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We introduce a fractional Langevin equation with α-stable noise and show that its solution $Y_{κ} (t), t \geq 0$ is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of $Y_{κ} (t)$ via the measure of its codependence r(θ₁,θ₂,t). We prove that $Y_{κ} (t)$ is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of the Langevin...

Further applications of the T*-test to time-series analysis

E. Pleszczyńska (1971)

Applicationes Mathematicae

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First-order autoregressive processes with time-dependent random parameters

Forecasting Telecommunication New Service Demand by Analogy Method and Combined Forecast

Foregasting with adaptive filtering

Forward estimation for ergodic time series

Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series

Further applications of the T*-test to time-series analysis

Currently displaying 1 – 6 of 6