An object of class "trend", which is a list with the following
elements:
trend
trend component.
residual
residuals.
tau2
variance of the system noise \(\tau^2\).
sigma2
variance of the observational noise \(\sigma^2\).
llkhood
log-likelihood of the model.
aic
AIC.
Details
The trend model can be represented by a state space model
$$x_n = Fx_{n-1} + Gv_n,$$
$$y_n = Hx_n + w_n,$$
where \(F\), \(G\) and \(H\) are matrices with appropriate dimensions.
We assume that \(v_n\) and \(w_n\) are white noises that have
the normal distributions \(N(0,\tau^2)\) and \(N(0, \sigma^2)\),
respectively.
References
Kitagawa, G. (2010)
Introduction to Time Series Modeling. Chapman & Hall/CRC.