Trends

A trend is a gradual upward or downward shift in the level of the series or the tendency of the series values to increase or decrease over time.

Trends are either local or global, but a single series can exhibit both types. Historically, series plots of the stock market index show an upward global trend. Local downward trends have appeared in times of recession, and local upward trends have appeared in times of prosperity.

Trends can also be either linear or nonlinear. Linear trends are positive or negative additive increments to the level of the series, comparable to the effect of simple interest on principal. Nonlinear trends are often multiplicative, with increments that are proportional to the previous series value(s).

Global linear trends are fit and forecast well by both exponential smoothing and ARIMA models. In building ARIMA models, series showing trends are generally differenced to remove the effect of the trend.