|
on Econometrics |
| By: | J. Isaac Miller (Department of Economics, University of Missouri-Columbia) |
| Abstract: | We develop a random coefficients autoregressive (RCA) model with time-varying coefficients generated by a bounded nonlinear function of an exogenous time series that may be a mixingale or integrated. Moreover, we allow for exogenously-driven heteroskedasticity in the error term. By restricting the range of the function essentially to the unit interval, we show that the two series of autoregressive coefficients and variances of such a model are covariance stationary, even though these series may be nonergodic. Time series driven by such a data generating process are stationary, but may have (stochastic) unit or near-unit roots over periods of time. Under appropriate assumptions, we show that maximum likelihood estimation yields asymptotically normal or mixed normal parameter estimates. A data generating process of this form may engender commonly observed time series characteristics that defy the simple I(0)-I(1) dichotomy, but is more structural in nature than statistical I(d) models. Moreover, this approach provides a nonspurious way to model relationships between a nonstationary and a stationary time series. The utility of the proposed econometric model is demonstrated with an empirical application, in which inflation drives the autoregressive coefficient of interest rate volatility. |
| Keywords: | random coefficients autoregressive models, stochastic unit roots, nonlinear transformations, mixingales, near-epoch dependent processes, integrated processes, interest rate volatility |
| JEL: | C13 C22 C32 |
| Date: | 2006–01–15 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:0609&r=ecm |
| By: | Kenneth D. West; Todd Clark |
| Abstract: | Forecast evaluation often compares a parsimonious null model to a larger model that nests the null model. Under the null that the parsimonious model generates the data, the larger model introduces noise into its forecasts by estimating parameters whose population values are zero. We observe that the mean squared prediction error (MSPE) from the parsimonious model is therefore expected to be smaller than that of the larger model. We describe how to adjust MSPEs to account for this noise. We propose applying standard methods (West (1996)) to test whether the adjusted mean squared error difference is zero. We refer to nonstandard limiting distributions derived in Clark and McCracken (2001, 2005a) to argue that use of standard normal critical values will yield actual sizes close to, but a little less than, nominal size. Simulation evidence supports our recommended procedure. |
| JEL: | C22 C53 E17 F37 |
| Date: | 2006–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberte:0326&r=ecm |
| By: | David E. A. Giles (Department of Economics, University of Victoria) |
| Abstract: | A “spurious regression” is one in which the time-series variables are non-stationary and independent. It is well-known that in this context the OLS parameter estimates and the R2 converge to functionals of Brownian motions; the “t-ratios” diverge in distribution; and the Durbin-Watson statistic converges in probability to zero. We derive corresponding results for some common tests for the Normality and homoskedasticity of the errors in a spurious regression. |
| Keywords: | Spurious regression, normality, homoskedasticity, asymptotic theory, unit roots |
| JEL: | C12 C22 C52 |
| Date: | 2006–08–17 |
| URL: | http://d.repec.org/n?u=RePEc:vic:vicewp:0603&r=ecm |
| By: | Yuanhua Feng (Department of Mathematics and Statistics, University of Konstanz) |
| Abstract: | This paper considers simultaneous modelling of seasonality, slowly changing un- conditional variance and conditional heteroskedasticity in high-frequency financial returns. A new approach, called a seasonal SEMIGARCH model, is proposed to perform this by introducing multiplicative seasonal and trend components into the GARCH model. A data-driven semiparametric algorithm is developed for estimating the model. Asymptotic properties of the proposed estimators are investigated brie y. An approximate significance test of seasonality and the use of Monte Carlo confidence bounds for the trend are proposed. Practical performance of the proposal is investigated in detail using some German stock price returns. The approach proposed here provides a useful semiparametric extension of the GARCH model. |
| Keywords: | High-frequency financial data, nonparametric regression, seasonality in volatility, semiparametric GARCH model, trend in volatility |
| URL: | http://d.repec.org/n?u=RePEc:knz:cofedp:0218&r=ecm |
| By: | Christophe Kolodziejczyk (Department of Economics, University of Copenhagen) |
| Abstract: | In this note we derive the bias of the OLS estimator for a correlated random coefficient model with one random coefficient, but which is correlated with a binary variable. We provide set-identification to the parameters of interest of the model. We also show how to reduce the bias of the estimator. |
| Keywords: | correlated random coefficient model; bias; discrete choice |
| JEL: | C13 C21 |
| Date: | 2006–08 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuieca:2006_10&r=ecm |
