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on Econometrics |
| By: | Taoufik Bouezmarni; Jeroen V.K. Rombouts (IEA, HEC Montréal) |
| Abstract: | We propose a new nonparametric estimator for the density function of multivariate bounded data. As frequently observed in practice, the variables may be partially bounded (e.g., nonnegative) or completely bounded (e.g., in the unit interval). In addition, the variables may have a point mass. We reduce the conditions on the underlying density to a minimum by proposing a nonparametric approach. By using a gamma, a beta, or a local linear kernel (also called boundary kernels), in a product kernel, the suggested estimator becomes simple in implementation and robust to the well known boundary bias problem. We investigate the mean integrated squared error properties, including the rate of convergence, uniform strong consistency and asymptotic normality. We establish consistency of the least squares cross-validation method to select optimal bandwidth parameters. A detailed simulation study investigates the performance of the estimators. Applications using lottery and corporate finance data are provided. |
| Keywords: | Asymmetric kernels, multivariate boundary bias, nonparametric multivariate density estimation, asymptotic properties, bandwidth selection, least squares cross-validation. |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:iea:carech:0710&r=ecm |
| By: | Luc Bauwens; Arie Preminger; Jeroen V.K. Rombouts (IEA, HEC Montréal) |
| Abstract: | We develop a Markov-switching GARCH model (MS-GARCH) wherein the conditional mean and variance switch in time from one GARCH process to another. The switching is governed by a hidden Markov chain. We provide sufficient conditions for geometric ergodicity and existence of moments of the process. Because of path dependence, maximum likelihood estimation is not feasible. By enlarging the parameter space to include the state variables, Bayesian estimation using a Gibbs sampling algorithm is feasible. We illustrate the model on SP500 daily returns. |
| Keywords: | GARCH, Markov-switching, Bayesian inference. |
| JEL: | C11 C22 C52 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:iea:carech:0709&r=ecm |
| By: | Taoufik Bouezmarni; Jeroen V.K. Rombouts (IEA, HEC Montréal) |
| Abstract: | In this paper we estimate density functions for positive multivariate data. We propose a semiparametric approach. The estimator combines gamma kernels or local linear kernels, also called boundary kernels, for the estimation of the marginal densities with semiparametric copulas to model the dependence. This semiparametric approach is robust both to the well known boundary bias problem and the curse of dimensionality problem. We derive the mean integrated squared error properties, including the rate of convergence, the uniform strong consistency and the asymptotic normality. A simulation study investigates the finite sample performance of the estimator. We find that univariate least squares cross validation, to choose the bandwidth for the estimation of the marginal densities, works well and that the estimator we propose performs very well also for data with unbounded support. Applications in the field of finance are provided. |
| Keywords: | Asymptotic properties, asymmetric kernels, boundary bias, copula, curse of dimension, least squares cross validation. |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:iea:carech:0708&r=ecm |
| By: | Yasuhiro Omori (Faculty of Economics, University of Tokyo); Toshiaki Watanabe (Institute of Economic Research, Hitotsubashi University) |
| Abstract: | This article introduces a new efficient simulation smoother and disturbance smoother for asymmetric stochastic volatility models where there exists a correlation between today's return and tomorrow's volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable. |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2007cf507&r=ecm |
| By: | Jouchi Nakajima (Bank of Japan); Yasuhiro Omori (Faculty of Economics, University of Tokyo) |
| Abstract: | This paper proposes the efficient and fast Markov chain Monte Carlo estimation methods for the stochastic volatility model with leverage effects, heavy-tailed errors and jump components, and for the stochastic volatility model with correlated jumps. We illustrate our method using simulated data and analyze daily stock returns data on S&P500 index and TOPIX. Model comparisons are conducted based on the marginal likelihood for various SV models including the superposition model. |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2007cf514&r=ecm |
| By: | Andersson, Jonas (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration) |
| Abstract: | In this paper, the problem of calculating covariances and correlations between time series which are observed irregularly and at different points in time, is treated. The problem of dependence between the time stamp process and the return process is especially highlighted and the solution to this problem for a special case is given. Furthermore, estimators based on different interpolation methods are investigated. The covariances are in turn used to estimate a simple regression on such data. In particular, the difference of first order integrated processes, I(1) processes, are considered. These methods are relevant for stock returns and consequently of importance in e.g. portfolio optimization. |
| Keywords: | Irregularly spaced time series; covariance; correlation; financial returns |
| JEL: | C10 |
| Date: | 2007–07–06 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2007_019&r=ecm |
| By: | Wolfgang Polasek (Institute for Advanced Studies,Vienna, Austria and The Rimini Centre for Economic Analysis, Rimini, Italy); Richard Sellner (Institute for Advanced Studies,Vienna, Austria); Wolfgang Schwarzbauer (Institute for Advanced Studies,Vienna, Austria) |
| Abstract: | Long-term predictions with a system of dynamic panel models can have tricky properties since the time dimension in regional (cross) sectional models is usually short. This paper describes the possible approaches to make long-term-ahead forecast based on a dynamic panel set, where the dependent variable is a cross-sectional vector of growth rates. Since the variance of the forecasts will depend on number of updating steps, we compare the forecasts behavior of a aggregated and a disaggregated updating procedure. The cross section of the panel data can be modeled by a spatial AR (SAR) or Durbin model, including heteroscedasticity. Since the forecasts are non-linear functions of the model parameters we show what MCMC based approach will produce the best results. We demonstrate the approach by a example where we have to predict 20 years ahead of regional growth in 99 Austrian regions in a space-time dependent system of equations.Creation-Date: 200707 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:10-07&r=ecm |
| By: | Brendan K. Beare |
| Abstract: | In this paper a new mixing condition for sequences of random variables is considered. This mixing condition is termed ?-mixing. Whereas mixing conditions such as ?-mixing are typically defined in terms of entire ?-fields of sets generated by random variables in the distant past and future, ?-mixing is defined in terms of a smaller class of sets: the finite dimensional cylinder sets. This leads to a definition of mixing more general than those in current use. A Rosenthal inequality, law of large numbers, and functional central limit theorem are proved for ?-mixing processes. |
| Keywords: | Mixing, Weak Dependence, Hardy-Krause Variation |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:348&r=ecm |
| By: | Arntz, Melanie; Lo, Simon M. S.; Wilke, Ralf A. |
| Abstract: | In this paper we derive nonparametric bounds for the cumulative incidence curve within a competing risks model with partly identified interval data. As an advantage over earlier attempts our approach also gives valid results in case of dependent competing risks. We apply our framework to empirically evaluate the effect of unemployment benefits on observed migration of unemployed workers in Germany. Our findings weakly indicate that reducing the entitlement length for unemployment benefits increases migration among high-skilled individuals. |
| Keywords: | cumulative incidence curve, partially missing data, bounds analysis, difference-in-differences |
| JEL: | C14 C41 J61 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:zewdip:5875&r=ecm |