Detrending of time series refers to the process of removing a trend or a long-term systematic variation from a time series dataset, leaving only the short-term fluctuations or noise. The trend may be linear or nonlinear and may be due to factors such as population growth, economic cycles, seasonal patterns, or other long-term changes in the underlying system.
In Python, you can use several methods to detrend a time series. Here are some of the popular methods:
Moving Average: This method involves calculating the moving average of the time series data over a specified window size. The moving average acts as a smoothed version of the original data, allowing for the detection of the underlying trend. You can then subtract the moving average from the original data to obtain the detrended data.
Polynomial Regression: Polynomial regression fits a polynomial function to the time series data and extracts the trend as the function's output. The detrended data can then be obtained by subtracting the trend function from the original data.
Hodrick-Prescott Filter: The Hodrick-Prescott filter is a popular method used in macroeconomics to separate a time series into a trend and a cyclical component. The filter decomposes the data into a trend component and a cyclical component by minimizing the sum of the squared deviations of the trend component from the original data.
Here's an example of how to use the moving average method in Python to detrend a time series:
import pandas as pd
import matplotlib.pyplot as plt
# load time series data
data = pd.read_csv('time_series_data.csv')
# calculate moving average over a window of size 5
window_size = 5
moving_avg = data['value'].rolling(window=window_size).mean()
# subtract moving average from original data to get detrended data
detrended = data['value'] - moving_avg
# plot original and detrended data
plt.plot(data['value'], label='Original')
plt.plot(detrended, label='Detrended')
plt.legend()
plt.show()
This code reads the time series data from a CSV file, calculates the moving average over a window of size 5, subtracts the moving average from the original data to obtain the detrended data, and then plots both the original and detrended data. You can use similar code for other detrending methods as well.
There could be many options for detrending or fitting a trend. In Python, one choice is to fit a nonlinear trend and get the remainder as the detrend signal using. One such tool is this package at https://pypi.org/project/Rbeast/ where in the second example, the trend is removed, leaving only the seasonal variation. But depending on your use scenarios, a simple linear regression may be sufficient for the detrending purpose.
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