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on Econometric Time Series |
| By: | Kim, Young Shin; Rachev, Svetlozar T.; Bianchi, Michele Leonardo; Fabozzi, Frank J. |
| Abstract: | In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we review the classical tempered stable (CTS) GARCH model, which has similar statistical properties. By considering a proper density transformation between infinitely divisible random variables, these GARCH models allow to find the risk-neutral price process, and hence they can be applied to option pricing. We propose algorithms to generate scenario based on GARCH models with CTS and RDTS innovation. To investigate the performance of these GARCH models, we report a parameters estimation for Dow Jones Industrial Average (DJIA) index and stocks included in this index, and furthermore to demonstrate their advantages, we calculate option prices based on these models. It should be noted that only historical data on the underlying asset and on the riskfree rate are taken into account to evaluate option prices. -- |
| Keywords: | tempered infinitely divisible distribution,tempered stable distribution,rapidly decreasing tempered stable distribution,GARCH model option pricing |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:28&r=ets |
| By: | J. Isaac Miller (Department of Economics, University of Missouri-Columbia) |
| Abstract: | I analyze efficient estimation of a cointegrating vector when the regressand is observed at a lower frequency than the regressors. Previous authors have examined the effects of specific temporal aggregation or sampling schemes, finding conventionally efficient techniques to be efficient only when both the regressand and the regressors are average sampled. Using an alternative method for analyzing aggregation under more general weighting schemes, I derive an efficiency bound that is conditional on the type of aggregation used on the regressand. This conditional bound differs from the unconditional bound defined by the full-information high-frequency data generating process. I modify a conventionally efficient estimator, canonical cointegrating regression (CCR), to accommodate cases in which the aggregation weights are either unknown or known. In the unknown case, the correlation structure of the error term generally confounds identification of the conditionally efficient weights. In the commonly assumed known case, the correlation structure may be utilized to offset the potential information loss from aggregation, resulting in a conditionally efficient estimator. |
| Keywords: | oil price and the macroeconomy, oil market fundamental, oil price forecasts, Kalman filter |
| JEL: | C13 C22 |
| Date: | 2011–05–19 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:1103&r=ets |
| By: | Andrea Carriero; Todd Clark; Massimiliano Marcellino |
| Abstract: | In this paper we examine how the forecasting performance of Bayesian VARs is affected by a number of specification choices. In the baseline case, we use a Normal-Inverted Wishart prior that, when combined with a (pseudo-) iterated approach, makes the analytical computation of multi-step forecasts feasible and simple, in particular when using standard and fixed values for the tightness and the lag length. We then assess the role of the optimal choice of the tightness, of the lag length and of both; compare alternative approaches to multi-step forecasting (direct, iterated, and pseudo-iterated); discuss the treatment of the error variance and of cross-variable shrinkage; and address a set of additional issues, including the size of the VAR, modeling in levels or growth rates, and the extent of forecast bias induced by shrinkage. We obtain a large set of empirical results, but we can summarize them by saying that we find very small losses (and sometimes even gains) from the adoption of specification choices that make BVAR modeling quick and easy. This finding could therefore further enhance the diffusion of the BVAR as an econometric tool for a vast range of applications. |
| Keywords: | Bayesian statistical decision theory ; Forecasting ; Vector autoregression |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedcwp:1112&r=ets |
| By: | Xiaohong Chen (Cowles Foundation, Yale University) |
| Abstract: | In this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plug-in PSE estimators of functionals that are either smooth (i.e., root-n estimable) or non-smooth (i.e., slower than root-n estimable); (3) simple criterion-based inference for plug-in PSE estimation of smooth or non-smooth functionals; and (4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH, and copula-based multivariate financial models are used to illustrate the general results. |
| Keywords: | Nonlinear time series, Temporal dependence, Tail dependence, Penalized sieve M estimation, Penalized sieve minimum distance, Semiparametric two-step, Nonlinear ill-posed inverse, Mixtures, Conditional moment restrictions, Nonparametric endogeneity, Dynamic asset pricing, Varying coefficient VAR, GARCH, Copulas, Value-at-risk |
| JEL: | C13 C14 C20 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1804&r=ets |
| By: | Viorel Costeanu; Dan Pirjol |
| Abstract: | We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. This relation is preserved also to order O(T) in the small-time expansion, and differences with the log-normal case appear first at O(T^2). The results are illustrated on a few examples of local volatility models with analytical local volatility, finding generally good agreement with exact or numerical solutions. We point out that the asymptotic expansion can fail if applied naively for models with nonanalytical local volatility, for example which have discontinuous derivatives. Using perturbation theory methods, we show that the ATM normal implied volatility for such a model contains a term ~ \sqrt{T}, with a coefficient which is proportional with the jump of the derivative. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1105.3359&r=ets |
| By: | Heinen, Florian; Michael, Stefanie; Sibbertsen, Philipp |
| Abstract: | Determining good parameter estimates in ESTAR models is known to be diffcult. We show that the phenomena of getting strongly biased estimators is a consequence of the so-called identifcation problem, the problem of properly distinguishing the transition function in relation to extreme parameter combinations. This happens in particular for either very small or very large values of the error term variance. Furthermore, we introduce a new alternative model -the TSTAR model- which has similar properties as the ESTAR model but reduces the effects of the identifcation problem. We also derive a linearity and a unit root test for this model. |
| Keywords: | Nonlinearities, Smooth transition, Linearity testing, Unit root testing, Real exchange rates |
| JEL: | C12 C22 C52 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-474&r=ets |