Choosing the Right Model

Time Series Analysis in Python

Rob Reider

Adjunct Professor, NYU-Courant Consultant, Quantopian

Identifying the Order of an AR Model

The order of an AR(p) model will usually be unknown
Two techniques to determine order
- Partial Autocorrelation Function
- Information criteria

Partial Autocorrelation Function (PACF)

Plot PACF in Python

Same as ACF, but use plot_pacf instead of plt_acf

Import module

from statsmodels.graphics.tsaplots import plot_pacf

Plot the PACF
```
plot_pacf(x, lags= 20, alpha=0.05)
```

Comparison of PACF for Different AR Models

AR(1)
AR(3)

AR(2)
White Noise

Information Criteria

Information criteria: adjusts goodness-of-fit for number of parameters
Two popular adjusted goodness-of-fit measures
- AIC (Akaike Information Criterion)
- BIC (Bayesian Information Criterion)

Information Criteria

Estimation output

Getting Information Criteria From statsmodels

You learned earlier how to fit an AR model

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

And to get full output
```
result.summary()
```
Or just the parameters
```
result.params
```
To get the AIC and BIC
```
result.aic
result.bic
```

Information Criteria

Fit a simulated AR(3) to different AR(p) models
Choose p with the lowest BIC

Let's practice!

Time Series Analysis in Python

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