Introduction The ARIMA (autoregressive integrated moving average) models are also known as Box–Jenkins models. ARIMA models are applied in some cases where data show evidence of non-stationarity, where an initial differencing step (corresponding to the “integrated” part of the model) can be applied one or more times to eliminate the non-stationarity.
The AR part of ARIMA indicates that the evolving variable of interest is regressed on its own lagged (i.
Introduction State-space models were originally developed by control engineers, particularly for applications that require continuous updating of the current position. An example, from the field of navigation systems, is updating an user equipment’s position. The models have also found increasing use in many types of time-series problems, including parameter estimation, smoothing, and prediction. Structural time-series models are state-space models for time-series data. They are useful in practice because they are