Li Song

A Time-Varying FARIMA Model for Internet Traffic

We present a time-varying fractional autoregressive integrated moving average model and the methodology to fit this model to a non-stationary time series with local stationarity. Our experiments illustrate that the proposed model is able to capture the non-stationarity of traffic with time-varying parameters. An application to Internet traffic data is presented.

Structural changes estimation for strongly dependent processes

In this paper, we consider the problem of estimating multiple structural breaks in a long-memory fractional autoregressive integrated moving-average time series. The number of break points as well as their locations, the orders and the parameters of each regime are assumed to be unknown. A selection criterion based on the minimum description length principle is proposed and a genetic algorithm is implemented for its optimization. Monte Carlo simulation results show the effectiveness of this criterion and an application to the Nile River data is considered.

A selection criterion for piecewise stationary long-memory models

This article considers the problem of estimating multiple structural breaks in a long-memory FARIMA signal. The number of break points as well as their locations, the orders and the parameters of each regime are assumed to be unknown. A selection criterion based on the minimum description length (MDL) principle is proposed and is compared favorably with two existing criteria by means of Monte Carlo simulations.

Piecewise FARIMA models for long-memory time series

We consider the problem of modelling a long-memory time series using piecewise fractional autoregressive integrated moving average processes. The number as well as the locations of structural break points (BPs) and the parameters of each regime are assumed to be unknown. A four-step procedure is proposed to find out the BPs and to estimate the parameters of each regime. Its effectiveness is shown by Monte Carlo simulations and an application to real traffic data modelling is considered.

Break detection in nonstationary strongly dependent long time series

We consider the problem of fitting a piecewise fractional autoregressive integrated moving average model to strongly dependent signals with large data. The number as well as the locations of structural break points, the model order and the parameters of each regime are assumed to be unknown. A four-step method based on distances between parameter estimates is proposed, to avoid the optimization problem which criterion based methods may be trapped in when there are a lot of data in the signal series. Monte Carlo simulations show the effectiveness of the method with different distances and an application to real traffic data modelling is considered.

A procedure for modeling non-stationary signals with long range dependence

Abstract The problem of modeling non-stationary signals with long range dependence is considered in this paper by using piecewise fractional autoregressive integrated moving average processes. In this piecewise model the number and the locations of structural change points as well as the parameters of each stationary regime are assumed to be unknown. We propose a procedure to find out all the parameters of the model. Its effectiveness is shown by Monte Carlo simulations and our method is applied to model Internet traffic data.

Modelling piecewise long memory signals based on MDL

We consider the problem of modelling piecewise fractional autoregressive integrated moving-average (FARIMA) model signal. The number m of break points as well as their locations, the order (p, q) and the parameters of each regime are assumed to be unknown. To estimate the unknown parameters, we propose a criterion based on the minimum description length (MDL) principle of Rissanen. A genetic algorithm is implemented to optimize this criterion. Monte Carlo simulation results show that criterion performs well for estimating the break points number as well as their locations, the order and the parameters of each regime.

Structural breaks estimation for long memory signals

We consider the problem of estimating the structural breaks in a long memory FARIMA process. The number m of break points as well as their locations, the order (p, d, q) and the parameters of each regime are assumed to be unknown. To estimate the unknown parameters, we propose two criteria based on the minimum description length (MDL) principle of Rissanen, namely a direct extension of MDL and an improved MDL criterion embedded with Bayes information criterion (BIC). A genetic algorithm is implemented to optimize these two criteria. Monte Carlo simulation results show that both criteria perform well for estimating the break points number and their locations. The direct extension of MDL tends to over-estimate the regimes model order which is not the case of the improved MDL criterion.