Introducing the day-of-the-year temperature model

Continuing with the work we did in the previous example, I would like to propose a new model, where temperature is a function of the day of the year (between 1 and 366). Of course, this model is not complete, but can be used as a component in a more advanced model, which should take into account the previous autoregressive model that we did with lag 2. The procedure for this model is illustrated as follows:

1. Fit the temperature data before the cutoff point to a quadratic polynomial just as in the previous section but without averaging:

   poly = np.polyfit(days[:cutoff], temp[:cutoff], 2)
   print poly

   Believe it or not, we get the same polynomial coefficients we got earlier:

   [ -4.91072584e-04   1.92682505e-01  -3.97182941e+00]
   

2. Calculate the absolute difference between the predicted and actual values:

   delta = np.abs(np.polyval(poly, days[cutoff:]) - temp[cutoff:])

3. Plot a histogram of the absolute error:

   plt.hist(delta, bins = 10, normed = True)
   plt.show...