The Autocorrelation Functions in SETARMA Models

Asymptotic properties of conditional least-squares estimators for array time series

“…For the diagonal elements, at this time, their existence is an assumption. We can consider the alternative model of Amendola et al (2007) where, defining x (i) t , i = 1, 2 as the two second hand sides of (3.8), we suppose x t = x…”

“…(2) t , if x t−1 > 0. Using that the variance for the two regimes are, respectively, σ 2 /(1 − θ 2 1 ) and σ 2 /(1 − θ 2 2 ), we can then use Proposition 1 in Amendola et al (2007) to obtain (3.10)…”

Least Squares Predictors for Threshold Models: Properties and Forecast Evaluation

“…The interest arisen from these models is testified by the relevant number of variants proposed in literature, with respect to the original one introduced in Tong (1978). Among them, in the present paper the attention is focused on a variant, introduced in Amendola et al (2006), of the so called Self Exciting Threshold Autoregressive Moving Average (SETARMA) model (Tong, 1983) which is a direct generalization of the linear ARMA structure (Box & Jenkins, 1976). The k-regimes model of order (k; p 1 , .…”

“…< r k = +∞, r i are the threshold values, d is the threshold delay, p i and q i are positive integers. Amendola et al (2006) show that, under well defined conditions on the process X t , model (1), with k = 2, can be alternatively written…”