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on Econometric Time Series |
| 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=ets |
| 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=ets |
| 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=ets |
| 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=ets |
| By: | Nikolaus Hautsch |
| Abstract: | We introduce a multivariate multiplicative error model which is driven by component- specific observation driven dynamics as well as a common latent autoregressive factor. The model is designed to explicitly account for (information driven) common factor dynamics as well as idiosyncratic effects in the processes of high-frequency return volatilities, trade sizes and trading intensities. The model is estimated by simulated maximum likelihood using efficient importance sampling. Analyzing five minutes data from four liquid stocks traded at the New York Stock Exchange, we find that volatilities, volumes and intensities are driven by idiosyncratic dynamics as well as a highly persistent common factor capturing most causal relations and cross-dependencies between the individual variables. This confirms economic theory and suggests more parsimonious specifications of high-dimensional trading processes. It turns out that common shocks affect the return volatility and the trading volume rather than the trading intensity. |
| Keywords: | Multiplicative error models, common factor, efficient importance sampling, intraday trading process. |
| JEL: | C15 C32 C52 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2007-052&r=ets |
| By: | Gary Koop (University of Strathclyde, UK and Rimini Centre for Economic Analysis, Rimini, Italy); Roberto Leon-Gonzalez (University of Leicester, UK and University of Queensland); Rodney Strachan (University of Queensland) |
| Abstract: | This paper develops methods of Bayesian inference in a cointegrating panel data model. This model involves each cross-sectional unit having a vector error correction representation. It is flexible in the sense that different cross-sectional units can have different cointegration ranks and cointegration spaces. Furthermore, the parameters which characterize short-run dynamics and deterministic components are allowed to vary over cross-sectional units. In addition to a noninformative prior, we introduce an informative prior which allows for information about the likely location of the cointegration space and about the degree of similarity in coefficients in different cross-sectional units. A collapsed Gibbs sampling algorithm is developed which allows for efficient posterior inference. Our methods are illustrated using real and artificial data. |
| Keywords: | Bayesian, panel data cointegration, error correction model, reduced rank regression, Markov Chain Monte Carlo. |
| JEL: | C11 C32 C33 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:02-07&r=ets |