|
on Econometric Time Series |
| By: | Helmut Lütkepohl |
| Abstract: | It is emphasized that the shocks in structural vector autoregressions are only identified up to sign and it is pointed out that this feature can result in very misleading confidence intervals for impulse responses if simulation methods such as Bayesian or bootstrap methods are used. The confidence intervals heavily depend on which variable is used for fixing the sign of the initial responses. In particular, when the shocks are identified via long-run restrictions the problem can be severe. It is pointed out that a suitable choice of variable for fixing the sign of the initial responses can result in substantial reductions in the confidence bands for impulse responses. |
| Keywords: | Vector autoregressive process, impulse responses, bootstrap, Bayesian estimation |
| JEL: | C32 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:diw:diwwpp:dp1235&r=ets |
| By: | Meenagh, David (Cardiff Business School); Minford, Patrick (Cardiff Business School); Wickens, Michael (Cardiff Business School) |
| Abstract: | We extend the method of indirect inference testing to data that is not filtered and so may be non-stationary. We apply the method to an open economy real business cycle model on UK data. We review the method using a Monte Carlo experiment and find that it performs accurately and has good power. |
| Keywords: | Bootstrap; DSGE; VECM; indirect inference; Monte Carlo |
| JEL: | C12 C32 C52 E1 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:cdf:wpaper:2012/17&r=ets |
| By: | Maican, Florin G. (Department of Economics, School of Business, Economics and Law, Göteborg University); Sweeney, Richard J. (McDonough School of Business, Georgetown University) |
| Abstract: | This paper examines power issues for the ADF and four break models (Perron 1989, Zivot and Andrews 1992) when the DGP corresponds to one of the break models. Choosing to test an incorrect break model can but need not greatly reduce the probability of rejecting the null. Break points that are relatively early in the sample period have substantial effects of increasing power. For modest shifts in time trends, simply including a time trend without shift in the model preserves power, but not for large time-trend shifts.<p> |
| Keywords: | Unit root; Monte Carlo; Break models |
| JEL: | C15 C22 C32 C33 E31 F31 |
| Date: | 2012–08–27 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0536&r=ets |
| By: | Stefan Gerhold; Max Kleinert; Piet Porkert; Mykhaylo Shkolnikov |
| Abstract: | We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applicable to solutions of stochastic differential equations with locally bounded and continuous coefficients. The limit theorems are subsequently extended to functional central limit theorems on the process level. We present two applications of the results in the field of mathematical finance: to the pricing of at-the-money digital options with short maturities and short time implied volatility skews. |
| Date: | 2012–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1208.4282&r=ets |
| By: | Jean-Pierre Fouque; Matthew Lorig; Ronnie Sircar |
| Abstract: | Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and S{\o}lna (2011, CUP) analyzes models in which the volatility of the underlying is driven by two diffusions -- one fast mean-reverting and one slow-varying, and provides a first order approximation for European option prices and for the implied volatility surface, which is calibrated to market data. Here, we present the full second order asymptotics, which are considerably more complicated due to a terminal layer near the option expiration time. We find that, to second order, the implied volatility approximation depends quadratically on log-moneyness, capturing the convexity of the implied volatility curve seen in data. We introduce a new probabilistic approach to the terminal layer analysis needed for the derivation of the second order singular perturbation term, and calibrate to S&P 500 options data. |
| Date: | 2012–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1208.5802&r=ets |
| By: | Jozef Barunik; Michaela Barunikova |
| Abstract: | This paper revisits the fractional cointegrating relationship between ex-ante implied volatility and ex-post realized volatility. We argue that the concept of corridor implied volatility (CIV) should be used instead of the popular model-free option-implied volatility (MFIV) when assessing the fractional cointegrating relation as the latter may introduce bias to the estimation. For the realized volatility, we use recently proposed methods which are robust to noise as well as jumps and interestingly we find that it does not affect the implied-realized volatility relation. In addition, we develop a new tool for the estimation of fractional cointegrating relation between implied and realized volatility based on wavelets, a wavelet band least squares (WBLS). The main advantage of WBLS in comparison to other frequency domain methods is that it allows us to work conveniently with potentially non-stationary volatility due to the properties of wavelets. We study the dynamics of the relationship in the time-frequency domain with the wavelet coherence confirming that the dependence comes solely from the lower frequencies of the spectra. Motivated by this result we estimate the relationship only on this part of the spectra using WBLS and compare our results to the fully modified narrow-band least squares (FMNBLS) based on the Fourier frequencies. In the estimation, we use the S&P 500 and DAX monthly and bi-weekly option prices covering the recent financial crisis and we conclude that in the long-run, volatility inferred from the option prices using the corridor implied volatility (CIV) provides an unbiased forecast of the realized volatility. |
| Date: | 2012–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1208.4831&r=ets |
| By: | Harvey, A.; Sucarrat, G. |
| Abstract: | An EGARCH model in which the conditional distribution is heavy-tailed and skewed is proposed. The properties of the model, including unconditional moments, autocorrelations and the asymptotic distribution of the maximum likelihood estimator, are obtained. Evidence for skewness in conditional t-distribution is found for a range of returns series and the model is shown to give a better .t than the corresponding skewed-t GARCH model. |
| Keywords: | General error distribution; heteroskedasticity; leverage; score; Student?s t, two components. |
| JEL: | C22 G17 |
| Date: | 2012–08–17 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1236&r=ets |
| By: | Kaufmann, Hendrik; Kruse, Robinson; Sibbertsen, Philipp |
| Abstract: | A simple procedure for the specification of the transition function describing the regime switch in nonlinear autoregressive models is proposed. This procedure is based on auxiliary regressions of unit root tests and is applicable to a variety of transition functions. In contrast to other procedures, complicated and computer-intense estimation of the candidate models is not necessary. Our approach entirely relies on OLS estimation of auxiliary regressions instead. We use standard information criteria for the selection of the unknown transition function. Our Monte Carlo simulations reveal that the approach works well in practice. Empirical applications to the S&P500 price-earnings ratio and the US interest spread highlight the merits of our suggested procedure. |
| Keywords: | Nonlinearity, Smooth transition, Threshold model, Model selection, Unit root |
| JEL: | C15 C22 C52 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:han:dpaper:dp-500&r=ets |
| By: | Pierre Chausse (Department of Economics, University of Waterloo); Dinghai Xu (Department of Economics, University of Waterloo) |
| Abstract: | This paper investigates alternative generalized method of moments (GMM) estimation procedures of a stochastic volatility model with realized volatility measures. The extended model can accommodate a more general correlation structure. General closed form moment conditions are derived to examine the model properties and to evaluate the performance of various GMM estimation procedures under Monte Carlo environment, including standard GMM, principal component GMM, robust GMM and regularized GMM. An application to five company stocks and one stock index is also provided for an empirical demonstration. |
| JEL: | G17 G32 C58 C01 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:wat:wpaper:1203&r=ets |
| By: | Dinghai Xu (Department of Economics, University of Waterloo) |
| Abstract: | This paper develops a simple alternative estimation method for the GARCH models based on the empirical characteristic function. A set of Monte Carlo experiments is carried out to assess the performance of the proposed estimator. The results reveal that the proposed estimator has good finite sample properties and is comparable to the conventional maximum likelihood estimator. The method is applied to the foreign exchange data for empirical illustration. |
| JEL: | C01 C58 |
| Date: | 2012–05 |
| URL: | http://d.repec.org/n?u=RePEc:wat:wpaper:1204&r=ets |