
on Econometric Time Series 
By:  Carlos Medel; Pablo Pincheira 
Abstract:  We analyse the forecasting performance of several strategies when estimating the nearunity AR(1) model. We focus on the Andrews’ (1993) exact medianunbiased 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 BCRW performs well in a nearunity 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 ddimensional lattice. This region need not be rectangular, but can be irregularlyshaped. 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 nontrivial edgeeffects 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 Markovswitching parameters (MSVARs) fit the data better than do their constantparameter predecessors. However, Bayesian inference for MSVARs with existing algorithms remains challenging. For our first contribution, we show that Sequential Monte Carlo (SMC) estimators accurately estimate Bayesian MSVAR posteriors. Relative to multistep, modelspecific 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; RegimeSwitching 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:2015116&r=ets 
By:  Aknouche, Abdelhakim 
Abstract:  A unified quasimaximum 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, Quasimaximum 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 continuoustime 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 continuoustime waves of GIP(t), GDP(t), GNP(t), PPP(t) and 2) the discretetime 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), continuoustime signals, spectrum analysis of continuoustime signals, amplitude / frequency / wavelength / period / phase of continuoustime signal, mixing / harmonics / nonlinearities of continuoustime signals, continuoustime waves with rotating polarization vector, continuoustime signal generators, discretetime signals, spectrum analysis of discretetime signals, amplitude / frequency / wavelength / period / phase of discretetime digital signal, mixing / harmonics / nonlinearities of discretetime digital signals, Ledenyov discretetime digital waves, discretetime 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, quasimaximum 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 Guerronquintana (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 VARbased 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:vuecon1400014&r=ets 