How to evaluate timeseries models using AIC?
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# How to evaluate timeseries models using AIC?

This recipe helps you evaluate timeseries models using AIC

0

## Recipe Objective

The Akaike Information Critera (AIC) is a widely used measure of a statistical model. It basically quantifies the goodness of fit and the simplicity/parsimony, of the model into a single statistic. When comparing two models, the one with the lower AIC is generally 'better'.

So this recipe is a short example on how to evaluate time series models using AIC. Let's get started.

## Step 1 - Import the library

``` import numpy as np import pandas as pd from statsmodels.tsa.arima_model import ARIMA ```

Let's pause and look at these imports. Numpy and pandas are general ones. Here matplotlib.pyplot will help us in plotting. statsmodels.tsa.arima_model will help us in model building.

## Step 2 - Setup the Data

``` df = pd.read_csv('https://raw.githubusercontent.com/selva86/datasets/master/a10.csv', parse_dates=['date']) ```

Here, we have used one time series data from github. Also, we have set our index to date.

## Step 3 - Calculating AIC

``` for i in range(0,2): for j in range(0,2): for k in range(0,2): model = ARIMA(df.value, order=(i, j, k)).fit() print(model.aic) ```

Best AIC can easily be calcuated through libraries. Here we have tried to understand what actually is happening inside. With variation of values of orders, AIC can be seen varying.

## Step 4 - Lets look at our dataset now

Once we run the above code snippet, we will see:

```1310.0276476996216
1152.1010884622729
906.8908037492013
858.8861982732806
908.9724818749953
874.8436348634339
879.5863881212866
843.8379425029493
```

Clearly, order (1,1,1) is best fitted solution to our model. It can be extended further to 2 degrees to have a better understanding of results.

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