منابع مشابه
Extremes of supOU processes
Barndorff-Nielsen and Shephard [3] investigate supOU processes as volatility models. Empirical volatility has tails heavier than normal, long memory in the sense that the empirical autocorrelation function decreases slower than exponential, and exhibits volatility clusters on high levels. We investigate supOU processes with respect to these stylized facts. The class of supOU processes is vast a...
متن کاملThe multivariate supOU stochastic volatility model
Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order structure of the volatility, the log returns, as well as their “squares” are discussed in detail. M...
متن کاملTail Behavior of Multivariate Lévy-Driven Mixed Moving Average Processes and supOU Stochastic Volatility Models
Multivariate Lévy-driven mixed moving average (MMA) processes of the type Xt = ∫ ∫ f(A, t − s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) CARMA processes and increments of fractional Lévy processes. In this paper, we introduce multivariate MMA pro...
متن کاملMixing Conditions for Multivariate Infinitely Divisible Processes with an Application to Mixed Moving Averages and the supOU Stochastic Volatility Model
We consider strictly stationary infinitely divisible processes and first extend the mixing conditions given in Maruyama [18] and Rosiński and Żak [23] from the univariate to the d-dimensional case. Thereafter, we show that multivariate Lévy-driven mixed moving average processes satisfy these conditions and hence a wide range of well-known processes such as superpositions of Ornstein-Uhlenbeck (...
متن کاملMultivariate COGARCH(1,1) processes
Multivariate COGARCH(1,1) processes are introduced as a continuous-time models for multidimensional heteroskedastic observations. Our model is driven by a single multivariate Lévy process and the latent timevarying covariance matrix is directly specified as a stochastic process in the positive semidefinite matrices. After defining the COGARCH(1,1) process, we analyze its probabilistic propertie...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2011
ISSN: 1050-5164
DOI: 10.1214/10-aap690