Time for action – fitting to polynomials

The NumPy polyfit function can fit a set of data points to a polynomial even if the underlying function is not continuous:

1. Continuing with the price data of BHP and VALE, let's look at the difference of their close prices and fit it to a polynomial of the third power:

   bhp=np.loadtxt('BHP.csv', delimiter=',', usecols=(6,), unpack=True)
   vale=np.loadtxt('VALE.csv', delimiter=',', usecols=(6,), unpack=True)
   t = np.arange(len(bhp))
   poly = np.polyfit(t, bhp - vale, int(sys.argv[1]))
   print "Polynomial fit", poly

   The polynomial fit (in this example, a cubic polynomial was chosen):

   Polynomial fit [  1.11655581e-03  -5.28581762e-02   5.80684638e-01   5.79791202e+01]
   

2. The numbers you see are the coefficients of the polynomial. Extrapolate to the next value with the polyval function and the polynomial object we got from the fit:

   print "Next value", np.polyval(poly, t[-1] + 1)

   The next value we predict will be:

   Next value 57.9743076081
   

3. Ideally, the difference between...