# Q#108: Removing a trend from time series data

*N**ote:** I believe it should be free and readily available for everyone to gain value from data, hence I pledge to keep this series free regardless of how large it grows.*

**What is a time series and what is a trend in a time series dataset? If there’s a trend in a series, how can we remove it and why would we want to remove it? Given this ****dataset**** (***df = pd.read_csv(‘**https://raw.githubusercontent.com/erood/interviewqs.com_code_snippets/master/Datasets/timeseries_v1.csv**')***), remove the trend from the series.**

# TRY IT YOURSELF

## ANSWER

# What is a Time Series?

A **time series** is a sequence of data points recorded or measured at successive points in time. Each data point is associated with a specific timestamp, making the analysis of time series data distinct from other types of data analysis. Time series data is prevalent in various domains such as finance, economics, environmental studies, and many more. Examples include stock prices, weather data, sales figures, and sensor readings.

# What is a Trend in a Time Series Dataset?

A **trend** in a time series dataset represents the long-term movement or direction in the data over time. It shows the general tendency of the data to increase, decrease, or remain stable over a period. Trends can be identified by observing the data over a longer time horizon, and they can be linear or nonlinear. Detecting trends is crucial for understanding underlying patterns and making informed predictions.

# Why Remove a Trend from a Time Series?

**Detrending** a time series involves removing the trend component to focus on other underlying patterns such as seasonality and cycles. Here are a few reasons why detrending is important:

**Improved Forecasting:**Many forecasting models assume that the data is stationary, meaning its statistical properties do not change over time. Removing the trend helps achieve stationarity.**Isolating Seasonal Effects:**Detrending allows for a clearer analysis of seasonal patterns and cyclic behaviors in the data.**Enhanced Model Performance:**Models like ARIMA (AutoRegressive Integrated Moving Average) perform better on stationary data.

# How to Remove a Trend from a Time Series?

There are several methods to remove a trend from a time series:

**Differencing:**Subtracting consecutive observations to remove linear trends.**Decomposition:**Splitting the time series into trend, seasonality, and residual components.**Regression:**Fitting a regression model to the data and subtracting the fitted values.

# Practical Example: Removing a Trend from a Dataset

Let’s apply detrending to a sample dataset. We’ll use Python to import the dataset and remove the trend.

`# Import libraries`

%matplotlib inline

import pandas as pd

import matplotlib.pyplot as plt

import numpy as np

# Import data

df = pd.read_csv('https://raw.githubusercontent.com/erood/interviewqs.com_code_snippets/master/Datasets/timeseries_v1.csv')

# Display the first few rows of the dataset

print(df.head())

# Plot the original time series

plt.figure(figsize=(10, 5))

plt.plot(df['value'])

plt.title('Original Time Series')

plt.xlabel('Time')

plt.ylabel('Value')

plt.show()

# Differencing Method

Differencing is a simple yet effective method to remove trends. It involves subtracting the previous observation from the current observation.

`# Differencing to remove trend`

df['value_diff'] = df['value'].diff()

# Plot the differenced time series

plt.figure(figsize=(10, 5))

plt.plot(df['value_diff'])

plt.title('Differenced Time Series')

plt.xlabel('Time')

plt.ylabel('Differenced Value')

plt.show()

# Decomposition Method

Decomposition splits the time series into trend, seasonal, and residual components.

`from statsmodels.tsa.seasonal import seasonal_decompose`

# Decompose the time series

result = seasonal_decompose(df['value'], model='additive', period=1)

df['detrended'] = df['value'] - result.trend

# Plot the decomposed components

plt.figure(figsize=(10, 5))

plt.subplot(411)

plt.plot(df['value'], label='Original')

plt.legend(loc='upper left')

plt.subplot(412)

plt.plot(result.trend, label='Trend')

plt.legend(loc='upper left')

plt.subplot(413)

plt.plot(result.seasonal, label='Seasonality')

plt.legend(loc='upper left')

plt.subplot(414)

plt.plot(df['detrended'], label='Detrended')

plt.legend(loc='upper left')

plt.tight_layout()

plt.show()