DCS models with trend and seasonal components are described in Sect.
Nonstationary ARIMA-type models may also be constructed as may structural times series models with trend and seasonal components.
The third paper, "Robust Time Series Models with Trend and Seasonal Components" by Michele Calvano, Andrew Harvey and Alessandra Luati, shows how to deal with outliers in models derived from a Student-t and EGB2 models, in particular, the paper proposed the dynamic conditional score t model.
Spatial effects were modeled with thin plate splines, and time effects were modeled with trend, cyclic, and autoregressive terms.
We only report in full parameter estimates for the model with serial dependence and without trend; as we have discussed the estimates of seasonal components in the models with trend but no serial dependence are identical save for sampling variation induced by the MCMC algorithm.
An ARIMA(1,1,2) model without constant is a linear exponential smoothing model with damped trend, i.e., a trend that eventually flattens out in longer-term forecasts.
In the next step we compared our full model with a trend and different coloured noise added to the trend, and with explicit density-compensation at different rates to the theoretical predictions.
Numerical results show that the strength of fractured rocks increases with the increasing confining pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening.
The model with the trend variable allows to test whether our dependent variables predict variance in protest mobilization over time alone.
Using the automated selection feature, the model with cubic trend and annual periodicity is chosen for baseline P&I mortality.
