Different criteria exist to define long memory behavior. The two most used relate to the asymptotic decay of the autocovariance function of a process, and to the shape of its spectral density. In the case of a long memory process, the asymptotic decay of the autocovariance function is...

This paper studies the properties of the sieve bootstrap for a class of linear processes which exhibit strong dependence. The sieve bootstrap scheme is based on residual resampling from autoregressive approximations the order of which increases slowly with the sample size. The first-order...

This paper studies a novel idea for constructing continuous-time stationary Markov models. The approach undertaken is based on a latent representation of the corresponding transition probabilities that conveys to appealing ways to study and simulate the dynamics of the constructed processes....

In this paper we establish the uniqueness of the Lamperti transformation leading from self-similar to stationary processes, and conversely. We discuss alpha-stable processes, which allow to understand better the difference between the Gaussian and non-Gaussian cases. As a by-product we get a...

Bollinger bands are well-known in stock market as a popular technical analysis tool. We found that Black–Scholes stock price model had this Bollinger bands property also. In this paper, we give the proof of this phenomenon, and give a new distribution of a statistics generated by the Bollinger...