| By: | Ole E Barndorff-Nielsen; Peter Hansen; Asger Lunde; Neil Shephard |
| Abstract: | This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice. |
| JEL: | C13 C22 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:sbs:wpsefe:2006fe05&r=ecm |
| By: | Chin Nam Low; Heather Anderson; Ralph D. Snyder |
| Abstract: | This paper considers Beveridge-Nelson decomposition in a context where the permanent and transitory components both follow a Markov switching process. Our approach incorporates Markov switching into a single source of error state-space framework, allowing business cycle asymmetries and regime switches in the long run multiplier. |
| Keywords: | Beveridge-Nelson decomposition, Markov switching, Single source of error state space models |
| JEL: | C22 C51 E32 |
| Date: | 2006–08 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2006-17&r=ecm |
| By: | Orazio Attanasio; Margherita Borella |
| Abstract: | In this paper we propose a method to characterize the time series properties of individual consumption, income and interest rates using micro data, as studies in labour economics have characterized the time series properties of hours and earnings. Our approach, however, does not remove aggregate shocks. Having estimated the parameters of a flexible multivariate MA representation we relate the coefficients of our statistical model to structural parameters of theoretical models of consumption behaviour. Our approach offers a unifying framework that encompasses the Euler equation approach to the study of consumption and the studies that relate innovations to income to innovations to consumption, such as those that have found the so-called excess smoothness of consumption. Using a long time series of cross sections to construct synthetic panel data for the UK, we estimate our model and find that the restriction of Euler equations are typically not rejected, while the data show ‘excess smoothness’. |
| JEL: | C3 D1 E2 |
| Date: | 2006–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:12456&r=ecm |
| By: | Klaus Abberger (IFO Munich) |
| Abstract: | For a bivariate data set the dependence structure can not only be measured globally, for example with the Bravais-Pearson correlation coefficient, but the dependence structure can also be analyzed locally. In this article the exploration of dependencies in the tails of the bivariate distribution is discussed. For this a graphical method which is called chi-plot and which was introduced by Fisher and Switzer (1985, 2001) is used. Examples with simulated data sets illustrate that the chi-plot is suitable for the exploration of dependencies. This graphical method is then used to examine stock-return pairs. The kind of tail-dependence between returns has consequences, for example, for the calculation of the Value at Risk and should be modelled carefully. The application of the chi-plot to various daily stock-return pairs shows that different dependence structures can be found. This graph can therefore be an interesting aid for the modelling of returns. |
| Keywords: | Association, bivariate distribution, chi-plot, copula, correlation, local dependence, tail-dependence |
| URL: | http://d.repec.org/n?u=RePEc:knz:cofedp:0403&r=ecm |
| By: | Carl Bonham (Department of Economics, University of Hawaii at Manoa); Richard Cohen (College of Business and Public Policy, University of Alaska Anchorage); Shigeyuki Abe (Center for Contemporary Asian Studies, Doshisha University) |
| Abstract: | This paper examines the rationality and diversity of industry-level forecasts of the yen-dollar exchange rate collected by the Japan Center for International Finance. In several ways we update and extend the seminal work by Ito (1990). We compare three specifications for testing rationality: the ”conventional” bivariate regression, the univariate regression of a forecast error on a constant and other information set variables, and an error correction model (ECM). We find that the bivariate specification, while producing consistent estimates, suers from two defects: first, the conventional restrictions are sucient but not necessary for unbiasedness; second, the test has low power. However, before we can apply the univariate specification, we must conduct pretests for the stationarity of the forecast error. We find a unit root in the six-month horizon forecast error for all groups, thereby rejecting unbiasedness and weak eciency at the pretest stage. For the other two horizons, we find much evidence in favor of unbiasedness but not weak eciency. Our ECM rejects unbiasedness for all forecasters at all horizons. We conjecture that these results, too, occur because the restrictions test suciency, not necessity. In our systems estimation and micro- homogeneity testing, we use an innovative GMM technique (Bonham and Cohen (2001)) that allows for forecaster cross-correlation due to the existence of common shocks and/or herd eects. Tests of micro-homogeneity uniformly reject the hypothesis that forecasters across the four industries exhibit similar rationality characteristics. |
| Keywords: | Rational Expectations, Heterogeneity, Exchange Rate, Survey Forecast |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:hai:wpaper:200611&r=ecm |