Building Blocks of Linear Time Series Modeling

Three models are presented: AR (autoregressive), MA (moving average) and ARMA (autoregressive moving average) are common models used in time series forecasting. These three models are the various definition of each element of the General Linear Model: Y = a + b + c. For the study of linear behavior of data, these three models are helpful. However, the limitation of these models starts to surface when nonlinear behavior of data appears. Linear behavior is characterized by a straight line mapping the response variable (Y) to each unit change in the explanatory variable (X). If the research involves human emotion, preferences, or level of tolerance and the data series does not manifest a straight line, AR, MA and ARMA may not be as useful. Price tolerance versus utility, for instance is a good example to illustrate where the general linear model may not be useful. N such cases, a higher order polynomial modeling may be used.