On continuous-time autoregressive fractionally integrated moving average processes
Copyright policy )On continuous-time autoregressive fractionally integrated moving average processes
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.
Published in at http://dx.doi.org/10.3150/08-BEJ143 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
- University of Iowa United States
- Academia Sinica Taiwan
Time series, auto-correlation, regression, etc. in statistics (GARCH), antipersistence, fractional Brownian motion, spectral density, FOS: Mathematics, autocovariance, long memory, Mathematics - Statistics Theory, Statistics Theory (math.ST), Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Time series, auto-correlation, regression, etc. in statistics (GARCH), antipersistence, fractional Brownian motion, spectral density, FOS: Mathematics, autocovariance, long memory, Mathematics - Statistics Theory, Statistics Theory (math.ST), Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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