Recursive estimation for continuous time stochastic volatility models

AbstractVolatility plays an important role in portfolio management and option pricing. Recently, there has been a growing interest in modeling volatility of the observed process by nonlinear stochastic process [S.J. Taylor, Asset Price Dynamics, Volatility, and Prediction, Princeton University Press, 2005; H. Kawakatsu, Specification and estimation of discrete time quadratic stochastic volatility models, Journal of Empirical Finance 14 (2007) 424–442]. In [H. Gong, A. Thavaneswaran, J. Singh, Filtering for some time series models by using transformation, Math Scientist 33 (2008) 141–147], we have studied the recursive estimates for discrete time stochastic volatility models driven by normal errors. In this paper, we study the recursive estimates for various classes of continuous time nonlinear non-Gaussian stochastic volatility models used for option pricing in finance

RCA models with correlated errors

AbstractFinancial time series data cannot be adequately modelled by a normal distribution and empirical evidence on the non-normality assumption is very well documented in the financial literature; see [R.F. Engle, Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica 50 (1982) 987–1008] and [T. Bollerslev, Generalized autoregressive conditional heteroscedasticity, J. Econometrics 31 (1986) 307–327] for details. The kurtosis of various classes of RCA models has been the subject of a study by Appadoo et al. [S.S. Appadoo, M. Gharahmani, A. Thavaneswaran, Moment properties of some volatility models, Math. Sci. 30 (2005) 50–63] and Thavaneswaran et al. [A. Thavaneswaran, S.S. Appadoo, M. Samanta, Random coefficient GARCH models, Math. Comput. Modelling 41 (2005) 723–733]. In this work we derive the kurtosis of the correlated RCA model as well as the normal GARCH model under the assumption that the errors are correlated

Joint Estimation Using Quadratic Estimating Function

A class of martingale estimating functions is convenient and plays an important role for inference for nonlinear time series models. However, when the information about the first four conditional moments of the observed process becomes available, the quadratic estimating functions are more informative. In this paper, a general framework for joint estimation of conditional mean and variance parameters in time series models using quadratic estimating functions is developed. Superiority of the approach is demonstrated by comparing the information associated with the optimal quadratic estimating function with the information associated with other estimating functions. The method is used to study the optimal quadratic estimating functions of the parameters of autoregressive conditional duration (ACD) models, random coefficient autoregressive (RCA) models, doubly stochastic models and regression models with ARCH errors. Closed-form expressions for the information gain are also discussed in some detail

Bridging the gap between robotic technology and health care

Although technology and computation power have become more and more present in our daily lives, we have yet to see the same tendency in robotics applied to health care. In this work we focused on the study of four distinct applications of robotic technology to health care, named Robotic Assisted Surgery, Robotics in Rehabilitation, Prosthetics and Companion Robotic Systems. We identified the main roadblocks that are limiting the progress of such applications by an extensive examination of recent reports. Based on the limitations of the practical use of current robotic technology for health care we proposed a general modularization approach for the conception and implementation of specific robotic devices. The main conclusions of this review are: (i) there is a clear need of the adaptation of robotic technology (closed loop) to the user, so that robotics can be widely accepted and used in the context of heath care; (ii) for all studied robotic technologies cost is still prohibitive and limits their wide use. The reduction of costs influences technology acceptability; thus innovation by using cheaper computer systems and sensors is relevant and should be taken into account in the implementation of robotic systems

Track A Basic Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138319/1/jia218438.pd

• SMOOTHING SIGNALS FOR SEMIMARTINGALES

The kernel function and convolution-smoothing methods developed to estimate a probability density function and distribution are essentially a way of smoothing the empirical distribution function. This paper shows how one can generalize these methods to estimate signals for a semimartingale model. A convolution-smoothed estimate is used to obtain an absolutely continuous estimate for an absolutely continuous signal of a semimartingale model. This provides a method of obtaining a convolution-smoothed estimate of the cumulative hazard function in the censored case, an open problem proposed by ~lack (Bulletin of Informatics and Cybernetics 21 (1984) 29-3.5). Asymptotic properties of the convolution-smoothed estimate are discussed in some detail

Smoothing signals for semimartingales

The kernel function and convolution-smoothing methods developed to estimate a probability density function and distribution are essentially a way of smoothing the empirical distribution function. This paper shows now one can generalize these methods to estimate signals for a semimartingale model. A convolution-smoothed estimate is used to obtain an absolutely continuous estimate for an absolutely continuous signal of a semimartingale model. This provides a method of obtaining a convolution-smoothed estimate of the cumulative hazard function in the censored case, an open problem proposed by Mack (Bulletin of Informatics and Cybernetics 21 (1984) 29-35). Asymptotic properties of the convolution-smoothed estimate are discussed in some detail.convolution-smoothing kernel functions semimartingales signals smoothing

An Introduction to Volatility Models with Indices

AbstractThis paper considers a class of volatility models generated by autoregressive (AR) type models with indices. Some results associated with the autocorrelation function (acf) of this class are given and the spectral density is obtained in terms of the kurtosis of the error distribution and model parameters