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.