|
on Econometric Time Series |
| By: | Søren Johansen (Department of Economics, University of Copenhagen) |
| Abstract: | An analysis of some identification problems in the cointegrated VAR is given. We give a new criteria for identification by linear restrictions on individual relations which is equivalent to the rank condition. We compare the asymptotic distribution of the estimators of a and ß; when they are identified by linear restrictions on ß; and when they are identified by linear restrictions on a; in which case a component of ß^ is asymptotically Gaussian. Finally we discuss identification of shocks by introducing the contemporaneous and permanent effect of a shock and the distinction between permanent and transitory shocks, which allows one to identify permanent shocks from the long-run variance and transitory shocks from the short-run variance. |
| Keywords: | identification; cointegration; common trends |
| JEL: | C32 |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:0724&r=ets |
| By: | Søren Johansen (Department of Economics, University of Copenhagen) |
| Abstract: | Yule (1926) introduced the concept of spurious or nonsense correlation, and showed by simulation that for some nonstationary processes, that the empirical correlations seem not to converge in probability even if the processes were independent. This was later discussed by Granger and Newbold (1974), and Phillips (1986) found the limit distributions. We propose to distinguish between empirical and population correlation coefficients and show in a bivariate autoregressive model for nonstationary variables that the empirical correlation and regression coefficients do not converge to the relevant population values, due to the trending nature of the data. We conclude by giving a simple cointegration analysis of two interests. The analysis illustrates that much more insight can be gained about the dynamic behavior of the nonstationary variables then simply by calculating a correlation coefficient. |
| JEL: | C22 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:0725&r=ets |
| By: | Søren Johansen (Department of Economics, University of Copenhagen); Morten Ørregaard Nielsen (Cornell University) |
| Abstract: | This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d – b; where d = b > 1/2 are parameters to be estimated. We model the data X?, …, X? given the initial values Xº-n, n = 0, 1, …, under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to ?find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II. |
| Keywords: | Dickey-Fuller test; fractional unit root; likelihood inference |
| JEL: | C22 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:0727&r=ets |
| By: | Kalogeropoulos, Konstantinos; Dellaportas, Petros; Roberts, Gareth O. |
| Abstract: | We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite constraints of the diffusion matrix. Second, a diffusion may only be observed at a finite set of points and the marginal likelihood for the parameters based on these observations is generally not available. We overcome the first issue by using the Cholesky factorisation on the diffusion matrix. To deal with the likelihood unavailability, we generalise the data augmentation framework of Roberts and Stramer (2001 Biometrika 88(3):603-621) to d-dimensional correlated diffusions including multivariate stochastic volatility models. Our methodology is illustrated through simulation based experiments and with daily EUR /USD, GBP/USD rates together with their implied volatilities. |
| Keywords: | Markov chain Monte Carlo; Multivariate stochastic volatility; Multivariate CIR model; Cholesky Factorisation. |
| JEL: | C13 G12 C15 C11 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:5696&r=ets |
| By: | Kalogeropoulos, Konstantinos; Roberts, Gareth O.; Dellaportas, Petros |
| Abstract: | We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which overcomes the inherent difficulties of time change transformations is also presented. The algorithm is fast to implement and applies to models with stochastic volatility. The methodology is tested through simulation based experiments and illustrated on data consisting of US treasury bill rates. |
| Keywords: | Imputation; Markov chain Monte Carlo; Stochastic volatility |
| JEL: | C13 G12 C15 C11 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:5697&r=ets |
| By: | Francis X. Diebold (University of Pennsylvania and NBER); Kamil Yılmaz (Department of Economics, Koç University) |
| Abstract: | We provide a simple and intuitive measure of interdependence of asset returns and/or volatilities. In particular, we formulate and examine precise and separate measures of return spillovers and volatility spillovers. Our framework facilitates study of both non-crisis and crisis episodes, including trends and bursts in spillovers, and both turn out to be empirically important. In particular, in an analysis of sixteen global equity markets from the early 1990s to the present, we find striking evidence of divergent behavior in the dynamics of return spillovers vs. volatility spillovers: Return spillovers display a gently increasing trend but no bursts, whereas volatility spillovers display no trend but clear bursts. |
| Keywords: | Asset Market, Asset Return, Stock Market, Emerging Market, Market Linkage, Financial Crisis, Herd Behavior, Contagion |
| JEL: | F30 G15 F36 |
| Date: | 2005–10 |
| URL: | http://d.repec.org/n?u=RePEc:koc:wpaper:0705&r=ets |