Related papers: Invariance Principles for Tempered Fractionally In…
Autoregressive tempered fractionally integrated moving average (ARTFIMA) time series is a useful model for velocity data in turbulence flows. In this paper, we obtain an invariance principle for the partial sum of an ARTFIMA process. The…
Autoregressive tempered fractionally integrated moving average with stable innovations modifies the power-law kernel of the fractionally integrated time series model by adding an exponential tempering factor. The tempered time series is a…
In this article, we introduce and study a one sided tempered stable first order autoregressive model called TAR(1). Under the assumption of stationarity of the model, the marginal probability density function of the error term is found. It…
We obtain invariance principles for a wide class of fractionally integrated nonlinear processes. The limiting distributions are shown to be fractional Brownian motions. Under very mild conditions, we extend earlier ones on long memory…
This work defines two classes of processes, that we term {\it tempered fractional multistable motion} and {\it tempered multifractional stable motion}. They are extensions of fractional multistable motion and multifractional stable motion,…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…
A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…
Generalizations of tempered fractional Brownian from single index to two indices and variable index or tempered multifractional Brownian motion are studied. Tempered fractional Brownian motion and tempered multifractional Brownian motion…
We define two new classes of stochastic processes, called tempered fractional L\'{e}vy process of the first and second kinds (TFLP and TFLP $I\!I$, respectively). TFLP and TFLP $I\!I$ make up very broad finite-variance, generally…
In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the…
This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634--658,…
In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian motions (TFBMs) which are related to the notions of…
We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used for replica exchange molecular dynamics [Plattner et al., J.…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…
Tempered fractional Brownian motion is revisited from the viewpoint of reduced fractional Ornstein-Uhlenbeck process. Many of the basic properties of the tempered fractional Brownian motion can be shown to be direct consequences or…
In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…