Cubic curves

The forms cubic curves can take

Home Cubic regression Using the software Retrieving the data at Yahoo Finance Populating the database Download Contact

Topics

The principles of regression More about regression Cubic curves Cubic regression Phases of a cubic regression Examples of C.R. phases

Why cubic curves?

While finding a trend in a data series can be quite useful it is perhaps more interesting to use curves other than lines and more flexible to approximate such series. A candidate type of curve that comes to mind are cubics. Mathematically they are also called curves of the third degree because they represent polynomials of the third degree. A question that rises immediately is: "why not use quadratic curves (they are of the second degree)". The answer to that is: quadratic curves are a special case of cubic curves so we lose nothing by considering cubics only. Moreover cubics have two extrema: a minimum and a maximum, while quadratic curves have only one: a maximum or a minimum. Fig. 3 represents such a curve. It can be considered as a value that has been rising in the past, reached a maximum, and then fell down onto a minimum, but caught up afterwards to rise again.

Fig. 3   A typical cubic with rising trend having a maximum at -1 and a minimum at +1

On the other hand cubics, like straight lines, can be used to represent descending values. Fig. 4 represents such a curve. It represents a value that was declining in the past reached a dip, then raised up for a while and after reaching a maximum continued to fall again.

Fig. 4   A cubic with falling trend having a minimum at -1 and a maximum at +1