Moving-average temperature model with lag 1

The moving average model of a time series represents the data as oscillations around the mean of the data. It is assumed that the lag components are white noise (not a politically incorrect term as far as I know), which forms a linear combination. We will again use the leastsq function to fit a model:

1. We will start off with a simple moving-average model. It has only one lag component and therefore only one coefficient. The code snippet is as follows:

   def model(p, ma1):
      return p * ma1

2. Call the leastsq function. Here, we subtract the mean from the data:

   params = leastsq(error, p0, args=(temp[1:cutoff] - mu, temp[:cutoff-1] - mu))[0]
   print params

   The program prints the following parameter:

   [ 0.94809073]
   

   We get the following plot for the absolute error histogram, which is comparable to the autoregressive model results: