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on Econometric Time Series |
| By: | Viktor Todorov; George Tauchen |
| Abstract: | We develop a nonparametric estimator of the stochastic volatility density of a discretely-observed Ito semimartingale in the setting of an increasing time span and finer mesh of the observation grid. There are two steps. The first is aggregating the high-frequency increments into the realized Laplace transform, which is a robust nonparametric estimate of the underlying volatility Laplace transform. The second step is using a regularized kernel to invert the realized Laplace transform. The two steps are relatively quick and easy to compute, so the nonparametric estimator is practicable. We derive bounds for the mean squared error of the estimator. The regularity conditions are sufficiently general to cover empirically important cases such as level jumps and possible dependencies between volatility moves and either diffusive or jump moves in the semimartingale. Monte Carlo work indicates that the nonparametric estimator is reliable and reasonably accurate in realistic estimation contexts. An empirical application to 5-minute data for three large-cap stocks, 1997-2010, reveals the importance of big short-term volatility spikes in generating high levels of stock price variability over and above that induced by price jumps. The application also shows how to trace out the dynamic response of the volatility density to both positive and negative jumps in the stock price. |
| Keywords: | Laplace transform, stochastic volatility, ill-posed problems, regularization, nonparametric density estimation, high-frequency data |
| JEL: | C51 C52 G12 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:duk:dukeec:11-21&r=ets |
| By: | Viktor Todorov; George Tauchen; Iaryna Grynkiv |
| Abstract: | The paper examines volatility activity and its asymmetry and undertakes further specification analysis of volatility models based on it. We develop new nonparametric statistics using high frequency option-based VIX data to test for asymmetry in volatility jumps. We also develop methods to estimate and evaluate, using price data alone, a general encompassing model for volatility dynamics where volatility activity is unrestricted. The nonparametric application to VIX data, along with model estimation for S&P Index returns, suggests that volatility moves are best captured by infinite variation pure-jump martingale with symmetric jump distribution. The latter provides a parsimonious generalization of the jump-diffusions commonly used for volatility modeling. |
| Keywords: | Asymmetric Volatility Activity, High-Frequency Data, Laplace Transform, Signed Power Variation, Specification Testing, Stochastic Volatility, Volatility Jumps |
| JEL: | C51 C52 G12 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:duk:dukeec:11-23&r=ets |
| By: | Paul Viefers |
| Abstract: | In this paper a mixed-frequency VAR à la Mariano & Murasawa (2004) with Markov regime switching in the parameters is estimated by Bayesian inference. Unlike earlier studies, that used the pseuo-EM algorithm of Dempster, Laird & Rubin (1977) to estimate the model, this paper describes how to make use of recent advances in Bayesian inference on mixture models. This way, one is able to surmount some well-known issues connected to inference on mixture models, e.g. the label switching problem. The paper features a numerical simulation study to gauge the model performance in terms of convergence to true parameter values and a small empirical example involving US business cycles. |
| Keywords: | Markov mixture models, Label switching, Bayesian VAR, Mixed frequencies |
| JEL: | C32 E32 E37 E51 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1172&r=ets |
| By: | Chris McDonald; Leif Anders Thorsrud (Reserve Bank of New Zealand) |
| Abstract: | Forecasting the future path of the economy is essential for good monetary policy decisions. The recent financial crisis has highlighted the importance of tail events, and that assessing the central projection is not enough. The whole range of outcomes should be forecasted, evaluated and accounted for when making monetary policy decisions. As such, we construct density fore- casts using the historical performance of the Reserve Bank of New Zealand's (RBNZ) published point forecasts. We compare these implied RBNZ den- sities to similarly constructed densities from a suite of empirical models. In particular, we compare the implied RBNZ densities to combinations of density forecasts from the models. Our results reveal that the combined den- sities are comparable in performance and sometimes better than the implied RBNZ densities across many dierent horizons and variables. We also find that the combination strategies typically perform better than relying on the best model in real-time, that is the selection strategy. |
| JEL: | C52 C53 E52 |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:nzb:nzbdps:2011/03&r=ets |
| By: | Philippe J. Deschamps (Department of Quantitative Economics) |
| Abstract: | Efficient posterior simulators for two GARCH models with generalized hyperbolic disturbances are presented. The first model, GHt-GARCH, is a threshold GARCH with a skewed and heavy-tailed error distribution; in this model, the latent variables that account for skewness and heavy tails are identically and independently distributed. The second model, ODLV-GARCH, is formulated in terms of observation-driven latent variables; it automatically incorporates a risk premium effect. Both models nest the ordinary threshold t-GARCH as a limiting case. The GHt-GARCH and ODLV-GARCH models are compared with each other and with the threshold t-GARCH using five publicly available asset return data sets, by means of Bayes factors, information criteria, and classical forecast evaluation tools. The GHt-GARCH and ODLV-GARCH models both strongly dominate the threshold t-GARCH, and the Bayes factors generally favor GHt-GARCH over ODLV-GARCH. A Markov switching extension of GHt-GARCH is also presented. This extension is found to be an empirical improvement over the single-regime model for one of the five data sets. |
| Keywords: | Autoregressive conditional heteroskedasticity; Markov chain Monte Carlo; bridge sampling; heavy-tailed skewed distributions; generalized hyperbolic distribution; generalized inverse Gaussian distribution |
| JEL: | C11 C16 C53 |
| Date: | 2011–10–28 |
| URL: | http://d.repec.org/n?u=RePEc:fri:dqewps:wp0016&r=ets |
| By: | Ronayne, David (University of Warwick) |
| Abstract: | This paper compares standard and local projection techniques in the production of impulse response functions both theoretically and empirically. Through careful selection of a structural decomposition, the comparison continues to an application of US data to the textbook ISLM model. It is argued that local projection techniques offer a remedy to the bias of the conventional method especially at horizons longer than the vector autoregression‘s lag length. The application highlights that the techniques can have different answers to important questions. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:971&r=ets |
| By: | Espasa, Antoni; Pellegrini, Santiago; Ruiz, Esther |
| Abstract: | Differencing is a very popular stationary transformation for series with stochastic trends. Moreover, when the differenced series is heteroscedastic, authors commonly model it using an ARMA-GARCH model. The corresponding ARIMA-GARCH model is then used to forecast future values of the original series. However, the heteroscedasticity observed in the stationary transformation should be generated by the transitory and/or the long-run component of the original data. In the former case, the shocks to the variance are transitory and the prediction intervals should converge to homoscedastic intervals with the prediction horizon.We show that, in this case, the prediction intervals constructed from the ARIMA-GARCH models could be inadequate because they never converge to homoscedastic intervals. All of the results are illustrated using simulated and real time series with stochastic levels. |
| Keywords: | ARIMA-GARCH models; Local level model; Nonlinear time series; State space models; Unobserved component models; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ner:carlos:info:hdl:10016/12257&r=ets |