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on Econometric Time Series |
| By: | Carlos Medel; Pablo Pincheira |
| Abstract: | We analyse the forecasting performance of several strategies when estimating the near-unity AR(1) model. We focus on the Andrews’ (1993) exact median-unbiased estimator (BC), the OLS estimator and the driftless random walk (RW). We also explore two pairwise combinations between these strategies. We do this to investigate whether BC helps in reducing forecast errors. Via simulations, we find that BC forecasts typically outperform OLS forecasts. When BC is compared to the RW we obtain mixed results, favouring the latter while the persistence of the true process increases. Interestingly, we find that the combination of BC-RW performs well in a near-unity scheme. |
| Date: | 2015–09 |
| URL: | http://d.repec.org/n?u=RePEc:chb:bcchwp:768&r=ets |
| By: | S.N. Lahiri; Peter M. Robinson |
| Abstract: | Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a d d-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are established for the cases of positive strong dependence, short range dependence, and negative dependence. We provide approximations to asymptotic variances that reveal differential rates of convergence under the three types of dependence. Further, in contrast to the one dimensional (i.e., the time series) case, it is shown that the form of the asymptotic variance in dimensions d>1 d>1 critically depends on the geometry of the sampling region under positive strong dependence and under negative dependence and that there can be non-trivial edge-effects under negative dependence for d>1 d>1. Precise conditions for the presence of edge effects are also given. |
| Keywords: | central limit theorem; edge effects; increasing domain asymptotics; long memory; negative dependence; positive dependence; sampling region; spatial lattice |
| JEL: | J1 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:65331&r=ets |
| By: | Bognanni, Mark (Federal Reserve Bank of Cleveland); Herbst, Edward (Board of Governors of the Federal Reserve System (U.S.)) |
| Abstract: | Vector autoregressions with Markov-switching parameters (MS-VARs) fit the data better than do their constant-parameter predecessors. However, Bayesian inference for MS-VARs with existing algorithms remains challenging. For our first contribution, we show that Sequential Monte Carlo (SMC) estimators accurately estimate Bayesian MS-VAR posteriors. Relative to multi-step, model-specific MCMC routines, SMC has the advantages of generality, parallelizability, and freedom from reliance on particular analytical relationships between prior and likelihood. For our second contribution, we use SMC's flexibility to demonstrate that the choice of prior drives the key empirical finding of Sims, Waggoner, and Zha (2008) as much as does the data. |
| Keywords: | Bayesian Analysis; Regime-Switching Models; Sequential Monte Carlo; Vector Autoregressions |
| JEL: | C11 C18 C32 C52 E3 E4 E5 |
| Date: | 2015–12–18 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2015-116&r=ets |
| By: | Aknouche, Abdelhakim |
| Abstract: | A unified quasi-maximum likelihood (QML) estimation theory for stationary and nonstationary simple Markov bilinear (SMBL) models is proposed. Such models may be seen as generalized random coefficient autoregressions (GRCA) in which the innovation and the random coefficient processes are fully correlated. It is shown that the QML estimate (QMLE) for the SMBL model is always asymptotically Gaussian without assuming strict stationarity, meaning that there is no knife edge effect. The asymptotic variance of the QMLE is different in the stationary and nonstationary cases but is consistently estimated using the same estimator. A perhaps surprising result is that in the nonstationary domain, all SMBL parameters are consistently estimated in contrast with unstable GARCH and GRCA models where the QMLE of the conditional variance intercept is inconsistent. As a result, strict stationarity testing for the SMBL is studied. Simulation experiments and a real application to strict stationarity testing for some financial stock returns illustrate the theory in finite samples. |
| Keywords: | Markov bilinear process, random coefficient process, stability, instability, Quasi-maximum likelihood, knife edge effect, strict stationarity testing. |
| JEL: | C10 C13 C18 C19 |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69572&r=ets |
| By: | Ledenyov, Dimitri O.; Ledenyov, Viktor O. |
| Abstract: | Article considers a research problem on the precise measurement of the macroeconomic variables changes in the time domain in the macroeconomics science. We propose to use the three dimensional (3D) wave diagram in the macroeconomics science for the first time, aiming to accurately characterize and to clearly visualize the GIP(t)/GDP(t)/GNP(t)/PPP(t) dependences changes in the time domain. We explain that the three dimensional (3D) wave diagram in the macroeconomics science has been created, using the theory on the continuous-time waves with the rotating polarization vector in the electrodynamics science. We show that the three dimensional (3D) wave diagram in the macroeconomics science can be used to accurately characterize and finely display the GIP(t), GDP(t), GNP(t), PPP(t) dependences changes in the time domain in the two possible cases: 1) the continuous-time waves of GIP(t), GDP(t), GNP(t), PPP(t) and 2) the discrete-time waves of GIP(t), GDP(t), GNP(t), PPP(t). We conclude that an introduction of the three dimensional (3D) wave diagram in the macroeconomics science can help to solve a challenging research problem on the precise measurement of the macroeconomic variables changes in the time domain. |
| Keywords: | three dimensional (3D) wave diagram, dependence of general information product on time GIP(t), dependence of general domestic product on time GDP(t), dependence of general national product on time GDP(t), dependence of purchase power parity on time PPP(t), continuous-time signals, spectrum analysis of continuous-time signals, amplitude / frequency / wavelength / period / phase of continuous-time signal, mixing / harmonics / nonlinearities of continuous-time signals, continuous-time waves with rotating polarization vector, continuous-time signal generators, discrete-time signals, spectrum analysis of discrete-time signals, amplitude / frequency / wavelength / period / phase of discrete-time digital signal, mixing / harmonics / nonlinearities of discrete-time digital signals, Ledenyov discrete-time digital waves, discrete-time digital signals generators, Juglar fixed investment cycle, Kitchin inventory cycle, Kondratieff long wave cycle, Kuznets infrastructural investment cycle, nonlinear dynamic economic system, economy of scale and scope, macroeconomics science, econometrics science, electrodynamics science, econophysics science |
| JEL: | E0 E01 E17 E20 E27 E3 E30 E32 E37 E50 E58 E60 O3 O33 |
| Date: | 2016–02–17 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:69576&r=ets |
| By: | Francisco Blasques (VU University Amsterdam, the Netherlands); Paolo Gorgi (VU University Amsterdam, the Netherlands, University of Padua, Italy); Siem Jan Koopman (VU University Amsterdam, the Netherlands, Aarhus University, Denmark); Olivier Wintenberger (University of Copenhagen, Denmark, Sorbonne Universités, UPMC University Paris, Sorbonne Universities, France) |
| Abstract: | We revisit Wintenberger (2013) on the continuous invertibility of the EGARCH(1,1) model. We note that the definition of continuous invertibility adopted in Wintenberger (2013) may not always be sufficient to deliver strong consistency of the QMLE. We also take the opportunity to provide other small clarifications and additions. |
| Keywords: | invertibility, quasi-maximum likelihood estimator, volatility models |
| JEL: | C01 C22 C51 |
| Date: | 2015–12–11 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150131&r=ets |
| By: | Pablo Guerron-quintana (Federal Reserve Bank of Philadelphia); Atsushi Inoue (Vanderbilt University); Lutz Kilian (University of Michigan) |
| 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 asymptotic 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 ensure 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: | C3 C5 |
| Date: | 2014–12–01 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:vuecon-14-00014&r=ets |