Trend Models

What are Trend Models?

A linear temporal trend is a series that tends to change by the same amount each period.

While linear time trend models benefit from simplicity, they are of limited use in finance and economics for two main reasons:

1. If the trend is downward, a linear model eventually produces negative values, which do not make sense when modelling quantities or prices.

2. Even if the trend is upward, a constant increase in the amount implies a decreasing growth rate over time. Many variables are more accurately modelled as growing at a constant rate rather than a constant amount.

Example of Trend Models:

A linear time trend can be modelled simply as,

y_t = δ₀ + δ₁t

where ε𝑡 is a white noise process. Note that the series is non-stationary because the observations depend on time.