Predicting temperature
Temperature is a thermodynamic variable, which quantifies being hot or cold. To predict temperature, we can apply our knowledge of thermodynamics and meteorology. This in general would result in the creation of complex weather models with a multitude of inputs. However, this is beyond the scope of this book, so we will try to keep our continuing example simple and manageable.
Autoregressive model with lag 1
What will the temperature be tomorrow? Probably, the same as today but a bit different. We can assume that temperature is a function of the temperature of the preceding day. This can be justified with the autocorrelation plot that we created earlier. To keep it simple, we will assume further that the function is a polynomial. We will define a cutoff point to be used for the fit. Ninety percent of the data should be used for that purpose. Let's model this idea with NumPy:
Fit the data to polynomials of different degrees with the
polyfitfunction as shown in the following...
