Estimating and Forecasting an AR Model

Time Series Analysis in Python

Rob Reider

Adjunct Professor, NYU-Courant Consultant, Quantopian

Estimating an AR Model

To estimate parameters from data (simulated)

from statsmodels.tsa.arima_model import ARMA
mod = ARMA(data, order=(1,0))
result = mod.fit()

ARMA has been deprecated and replaced with ARIMA

from statsmodels.tsa.arima.model import ARIMA
mod = ARIMA(data, order=(1,0,0))
result = mod.fit()

For ARMA, order=(p,q)
For ARIMA,order=(p,d,q)

Estimating an AR Model

Full output (true $\large \mu=0$ and $\large \phi=0.9$)
```
print(result.summary())
```

Estimating an AR Model

Only the estimates of $\large \mu$ and $\large \phi$ (true $\large \mu=0$ and $\large \phi=0.9$)
```
print(result.params)
```

array([-0.03605989,  0.90535667])

Forecasting With an AR Model

from statsmodels.graphics.tsaplots import plot_predict
fig, ax = plt.subplots()
data.plot(ax=ax)
plot_predict(result, start='2012-09-27', end='2012-10-06', alpha=0.05, ax=ax)
plt.show()

Arguments of function plot_predict()
- First argument is fitted model
- Set alpha=None for no confidence interval
- Set ax=ax to plot the data and prediction on same axes

Let's practice!

Time Series Analysis in Python