 KoalaTea

# Detrending Time Series in Python

## Intro

A common task in time series analysis is taking the difference or detrending of a series. This is often used to take a non-stationary time series and make it stationary. In this article, we will learn how to detrend a time series in Python.

## Data

Let's load a data set of monthly milk production. We will load it from the url below. The data consists of monthly intervals and kilograms of milk produced.

import pandas as pd

df.month = pd.to_datetime(df.month)
df = df.set_index('month')
df.head()
milk_prod_per_cow_kg
month
1962-01-01 265.05
1962-02-01 252.45
1962-03-01 288.00
1962-04-01 295.20
1962-05-01 327.15

## Detrending

Let's first plot our time series to see the trend.

df.plot()
<AxesSubplot:xlabel='month'>

There seems to be a a linear trend. Let's see what happens after detrending. To do detrending, we can use the detrend function from the scipy module.

from scipy import signal

detrended = signal.detrend(df.milk_prod_per_cow_kg)

detrended_df = pd.DataFrame(detrended)
detrended_df.plot()
<AxesSubplot:>

That is looking really good. The Linear trend seems to be gone.

## Removing a Seasonal Trend

After removing a linear trend, we also want to remove seasonality so that we can model the data. To do this we can use the seasonal_decompose function from the statsmodels package.

from statsmodels.tsa.seasonal import seasonal_decompose
res = seasonal_decompose(df.milk_prod_per_cow_kg, model='multiplicative', extrapolate_trend='freq')

detrended = df.milk_prod_per_cow_kg.values - res.trend

detrended_df = pd.DataFrame(detrended)
detrended_df.plot()
<AxesSubplot:xlabel='month'>