What can one expect from the cubic regression analysis of a stock quote?
Fig. 5 The cubic regression of a set of stock quotes taken over a two year period.
In the above figure the yellow line represents the daily value of a stock since about two years (512 working days). The red curve represents the cubic regression, the green and blue lines represent the positive, respectively negative mean deviation. Although we see that the stock has been rising for the last ±30 days the regression curve indicates that on the long run the stock will be falling. This is not a prediction but an indication: just think about all the long-term investors who bought the stock at 36 € some 500 days ago and started selling the stock, after it soared at 47 € and began tumbling down some 100 days ago. This opinion is one of a long term investor who will certainly be very reluctant to buy this stock. Carrying out the regression on a window of 100 days paints us an entirely different picture:
Fig. 6 The cubic regression of the same stock quotes over a 100 (working) days window.
A short term investor could tell you that the drop of the value of the stock is due to either a lack of interest from the traders, or a temporary ill management of the company, or any other reason. On the contrary he well tell you that there are sales going on, now that the prices are low, and it is the right moment to buy.
From the two preceding examples one can conclude that both rising (see fig 3) and falling (see fig 4) modes are possible. This results from the fact that cubic regression can be exercised over different windows.