How to get constant term in AR Model with statsmodels and Python?

Question

I'm trying to model my time series data using the AR model.

This is the code that I'm using.

# Compute AR-model (data is a python list of number)

model = AR(data)
result = model.fit()

plt.plot(data, 'b-', label='data')
plt.plot(range(result.k_ar, len(data)), result.fittedvalues, 'r-')
plt.show()

I've successfully get the p value using result.k_ar, parameter with result.params, epsilon term with result.sigma2. The problem is that I can't find a way to get the c (constant) term. Here is the code I write to compare the result.

# Plot

fit = []
for t in range(result.k_ar, len(data)):
    value = 0
    for i in range(1, result.k_ar+1):
        value += result.params[i-1] * data[t - i]
    fit.append(value)

plt.plot(data, 'b-', label='data')
plt.plot(range(result.k_ar, len(data)), fit, 'r-', label='fit')
plt.plot(range(result.k_ar, len(data)), result.fittedvalues, 'r-')
plt.show()

My result and the result from result.fittedvalues confirm my evident that there is some constant term added to the model. Thanks.

Answer 1

The constant is the zero-th element in params. E.g., params[0].

Your code should be

fit = []
for t in range(result.k_ar, len(data)):
    value = result.params[0]
    for i in range(2, result.k_ar + 2):
        value += result.params[i - 1] * data[t - i + 1]
    fit.append(value)

Or even easier, since we've made the lag matrix for you (this is what fittedvalues does)

np.dot(result.model.X, result.params)

As an aside, note that for AR this is actually the constant and not the mean. The mean is reported by the ARMA model, which is a bit more full-featured than the plain AR model. (It has a summary method that reports the constant. AR should too but doesn't.) The connection is

constant = mean(1 - arparams.sum())