We extend the notion of cointegration for time series taking values in a potentially infinite dimensional Banach space. Examples such include stochastic processes $C[0,1]$ equipped with supremum distance and those finite vector space non-Euclidean distance. then develop versions Granger–Johansen representation theorems I(1) I(2) autoregressive (AR) To achieve this goal, we first note that an AR...

The asymptotic covariance matrix of the empirical cepstrum is analyzed. We show that for Gaussian processes, cepstral coefficients derived from smoothed periodograms are asymptotically uncorrelated and their variances multiplied by the sample size T tend to unity. For an autoregressive process and its autoregressive cepstrum estimate, somewhat weaker results hold.

1.1. Point Processses and Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. Stochastic Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. The Autoregressive Conditional Duration Model . . . . . . . . . . . . . . . . . . . . . . . 2 1.3. The Autoregressive Conditional Intensity Model . . . . . . . . . . . . . . . ...

A nonlinear autoregressive model, the process feedback nonlinear autoregressive (PFNAR) model, in which the autoregressive coe0cients are a function of the combination of past data, is proposed. The autoregressive coe0cients of the PFNAR model consist of sequential autoregressive parts, and a data process feedback part that feeds back the in2uence from previous data points with “signi4cant dela...