Making time series stationary

ARIMA Models in Python

James Fulton

Climate informatics researcher

Overview

Statistical tests for stationarity
Making a dataset stationary

The augmented Dicky-Fuller test

Tests for trend non-stationarity
Null hypothesis is time series is non-stationary

Applying the adfuller test

from statsmodels.tsa.stattools import adfuller

results = adfuller(df['close'])

Interpreting the test result

print(results)

(-1.34, 0.60, 23, 1235, {'1%': -3.435, '5%': -2.913, '10%': -2.568}, 10782.87)

0th element is test statistic (-1.34)
- More negative means more likely to be stationary

1st element is p-value: (0.60)
- If p-value is small $\rightarrow$ reject null hypothesis. Reject non-stationary.

4th element is the critical test statistics

Interpreting the test result

print(results)

(-1.34, 0.60, 23, 1235, {'1%': -3.435, '5%': -2.863, '10%': -2.568}, 10782.87)

0th element is test statistic (-1.34)
- More negative means more likely to be stationary

1st element is p-value: (0.60)
- If p-value is small $\rightarrow$ reject null hypothesis. Reject non-stationary.

4th element is the critical test statistics

¹ https://www.statsmodels.org/dev/generated/statsmodels.tsa.stattools.adfuller.html

The value of plotting

Plotting time series can stop you making wrong assumptions

The value of plotting

Making a time series stationary

Taking the difference

Difference: $\Delta y_t = y_t - y_{t-1}$

Taking the difference

df_stationary = df.diff()

            city_population
date                       
1969-09-30              NaN
1970-03-31        -0.116156
1970-09-30         0.050850
1971-03-31        -0.153261
1971-09-30         0.108389

Taking the difference

df_stationary = df.diff().dropna()

            city_population
date                       
1970-03-31        -0.116156
1970-09-30         0.050850
1971-03-31        -0.153261
1971-09-30         0.108389
1972-03-31        -0.029569

Taking the difference

Other transforms

Examples of other transforms

Take the log
- np.log(df)
Take the square root
- np.sqrt(df)
Take the proportional change
- df.shift(1)/df

Let's practice!

ARIMA Models in Python