On the first-order bilinear time series model

Abstract

The paper investigates some properties of the first-order bilinear time series model: stationarity and invertibility. Estimates of the parameters are obtained by a modified least squares method and shown to be strongly consistent.

Consistency of quasi-maximum likelihood estimator for Markov-switching bilinear time series models

“…The most frequently used methods are the (generalized) method of moments (G) (MM) and the (conditional) least squares (C) (LS) method. The asymptotic properties of the (G) MM and (C) LS estimates have been also discussed under certain restrictions, see for example, Pham and Tran (1981), Guégan and Pham (1989), Liu (1990), Kim and Billard (1990), Grahn (1995), Wittwer (1989) and among others.…”

The stationarity and invertibility of a class of nonlinear ARMA models

“…Following Pham and Tran [23], we say that model (1) is invertible if ξ t converges to 0 in some sense as t tends to infinity for any initial values. This definition is more general than that of Granger and Andersen [12], who only require that ξ t converges to 0 in mean square.…”

Parameter estimation for a bilinear time series model

“…Subba Rao [8] studied the general problem of parameter estimation of a BL,(p, r, s, q) model by formulating it as a nonlinear optimization problem and estimated the parameters using the Newton-Raphson search procedure. Most of the approaches for direct estimation of the parameters from the measured statistics of the signal deal only with very low orders and as few as one to three parameters [4,5,7]. The difficulty arises because the task of developing expressions for the different moments of the bilinear time series becomes very cumbersome as the model order and the number of parameters increase.…”