Cubic and higher-degree polynomial models

If a quadratic model does not adequately describe the shape of the trend in a time series, it is tempting to try to further increase the order of the polynomial,

trend   =   b0  +  b1 time  +  b2 time2  +  b3 time3  +  ...

This kind of polynomial model can also be fitted by least squares.

A polynomial of degree 3 or 4 often provides a fairly smooth description of trend but polynomial models usually behave badly (with sudden increases or decreases) beyond the data points, so...

Polynomial models of degree greater than 2 should not be used for forecasting.