Showing papers by "Neil Shephard published in 2006"

Limit theorems for bipower variation in financial econometrics

Abstract: In this paper we provide an asymptotic analysis of generalised bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation and bipower variations which have been highlighted in recent years in financial econometrics. The analysis is carried out under some rather general Brownian semimartingale assumptions, which allow for standard leverage effects.

Power Variation and Time Change

Abstract: This paper provides limit distribution results for power variation, that is, sums of powers of absolute increments under nonequidistant subdivisions of time and for certain types of time-changed Brownian motion and $\alpha$-stable processes. Special cases of these processes are stochastic volatility models used extensively in financial econometrics.

Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space form

Abstract: In this paper we model the Gaussian errors in the standard Gaussian linear state space model as stochastic volatility processes. We show that conventional MCMC algorithms for this class of models are ineffective, but that the problem can be alleviated by reparameterizing the model. Instead of sampling the unobserved variance series directly, we sample in the space of the disturbances, which proves to lower correlation in the sampler and thus increases the quality of the Markov chain. Using our reparameterized MCMC sampler, it is possible to estimate an unobserved factor model for exchange rates between a group of n countries. The underlying n + 1 country-specific currency strength factors and the n + 1 currency volatility factors can be extracted using the new methodology. With the factors, a more detailed image of the events around the 1992 EMS crisis is obtained. We assess the fit of competitive models on the panels of exchange rates with an effective particle filter and find that indeed the factor mode...

Multipower Variation and Stochastic Volatility

Abstract: In this brief note we review some of our recent results on the use of high frequency financial data to estimate objects like integrated variance in stochastic volatility models. Interesting issues include multipower variation, jumps and market microstructure effects.

Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise

Abstract: This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed Gaussian limit theorems. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem. Realised kernels can also be selected to (i) be analysed using endogenously spaced data such as that in databases on transactions, (ii) allow for market frictions which are endogenous, (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice.

Subsampling realised kernels

Abstract: In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.