|
on Econometric Time Series |
| By: | Jiří Witzany (University of Economics, Prague, Czech Republic) |
| Abstract: | We formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model’s parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on the two most important Czech domestic financial market time series of the FX (CZK/EUR) and stock (PX index) returns. Four bivariate models with and without jumps and/or stochastic volatility are compared using the deviance information criterion (DIC) confirming importance of incorporation of jumps and stochastic volatility into the model. |
| Keywords: | jump-diffusion, stochastic volatility, MCMC, Value at Risk, Monte Carlo |
| JEL: | C11 C15 G1 |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:fau:wpaper:wp2011_35&r=ets |
| By: | Andros Kourtellos (Department of Economics, University of Cyprus); Thanasis Stengos (Department of Economics, University of Guelph); Chih Ming Tan (Department of Economics, Clark University) |
| Abstract: | This paper introduces the structural threshold regression model that allows for an endogeneous threshold variable as well as for endogenous regressors. This model provides a parsimonious way of modeling nonlinearities and has many potential applications in economics and finance. Our framework can be viewed as a generalization of the simple threshold regression framework of Hansen (2000) and Caner and Hansen (2004) to allow for the endogeneity of the threshold variable and regime specific heteroskedasticity. Our estimation of the threshold parameter is based on a concentrated least squares method that involves an inverse Mills ratio bias correction term in each regime. We derive its asymptotic distribution and propose a method to construct bootstrap confidence intervals. We also provide inference for the slope parameters based on GMM. Finally, we investigate the performance of the asymptotic approximations and the bootstrap using a Monte Carlo simulation that indicates the applicability of the method in finite samples. |
| JEL: | C13 C51 |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:49_11&r=ets |
| By: | Wolfgang Polasek (Institute for Advanced Studies, Vienna, Austria; University of Porto, Porto, Portugal) |
| Abstract: | The Hodrick-Prescott (HP) method is a popular smoothing method for economic time series to get a smooth or long-term component of stationary series like growth rates. We show that the HP smoother can be viewed as a Bayesian linear model with a strong prior using differencing matrices for the smoothness component. The HP smoothing approach requires a linear regression model with a Bayesian conjugate multi-normalgamma distribution. The Bayesian approach also allows to make predictions of the HP smoother on both ends of the time series. Furthermore, we show how Bayes tests can determine the order of smoothness in the HP smoothing model. The extended HP smoothing approach is demonstrated for the non-stationary (textbook) airline passenger time series. Thus, the Bayesian extension of the HP model defines a new class of model-based smoothers for (non-stationary) time series and spatial models. |
| Keywords: | Hodrick-Prescott (HP) smoothers, model selection by marginal likelihoods, multi-normal-gamma distribution, Spatial sales growth data, Bayesian econometrics |
| JEL: | C11 C15 C52 E17 R12 |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:46_11&r=ets |
| By: | Dominique, C-René; Rivera-Solis, Luis Eduardo |
| Abstract: | The Kolmogorov-Mandelbrot-van Ness Process is a zero mean Gaussian process indexed by the Hurst Parameter (H). When it models financial data, a controversy arises as to whether or not financial data exhibit short or long-range dependence. This paper argues that the Mixed Fractional Brownian is a more suitable tool for the purpose as it leaves no room for controversy. It is used here to model the S&P-500 Index, sampled daily over the period 1950-2011. The main results are as follows: The S&P-500 Index is characterized by both short and long-term dependence. More explicitly, it is characterized by at least 12 distinct scaling pa-rameters that are, ex hypothesis, determined by investors’ approach to the market. When the market is dominated by “blue-chippers” or ‘long-termists’, or when bubbles are ongoing, the index is persistent; and when the market is dominated by “con-trarians”, the index jumps to anti-persistence that is a far-from-equilibrium state in which market crashes are likely to occur. |
| Keywords: | Gaussian Processes; Mixed Fractional Brownian Motion; Hurst Exponent; Local Self-similarity; Persistence; Anti-persistence; Definiteness of covariance Functions; Dissipative dynamic systems |
| JEL: | C32 D53 C16 C02 |
| Date: | 2011–10–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:34860&r=ets |