|
on Econometric Time Series |
| By: | Worapree Maneesoonthorn; Catherine S. Forbes; Gael M. Martin |
| Abstract: | This paper investigates the dynamic behaviour of jumps in financial prices and volatility. The proposed model is based on a standard jump diffusion process for price and volatility augmented by a bivariate Hawkes process for the two jump components. The latter process specifies a joint dynamic structure for the price and volatility jump intensities, with the intensity of a volatility jump also directly affected by a jump in the price. The impact of certain aspects of the model on the higher-order conditional moments for returns is investigated. In particular, the differential effects of the jump intensities and the random process for latent volatility itself, are measured and documented. A state space representation of the model is constructed using both financial returns and non-parametric measures of integrated volatility and price jumps as the observable quantities. Bayesian inference, based on a Markov chain Monte Carlo algorithm, is used to obtain a posterior distribution for the relevant model parameters and latent variables, and to analyze various hypotheses about the dynamics in, and the relationship between, the jump intensities. An extensive empirical investigation using data based on the S&P500 market index over a period ending in early-2013 is conducted. Substantial empirical support for dynamic jump intensities is documented, with predictive accuracy enhanced by the inclusion of this type of specification. In addition, movements in the intensity parameter for volatility jumps are found to track key market events closely over this period. |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1401.3911&r=ets |
| By: | Michele Caivano (Bank of Italy); Andrew Harvey (University of Cambridge) |
| Abstract: | A time series model in which the signal is buried in non-Gaussian noise may throw up observations that are outliers when judged by the Gaussian yardstick. We describe an observation-driven model, based on an exponential generalized beta distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement, but that also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum likelihood estimator. The model is fitted to US macroeconomic time series and compared with Gaussian and Student-t models. A theory is then developed for an EGARCH model based on the EGB2 distribution and the model is fitted to exchange rate data. Finally, dynamic location and scale models are combined and applied to data on the UK rate of inflation. |
| Keywords: | : Beta distribution, EGARCH, fat tails, score, robustness, Winsorizing |
| JEL: | C22 G17 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:bdi:wptemi:td_947_14&r=ets |
| By: | Randolf Altmeyer; Markus Bibinger; ; |
| Abstract: | We consider noisy non-synchronous discrete observations of a continuous semimartingale. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: onedimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous observations for a bivariate spectral covolatility estimator and multivariate for a local method of moments. The results demonstrate that local adaptivity and smoothing noise dilution in the Fourier domain facilitate substantial efficiency gains compared to previous approaches. In particular, the derived asymptotic variances coincide with the benchmarks of semiparametric Cram´er-Rao lower bounds and the considered estimators are thus asymptotically efficient in idealized sub-experiments. Feasible central limit theorems allowing for confidence are provided. |
| Keywords: | adaptive estimation, asymptotic efficiency, local parametric estimation, microstructure noise, integrated volatility, non-synchronous observations, spectral estimation, stable limit theorem |
| JEL: | C14 C32 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014-005&r=ets |
| By: | Helmut Lütkepohl; Anna Staszewska-Bystrova; Peter Winker; |
| Abstract: | In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. These bands may be based on frequentist or Bayesian methods. If they are based on the joint distribution in the Bayesian framework or the joint asymptotic distribution possibly constructed with bootstrap methods in the frequentist framework often individual confidence intervals or credibility sets are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint confidence content lower than the desired one. If instead the joint distribution of the impulse response coefficients is taken into account and mapped into the band it is shown that such a band is typically rather conservative. It is argued that a smaller band can often be obtained by using the Bonferroni method. While these considerations are equally important for constructing forecast bands, we focus on the case of impulse responses in this study. |
| Keywords: | Impulse responses, Bayesian error bands, frequentist confidence bands, Wald statistic, vector autoregressive process |
| JEL: | C32 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2014-007&r=ets |
| By: | Blöchl, Andreas |
| Abstract: | The Hodrick-Prescott filter is the probably most popular tool for trend estimation in economics. Compared to other frequently used methods like the Baxter-King filter it allows to estimate the trend for the most recent periods of a time series. However, the Hodrick- Prescott filter suffers from an increasing excess variability at the margins of the series inducing a too flexible trend function at the margins compared to the middle. This paper will tackle this problem using spectral analysis and a flexible penalization. It will show that the excess variability can be reduced immensely by a flexible penalization, while the gain function for the middle of the time series is used as a measure to determine the degree of the flexible penalization. |
| Keywords: | Hodrick-Prescott filter; spectral analysis; trend estimation; gain function; flexible penalization |
| JEL: | C22 C52 |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:17940&r=ets |