); Enrique Sentana (CEMFI) |
| Abstract: | We derive computationally simple score tests of serial correlation in the levels and squares of common and idiosyncratic factors in static factor models. The implicit orthogonality conditions resemble the orthogonality conditions resemble the orthogonality conditions of models with observed factors but the weighting matrices reflect their unobservability. We derive more powerful tests for elliptically symmetric distributions, which can be either parametrically or semiparametrically specified, and robustify the Gaussian tests against general nonnormality. Our Monte Carlo exercises assess the finite sample reliability and power of our proposed tests, and compare them to other existing procedures. Finally, we apply our methods to monthly US stock returns. |
| Keywords: | ARCH, financial returns, Kalman filter, LM tests, predictability. |
| JEL: | C32 C13 C12 C14 C16 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2009_0912&r=ets |
| By: | Mika Meitz (Koc University); Pentti Saikkonen (University of Helsinki) |
| Abstract: | This note studies the geometric ergodicity of nonlinear autoregressive models with conditionally heteroskedastic errors. A nonlinear autoregression of order p (AR(p)) with the conditional variance specified as the conventional linear autoregressive conditional heteroskedasticity model of order q (ARCH(q)) is considered. Conditions under which the Markov chain representation of this nonlinear AR– ARCH model is geometrically ergodic and has moments of known order are provided. The obtained results complement those of Liebscher [Journal of Time Series Analysis, 26 (2005), 669–689] by showing how his approach based on the concept of the joint spectral radius of a set of matrices can be extended to establish geometric ergodicity in nonlinear autoregressions with conventional ARCH(q) errors. |
| Keywords: | Nonlinear Autoregression, Autoregressive Conditional Heteroskedasticity, Nonlinear Time Series Models, Geometric Ergodicity, Mixing, Strict Stationarity, Existence of Moments, Markov Models |
| JEL: | C10 C22 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:koc:wpaper:1003&r=ets |
| By: | Mika Meitz (Koc University); Pentti Saikkonen (University of Helsinki) |
| Abstract: | This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors. |
| Keywords: | Nonlinear Autoregression, Generalized Autoregressive Conditional Heteroskedasticity, Nonlinear Time Series Models, Quasi-Maximum Likelihood Estimation, Strong Consistency, Asymptotic Normality |
| JEL: | C13 C22 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:koc:wpaper:1002&r=ets |
| By: | Chirok Han (Korea University); Peter C.B. Phillips (Cowles Foundation, Yale University); Donggyu Sul (University of Texas Dallas) |
| Abstract: | While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly mechanism for preserving information and signal strength in autoregressions with some very desirable properties. In first order autoregression, a partially aggregated estimator based on moment conditions in differences is shown to have a limiting normal distribution which holds uniformly in the autoregressive coefficient rho including stationary and unit root cases. The rate of convergence is root of n when |rho| < 1 and the limit distribution is the same as the Gaussian maximum likelihood estimator (MLE), but when rho = 1 the rate of convergence to the normal distribution is within a slowly varying factor of n. A fully aggregated estimator is shown to have the same limit behavior in the stationary case and to have nonstandard limit distributions in unit root and near integrated cases which reduce both the bias and the variance of the MLE. This result shows that it is possible to improve on the asymptotic behavior of the MLE without using an artificial shrinkage technique or otherwise accelerating convergence at unity at the cost of performance in the neighborhood of unity. |
| Keywords: | Aggregating information, Asymptotic normality, Bias Reduction, Differencing, Efficiency, Full aggregation, Maximum likelihood estimation |
| JEL: | C22 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1746&r=ets |
| By: | Yixiao Sun (Dept. of Economics, UC, San Diego); Peter C.B. Phillips (Cowles Foundation, Yale University); Sainan Jin (School of Economics, Singapore Management University) |
| Abstract: | Using the power kernels of Phillips, Sun and Jin (2006, 2007), we examine the large sample asymptotic properties of the t-test for different choices of power parameter (rho). We show that the nonstandard fixed-rho limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-rho limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also second-order correct under the large-rho asymptotics. As a further contribution, we propose a new practical procedure for selecting the test-optimal power parameter that addresses the central concern of hypothesis testing: the selected power parameter is test-optimal in the sense that it minimizes the type II error while controlling for the type I error. A plug-in procedure for implementing the test-optimal power parameter is suggested. Simulations indicate that the new test is as accurate in size as the nonstandard test of Kiefer and Vogelsang (2002a, 2002b; KV), and yet it does not incur the power loss that often hurts the performance of the latter test. The new test therefore combines the advantages of the KV test and the standard (MSE optimal) HAC test while avoiding their main disadvantages (power loss and size distortion, respectively). The results complement recent work by Sun, Phillips and Jin (2008) on conventional and bT HAC testing. |
| Keywords: | Asymptotic expansion, HAC estimation, Long run variance, Loss function, Optimal smoothing parameter, Power kernel, Power maximization, Size control, Type I error, Type II error |
| JEL: | C13 C14 C22 C51 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1749&r=ets |
| By: | Roberto Leon-Gonzalez; Fuyu Yang |
