Univariate time-series models

Multiple linear-regression models expressed the variable of interest as a linear combination of the inputs, plus a random disturbance. In contrast, univariate time-series models relate the current value of the time series to a linear combination of lagged values of the series, current noise, and possibly past noise terms.

While exponential smoothing models are based on a description of the trend and seasonality in the data, ARIMA models aim to describe the autocorrelations in the data. ARIMA(p, d, q) models require stationarity and leverage two building blocks:

• Autoregressive (AR) terms consisting of p lagged values of the time series
• Moving average (MA) terms that contain q lagged disturbances

The I stands for integrated because the model can account for unit-root non-stationarity by differentiating the series d times. The term autoregression underlines that ARIMA models imply a regression of the time series on its own values...