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on Econometric Time Series |
| By: | Alexander Karalis Isaac (Birkbeck, University of London; University of Warwick) |
| Abstract: | I derive the first four moments of the Markov-switching VAR and use the results to reconsider the conflict between the Great Moderation and Financial Crisis literatures. In contrast to the linear model, a three-regime Markov-switching model captures the skewness and kurtosis of US GDP growth 1954-2011. However, a specification with four regimes splits the sample in 1984, a result familiar from the Great Moderation literature. The higher moments of the MSVAR, not previously studied in the literature, reveal the Great Moderation to be a trade off between variance and kurtosis. U.S. GDP growth shifts from an almost Gaussian structure 1954-84 into a pattern with low variance, negative skewness and high kurtosis. The Markov-switching model which splits the sample accurately captures the new moment structure. |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:bbk:bbkcam:1405&r=ets |
| By: | Guerron-Quintana, Pablo; Inoue, Atsushi; Kilian, Lutz |
| Abstract: | One of the leading methods of estimating the structural parameters of DSGE mod- els is the VAR-based impulse response matching estimator. The existing asympotic theory for this estimator does not cover situations in which the number of impulse response parameters exceeds the number of VAR model parameters. Situations in which this order condition is violated arise routinely in applied work. We establish the consistency of the impulse response matching estimator in this situation, we derive its asymptotic distribution, and we show how this distribution can be approximated by bootstrap methods. Our methods of inference remain asymptotically valid when the order condition is satisfied, regardless of whether the usual rank condition for the application of the delta method holds. Our analysis sheds new light on the choice of the weighting matrix and covers both weakly and strongly identified DSGE model parameters. We also show that under our assumptions special care is needed to en- sure the asymptotic validity of Bayesian methods of inference. A simulation study suggests that the frequentist and Bayesian point and interval estimators we propose are reasonably accurate in finite samples. We also show that using these methods may affect the substantive conclusions in empirical work. |
| Keywords: | structural estimation,DSGE,VAR,impulse response,nonstandard asymptotics,bootstrap,weak identification,robust inference |
| JEL: | C32 C52 E30 E50 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cfswop:498&r=ets |
| By: | Hanying Liang (Tongji University); Peter C.B. Phillips (Cowles Foundation, Yale University); Hanchao Wang (Zhejiang University); Qiying Wang (University of Sydney) |
| Abstract: | Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on function space weak convergence. In establishing weak convergence of sample covariances to stochastic integrals, the literature commonly uses martingale and semimartingale structures. While these structures have wide relevance, many applications in econometrics involve a cointegration framework where endogeneity and nonlinearity play a major role and lead to complications in the limit theory. This paper explores weak convergence limit theory to stochastic integral functionals in such settings. We use a novel decomposition of sample covariances of functions of I(1) and I(0) time series that simplifies the asymptotic development and we provide limit results for such covariances when linear process, long memory, and mixing variates are involved in the innovations. The limit results extend earlier findings in the literature, are relevant in many econometric applications, and involve simple conditions that facilitate implementation in practice. A nonlinear extension of FM regression is used to illustrate practical application of the methods. |
| Keywords: | Decomposition, FM regression, Linear process, Long memory, Stochastic integral, Semimartingale, alpha-mixing |
| JEL: | C22 C65 |
| Date: | 2014–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1971&r=ets |
| By: | Peter C.B. Phillips (Cowles Foundation, Yale University) |
| Abstract: | Limit theory is developed for the dynamic panel GMM estimator in the presence of an autoregressive root near unity. In the unit root case, Anderson-Hsiao lagged variable instruments satisfy orthogonality conditions but are well-known to be irrelevant. For a fixed time series sample size (T) GMM is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross section sample size n approaches infinity. But when T approaches infinity, either for fixed n or as n approaches infinity, GMM is square root{T} consistent and its limit distribution is a ratio of random variables that converges to twice a standard Cauchy as n approaches infinity. In this case, the usual instruments are uncorrelated with the regressor but irrelevance does not prevent consistent estimation. The same Cauchy limit theory holds sequentially and jointly as (n,T) approaches infinity with no restriction on the divergence rates of n and T. When the common autoregressive root rho = 1 + c/square root{T} the panel comprises a collection of mildly integrated time series. In this case, the GMM estimator is square root{n}n consistent for fixed T and square root{(nT)} consistent with limit distribution N(0,4) when n, T approaches infinity sequentially or jointly. These results are robust for common roots of the form rho = 1 + c/T^{gamma} for all gamma in (0,1) and joint convergence holds. Limit normality holds but the variance changes when gamma = 1. When gamma > 1 joint convergence fails and sequential limits differ with different rates of convergence. These findings reveal the fragility of conventional Gaussian GMM asymptotics to persistence in dynamic panel regressions. |
| Keywords: | Cauchy limit theory, Dynamic panel, GMM estimation, Instrumental variable, Irrelevant instruments, Panel unit roots, Persistence |
| JEL: | C23 C36 |
| Date: | 2014–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1962&r=ets |
| By: | Pettenuzzo, Davide; Timmermann, Allan G; Valkanov, Rossen |
| Abstract: | We propose a new approach to predictive density modeling that allows for MIDAS effects in both the first and second moments of the outcome and develop Gibbs sampling methods for Bayesian estimation in the presence of stochastic volatility dynamics. When applied to quarterly U.S. GDP growth data, we find strong evidence that models that feature MIDAS terms in the conditional volatility generate more accurate forecasts than conventional benchmarks. Finally, we find that forecast combination methods such as the optimal predictive pool of Geweke and Amisano (2011) produce consistent gains in out-of-sample predictive performance. |
| Keywords: | Bayesian estimation; GDP growth; MIDAS regressions; out-of-sample forecasts; stochastic volatility |
| JEL: | C11 C32 C53 E37 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10160&r=ets |