Quadratic models

If the trend in a time series is nonlinear, a linear model should not be used. A simple model that can explain some simple types of curvature is a quadratic model:

trend   =   b0  +  b1 time  +  b2 time2

This has three parameters that can be adjusted to improve the fit of the model. Residuals are again defined as

ei  =  yi − trendi

and the least squares estimates of b0, b1 and b2 are the values that minimise the residual sum of squares,

Σ ei2