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on Econometric Time Series |
| By: | Nina Munkholt Jakobsen (University of Copenhagen); Michael Sørensen (University of Copenhagen and CREATES) |
| Abstract: | Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find easily verified conditions on approximate martingale estimating functions under which estimators are consistent, rate optimal, and efficient under high frequency (in-fill) asymptotics. The asymptotic distributions of the estimators are shown to be normal variance-mixtures, where the mixing distribution generally depends on the full sample path of the diffusion process over the observation time interval. Utilising the concept of stable convergence, we also obtain the more easily applicable result that for a suitable data dependent normalisation, the estimators converge in distribution to a standard normal distribution. The theory is illustrated by a small simulation study comparing an efficient and a non-efficient estimating function. |
| Keywords: | Approximate martingale estimating functions, discrete time sampling of diffusions, in-fill asymptotics, normal variance-mixtures, optimal rate, random Fisher information, stable convergence, stochastic differential equation. |
| JEL: | C22 |
| Date: | 2015–08–06 |
| URL: | http://d.repec.org/n?u=RePEc:aah:create:2015-33&r=ets |
| By: | Daniel De Almeida; Luiz Hotta; Esther Ruiz |
| Abstract: | The parameters of popular multivariate GARCH (MGARCH) models are restricted so that their estimation is feasible in large systems and covariance stationarity and positive definiteness of conditional covariance matrices are guaranteed. These restrictions limit the dynamics that the models can represent, assuming, for example, that volatilities evolve in an univariate fashion, not being related neither among them nor with the correlations. This paper updates previous surveyson parametric MGARCH models focusing on their limitations to represent the dynamics observed in real systems of financial returns. The conclusions are illustrated using simulated data and a five-dimensional system of exchange rate returns. |
| Keywords: | BEKK , DCC , Multivariate conditional heteroscedasticity , Variance targeting , VECH |
| JEL: | C32 C52 C58 |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:cte:wsrepe:ws1516&r=ets |
| By: | Joshua C.C. Chan; Angelia L. Grant |
| Abstract: | We compare a number of widely used trend-cycle decompositions of output in a formal Bayesian model comparison exercise. This is motivated by the often markedly different results from these decompositions—different decompositions have broad implications for the relative importance of real versus nominal shocks in explaining variations in output. Using US quarterly real GDP, we find that the overall best model is an unobserved components model with two features: 1) a nonzero correlation between trend and cycle innovations; 2) a break in output growth in 2007. Under this specification, annualized trend output growth decreases from about 3.4% to 1.5% after the break. The results also indicate that real shocks are more important than nominal shocks. |
| Keywords: | Bayesian model comparison, unobserved components, structural break, business cycle |
| JEL: | C11 C52 E32 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:een:camaaa:2015-31&r=ets |
| By: | Anurag Narayan Banerjee (Business school - Durham University); Guillaume Chevillon (SID - Information Systems, Decision Sciences and Statistics Department - Essec Business School); Marie Kratz (SID - Information Systems, Decision Sciences and Statistics Department - Essec Business School, MAP5 - MAP5 - Mathématiques Appliquées à Paris 5 - CNRS - UPD5 - Université Paris Descartes - Paris 5 - Institut National des Sciences Mathématiques et de leurs Interactions) |
| Abstract: | This paper proposes a Near Explosive Random-Coefficient autoregressive model for asset pricing which accommodates both the fundamental asset value and the recurrent presence of autonomous deviations or bubbles. Such a process can be stationary with or without fat tails, unit-root nonstationary or exhibit temporary exponential growth. We develop the asymptotic theory to analyze ordinary least-squares (OLS) estimation. One important theoretical observation is that the estimator distribution in the random coefficient model is qualitatively different from its distribution in the equivalent fixed coefficient model. We conduct recursive and full-sample inference by inverting the asymptotic distribution of the OLS test statistic, a common procedure in the presence of localizing parameters. This methodology allows to detect the presence of bubbles and establish probability statements on their apparition and devolution. We apply our methods to the study of the dynamics of the Case-Shiller index of U.S. house prices. Focusing in particular on the change in the price level, we provide an early detection device for turning points of booms and bust of the housing market. |
| Date: | 2013–09–23 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00870795&r=ets |
| By: | Hacène Djellout (Laboratoire de Mathématiques - UBP - Université Blaise Pascal - Clermont-Ferrand 2 - CNRS); Hui Jiang (Nanjing University of Aeronautics and Astronautics - Department of Mathematics) |
| Abstract: | Recently a considerable interest has been paid on the estimation problem of the realized volatility and covolatility by using high-frequency data of financial price processes in financial econometrics. Threshold estimation is one of the useful techniques in the inference for jump-type stochastic processes from discrete observations. In this paper, we adopt the threshold estimator introduced by Mancini where only the variations under a given threshold function are taken into account. The purpose of this work is to investigate large and moderate deviations for the threshold estimator of the integrated variance-covariance vector. This paper is an extension of the previous work in Djellout Guillin and Samoura where the problem has been studied in absence of the jump component. We will use the approximation lemma to prove the LDP. As the reader can expect we obtain the same results as in the case without jump. |
| Date: | 2015–04–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01147189&r=ets |
| By: | Guillaume Chevillon (SID - Information Systems, Decision Sciences and Statistics Department - Essec Business School, CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique); Alain Hecq (Department of Quantitative Economics [Maastricht] - Maastricht University); Sébastien Laurent (AMU IAE - Institut d'Administration des Entreprises (IAE) - Aix-en-Provence - AMU - Aix-Marseille Université) |
| Abstract: | This paper shows that large dimensional vector autoregressive (VAR) models of finite order can generate long memory in the marginalized univariate series. We derive high-level assumptions under which the final equation representation of a VAR(1) leads to univariate fractional white noises and verify the validity of these assumptions for two specific models. We consider the implications of our findings for the variances of asset returns where the so-called golden-rule of realized variances states that they tend always to exhibit fractional integration of a degree close to 0:4. |
| Date: | 2015–05–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01158524&r=ets |
| By: | Geert Dhaene (ECON - Département d'économie - Sciences Po); Koen Jochmans (ECON - Département d'économie - Sciences Po) |
| Abstract: | We derive bias-corrected least-squares estimators of panel vector autoregressions with fixed effects. The correction is straightforward to implement and yields an estimator that is asymptotically unbiased under asymptotics where the number of time series observations grows at the same rate as the number of cross-sectional observations. This makes the estimator well suited for most macroeconomic data sets. Simulation results show that the estimator yields substantial improvements over within-group least-squares estimation. We illustrate the bias correction in a study of the relation between the unemployment rate and the economic growth rate at the U.S. state level. |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01174330&r=ets |