On continuous-time autoregressive fractionally integrated moving average processes

Details On continuous-time autoregressive fractionally integrated moving average processes On continuous-time autoregressive fractionally integrated moving average processes

2009-02-09

arxiv.org/abs/0902.1403v1

Bernoulli 2009, Vol. 15, No. 1, 178-194

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ143 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ143

In this paper, we consider a continuous-time autoregressive fractionally integrated moving average (CARFIMA) model, which is defined as the stationary solution of a stochastic differential equation driven by a standard fractional Brownian motion. Like the discrete-time ARFIMA model, the CARFIMA model is useful for studying time series with short memory, long memory and antipersistence. We investigate the stationarity of the model and derive its covariance structure. In addition, we derive the spectral density function of a stationary CARFIMA process.

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