17 research outputs found
Estimating Drift Parameters in a Fractional Ornstein Uhlenbeck Process with Periodic Mean
We construct a least squares estimator for the drift parameters of a
fractional Ornstein Uhlenbeck process with periodic mean function and long
range dependence. For this estimator we prove consistency and asymptotic
normality. In contrast to the classical fractional Ornstein Uhlenbeck process
without periodic mean function the rate of convergence is slower depending on
the Hurst parameter , namely
Well-balanced Lévy driven Ornstein-Uhlenbeck processes
In this paper we introduce the well-balanced Lévy driven Ornstein-Uhlenbeck process as a moving average process of the form X_t=integral(exp(-lambda*|t-u|)dL_u). In
contrast to Lévy driven Ornstein-Uhlenbeck processes the well-balanced form possesses
continuous sample paths and an autocorrelation function which is decreasing
more slowly. Furthermore, depending on the size of lambda it allows both for positive
and negative correlation of increments. As Ornstein-Uhlenbeck processes X_t is a
stationary process starting at X_0=integral(exp(-lambda*u)dL_u). However, by taking a difference
kernel we can construct a process with stationary increments starting at zero,
which possesses the same correlation structure
Estimation of Integrated Volatility in Stochastic Volatility Models
In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the p-th power variation, i.e. the sum of p-th absolute powers of the log-returns. We derive consistency and distributional results for the estimators given high frequency data, especially taking into account what kind of process we may add to our model without e#ecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, e.g. adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification