DIFFERENTIAL GEOMETRY OF ARFIMAPROCESSES

Abstract

Autoregressive fractionally integrated moving average (ARFIMA) processes are widely used for modeling time series exhibiting both long-memory and short-memory behavior. Properties of Toeplitz matrices associated with the spectral density functions of Gaussian ARFIMAprocesses are used to compute differential geometric quantities.

Keywords:

• Affine transformations
• Curvature
• Fractional differencing
• Long-memory models
• Riemannian metric tensor

ACKNOWLEDGMENTS

The author is grateful to Zuqiang Qiou for his help with some computations.