|
on Econometric Time Series |
| By: | Terence D.Agbeyegbe (Hunter College, CUNY); Elena Goldman (Lubin School of Business, Pace University) |
| Abstract: | This paper shows how a Metropolis-Hastings algorithm with efficient jump can be constructed for the estimation of multiple threshold time series of the U.S. short term interest rates. The results show that interest rates are persistent in a lower regime and exhibit weak mean reversion in the upper regime. For model selection and specication several techniques are used such as marginal likelihood and information criteria, as well as estimation with and without truncation restrictions imposed on thresholds. |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:htr:hcecon:406&r=ets |
| By: | Whitney Newey (Institute for Fiscal Studies and Massachussets Institute of Technology); Richard Smith (Institute for Fiscal Studies and University of Warwick) |
| Abstract: | In an effort to improve the small sample properties of generalized method of moments (GMM) estimators, a number of alternative estimators have been suggested. These include empirical likelihood (EL), continuous updating, and exponential tilting estimators. We show that these estimators share a common structure, being members of a class of generalized empirical likelihood (GEL) estimators. We use this structure to compare their higher order asymptotic properties. We find that GEL has no asymptotic bias due to correlation of the moment functions with their Jacobian, eliminating an important source of bias for GMM in models with endogeneity. We also find that EL has no asymptotic bias from estimating the optimal weight matrix, eliminating a further important source of bias for GMM in panel data models. We give bias corrected GMM and GEL estimators. We also show that bias corrected EL inherits the higher order property of maximum likelihood, that it is higher order asymptotically effcient relative to the other bias corrected estimators. |
| JEL: | C13 C30 |
| Date: | 2003–06 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:wp04/03&r=ets |
| By: | Richard Smith (Institute for Fiscal Studies and University of Warwick) |
| Abstract: | This paper proposes a new class of HAC covariance matrix estimators. The standard HAC estimation method re-weights estimators of the autocovariances. Here we initially smooth the data observations themselves using kernel function based weights. The resultant HAC covariance matrix estimator is the normalised outer product of the smoothed random vectors and is therefore automatically positive semi-definite. A corresponding efficient GMM criterion may also be defined as a quadratic form in the smoothed moment indicators whose normalised minimand provides a test statistic for the over-identifying moment conditions. |
| Keywords: | GMM, HAC Covariance Matrix Estimation, Overidentifying Moments |
| JEL: | C13 C30 |
| Date: | 2004–12 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:wp17/04&r=ets |
| By: | Jean Boivin; Serena Ng |
| Abstract: | Forecasting using `diffusion indices' has received a good deal of attention in recent years. The idea is to use the common factors estimated from a large panel of data to help forecast the series of interest. This paper assesses the extent to which the forecasts are influenced by (i) how the factors are estimated, and/or (ii) how the forecasts are formulated. We find that for simple data generating processes and when the dynamic structure of the data is known, no one method stands out to be systematically good or bad. All five methods considered have rather similar properties, though some methods are better in long horizon forecasts, especially when the number of time series observations is small. However, when the dynamic structure is unknown and for more complex dynamics and error structures such as the ones encountered in practice, one method stands out to have smaller forecast errors. This method forecasts the series of interest directly, rather than the common and idiosyncratic components separately, and it leaves the dynamics of the factors unspecified. By imposing fewer constraints, and having to estimate a smaller number of auxiliary parameters, the method appears to be less vulnerable to misspecification, leading to improved forecasts. |
| JEL: | E37 E47 C3 C53 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:11285&r=ets |
| By: | Nicola Bruti-Liberati (School of Finance and Economics, University of Technology, Sydney); Filippo Martini (Faculty of Information Technology, University of Technology, Sydney); Massimo Piccardi (Faculty of Information Technology, University of Technology, Sydney); Eckhard Platen (School of Finance and Economics, University of Technology, Sydney) |
| Abstract: | Monte Carlo simulation of weak approximations of stochastic differential equations constitutes an intensive computational task. In applications such as finance, for instance, to achieve "real time" execution, as often required, one needs highly efficient implementations of the multi-point distributed random number generator underlying the simulations. In this paper a fast and flexible dedicated hardware solution on a field programmable gate array is presented. A comparative performance analysis between a software-only and the proposed hardware solution demonstrates that the hardware solution is bottleneck-free, retains the flexibility of the software solution and significantly increases the computational efficiency. Moreover, simulations in applications such as economics, insurance, physics, population dynamics, epidemiology, structural mechanics, chemistry and biotechnology can benefit from the obtained speedup. |
| Keywords: | random number generators; random bit generators; hardware implementation; field programmable gate arrays (FPGAs); Monte Carlo simulation; weak Taylor schemes; multi-point distributed random variables |
| JEL: | G10 G13 |
| Date: | 2005–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:rpaper:156&r=ets |
| By: | Nicola Bruti-Liberati (School of Finance and Economics, University of Technology, Sydney); Eckhard Platen (School of Finance and Economics, University of Technology, Sydney) |
| Abstract: | In financial modelling, filtering and other areas the underlying dynamics are often specified via stochastic differential equations (SDEs) of jump-di®usion type. The class of jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently, there is a need for the systematic use of discrete time approximations in corresponding simulations. This paper presents a survey and new results on strong numerical schemes for SDEs of jump-di®usion type. These are relevant for scenario analysis, filtering and hedge simulation in finance. It provides a convergence theorem for the construction of strong approximations of any given order of convergence for SDEs driven by Wiener processes and Poisson random measures. The paper covers also derivative free, drift-implicit and jump adapted strong approximations. For the commutative case particular schemes are obtained. Finally, a numerical study on the accuracy of several strong schemes is presented. |
| Keywords: | jump-diffusion processes; stochastic Taylor expansion; discrete time approximation; simulation; strong convergence |
| JEL: | G10 G13 |
| Date: | 2005–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:rpaper:157&r=ets |
| By: | Joon Y. Park (Department of Economics, Rice University and SKKU); Mototsugu Shintani (Department of Economics, Vanderbilt University) |
| Abstract: | This paper considers the test of a unit root in transitional autoregressive models. In particular, we develop the asymptotic theory of the inf-t test for the null hypothesis of a unit root in a wide class of nonlinear autoregressive models having parameters that are identified only under the alternative of stationarity. Our framework is very general and allows for virtually all potentially interesting models with the threshold, discrete and smooth transition functions. The specifications of shortrun dynamics used in the paper are also fully general, and comparable to those used in the linear unit root models. Most importantly, our asymptotics take it into consideration that the parameter space has a random limit. This is an essential feature of the unit root test in transitional autoregressive models, which has been ignored in the literature. For this very general class of transitional autoregressive models, we show that the inf-t test has well-defined limit distribution depending only upon the transition function and the limit parameter space. The critical values of the test are provided for some of the commonly used models under the conventional specification of the parameter space. Our simulation study shows that the test has good size with the power that is significantly higher than the usual ADF test even for samples of relatively small sizes. We apply the test to various economic time series and find strong evidence for the rejection of random walks in favor of stationary transitional autoregressive models. |
| Keywords: | unit root test, threshold autoregressive models (TAR), logistic and exponential smooth transition autoregressive models (LSTAR and ESTAR) |
| JEL: | C12 C16 C22 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0510&r=ets |