| Abstract: | We develop Bayesian techniques for estimation and model comparison in a novel Generalised Stochastic Unit Root (GSTUR) model. This allows us to investigate the presence of a deterministic time trend in economic series, while allowing the degree of persistence to change over time. In particular the model allows for shifts from stationarity I(0) to nonstationarity I(1) or vice versa. The empirical analysis demonstrates that the GSTUR model provides new insights on the properties of some macroeconomic time series such as stock market indices, in ation and ex- change rates. |
| Keywords: | Stochastic Unit Root, MCMC, Bayesian |
| JEL: | C11 C32 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2010-006&r=ets |
| By: | Christian Gouriéroux; Peter C. B. Phillips; Jun Yu (Singapore Management University) |
| Abstract: | It is well-known that maximum likelihood (ML) estimation of the autoregressive parameter of a dynamic panel data model with .xed e¤ects is inconsistent under .xed time series sample size (T) and large cross section sample size (N) asymptotics. The estimation bias is particularly relevant in practical applications when T is small and the autoregressive parameter is close to unity. The present paper proposes a general, computationally inexpensive method of bias reduction that is based on indirect inference (Gouriéroux et al., 1993), shows unbiasedness and analyzes efficiency. The method is implemented in a simple linear dynamic panel model, but has wider applicability and can, for instance, be easily ex-tended to more complicated frameworks such as nonlinear models. Monte Carlo studies show that the proposed procedure achieves substantial bias reductions with only mild increases in variance, thereby substantially reducing root mean square errors. The method is compared with certain consistent estimators and bias-corrected ML estimators previously proposed in the literature and is shown to have superior .nite sample properties to GMM and the bias-corrected ML of Hahn and Kuersteiner (2002). Finite sample performance is compared with that of a recent estimator proposed by Han and Phillips (2005). |
| Keywords: | Autoregression, Bias reduction, Dynamic panel, Fixed e¤ects Indirect inference |
| JEL: | C33 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:eab:develo:1508&r=ets |
| By: | Peter C. B. Phillips; Jun Yu (Singapore Management University) |
| Abstract: | This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention has been devoted to the development of methods designed to approximate the likelihood. These approaches range from crude Euler-type approximations and higher order stochastic Taylor series expansions to more complex polynomial-based expansions and infill approximations to the likelihood based on a continuous time data record. The methods are discussed, their properties are outlined and their relative finite sample performance compared in a simulation experiment with the nonlinear CIR diffusion model, which is popular in empirical finance. Bias correction methods are also considered and particular attention is given to jackknife and indirect inference estimators. The latter retains the good asymptotic properties of ML estimation while removing finite sample bias. This method demonstrates superior performance in finite samples. |
| Keywords: | Maximum likelihood, Transition density, Discrete sampling, Continuous record, Realized volatility, Bias reduction, Jackknife, Indirect inference |
| JEL: | C22 C32 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:eab:develo:1558&r=ets |
| By: | Liangjun Su; Zhenlin Yang (Singapore Management University) |
| Abstract: | We propose an instrumental variable quantile regression (IVQR) estimator for spatial autoregressive (SAR) models. Like the GMM estimators of Lin and Lee (2006) and Kelejian and Prucha (2006), the IVQR estimator is robust against heteroscedasticity. Unlike the GMM estimators, the IVQR estimator is also robust against outliers and requires weaker moment conditions. More importantly, it allows us to characterize the heterogeneous impact of variables on different points (quantiles) of a response distribution. We derive the limiting distribution of the new estimator. Simulation results show that the new estimator performs well in finite samples at various quantile points. In the special case of median restriction, it outperforms the conventional QML estimator without taking into account of heteroscedasticity in the errors; it also outperforms the GMM estimators with or without considering the heteroscedasticity. |
| Keywords: | Spatial Autoregressive Model, Quantile Regression, Instrumental Variable, Quasi Maximum Likelihood, GMM, Robustness |
| JEL: | C13 C21 C51 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:eab:develo:1563&r=ets |
| By: | Koop, Gary; Korobilis, Dimitris |
| Abstract: | Macroeconomic practitioners frequently work with multivariate time series models such as VARs, factor augmented VARs as well as time-varying parameter versions of these models (including variants with multivariate stochastic volatility). These models have a large number of parameters and, thus, over-parameterization problems may arise. Bayesian methods have become increasingly popular as a way of overcoming these problems. In this monograph, we discuss VARs, factor augmented VARs and time-varying parameter extensions and show how Bayesian inference proceeds. Apart from the simplest of VARs, Bayesian inference requires the use of Markov chain Monte Carlo methods developed for state space models and we describe these algorithms. The focus is on the empirical macroeconomist and we offer advice on how to use these models and methods in practice and include empirical illustrations. A website provides Matlab code for carrying out Bayesian inference in these models. |
| Keywords: | Empirical macroeconometrics; Bayesian estimation; MCMC; vector autoregressions; factor models; time-varying parameters |
| JEL: | C51 C53 C50 C52 E58 C12 C87 E52 C15 C11 |
| Date: | 2009–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:20125&r=ets |