Data Science with Python — Time Series Analysis

This article is part of the “Datascience with Python” series. You can find the other stories of this series below:

Data Science with Python

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Time series are used in various fields such as finance, economics, engineering, and many more.

Time series analysis involves studying the pattern of data points collected over time to identify trends, seasonality, and anomalies. Python, with its powerful libraries and tools, has become a popular choice for time series analysis, and that’s what we will explore today.

What are Time Series?

A time series is a set of data points collected at regular intervals over time. Time series data can be seen in various fields, such as finance, economics, weather, and health, where data points are collected at different frequencies, such as daily, weekly, monthly, or yearly.

Time series data differ from other types of data as they have an intrinsic temporal ordering, meaning that each observation is associated with a specific time. Therefore, the analysis of time series data requires specific techniques that account for the temporal dependencies among data points.

Time series data also exhibit certain properties such as trend, seasonality, and irregularity, which can be used to identify patterns and insights from the data. Trends refer to a long-term upward or downward movement of the data over time, while seasonality refers to a regular pattern that occurs within a year or other specific time period. Irregularities, or noise, can be caused by random variation, measurement errors, or other external factors that affect the data.

Time Series Analysis with Python

Python has become a popular language for time series analysis due to its powerful libraries and tools. Two libraries commonly used for time series analysis are pandas and NumPy.

Pandas is a Python library that provides data manipulation and analysis tools, particularly for working with structured data. One of the key data structures in pandas is the DataFrame, which is a 2-dimensional table-like data structure with labeled axes. In time series analysis, pandas provides the ability to load, manipulate, and visualize time series data easily.

NumPy is a Python library that provides numerical computing tools and functions, particularly for working with arrays and matrices. In time series analysis, NumPy provides the ability to perform various mathematical operations on arrays of time series data, such as calculating moving averages and standard deviations.

In addition to pandas and NumPy, matplotlib is another popular Python library used for data visualization, particularly for creating static, interactive, and animated plots. In time series analysis, data visualization is a crucial step to identify patterns, trends, and anomalies in the data.

Time Series Decomposition

Time series decomposition is a technique used to break down a time series into its constituent components, namely trend, seasonality, and residuals. Trend refers to the long-term pattern of the data, while seasonality refers to the cyclic or repetitive pattern of the data that occurs over a fixed time period. Residuals refer to the random noise or fluctuations in the data that are not accounted for by the trend and seasonality components.

Time series decomposition can be performed using various methods, including the classical decomposition method, the moving average method, and the STL decomposition method. In Python, the classical decomposition method can be implemented using the decompose() function in the statsmodels library, while the moving average method can be implemented using the rolling() function in pandas.

Once the time series has been decomposed into its components, each component can be analyzed separately to identify patterns and insights in the data. For example, the trend component can be used to identify long-term patterns or changes in the data, while the seasonality component can be used to identify cyclic or repetitive patterns.

Time Series Forecasting

Time series forecasting is the process of predicting future values of a time series based on its past behavior. Forecasting can be done for various time horizons, such as short-term forecasting for the next few periods or long-term forecasting for several years or decades. Time series forecasting is an essential tool for decision-making in various fields.

In time series forecasting, two popular methods are the Autoregressive Integrated Moving Average (ARIMA) model and the Prophet model developed by Facebook. The ARIMA model is a statistical model that takes into account the autocorrelation and stationarity of the time series and is commonly used for short-term forecasting. The Prophet model is a more recent model that uses a combination of trend, seasonality, and holiday effects to forecast time series data and is commonly used for long-term forecasting.

In Python, the statsmodels library provides an implementation of the ARIMA model, while the Prophet model can be implemented using the Prophet library developed by Facebook.

In addition to these models, machine learning techniques such as linear regression, decision trees, and neural networks can also be used for time series forecasting. However, these models require more data preprocessing and feature engineering compared to the ARIMA and Prophet models.

Code Examples

Performing time series analysis is pretty straightforward using the statsmodels library. In addition, we can use matplotlibto visualize it. For example, to perform decomposition:

from statsmodels.tsa.seasonal import seasonal_decompose

# Perform time series decomposition
decomposition = seasonal_decompose(data, model='multiplicative')

# Visualize the decomposed time series
fig, ax = plt.subplots(4, 1, figsize=(10, 8))
ax[0].set_title('Original')
decomposition.observed.plot(ax=ax[0])
ax[1].set_title('Trend')
decomposition.trend.plot(ax=ax[1])
ax[2].set_title('Seasonality')
decomposition.seasonal.plot(ax=ax[2])
ax[3].set_title('Residual')
decomposition.resid.plot(ax=ax[3])
plt.tight_layout()
plt.show()

We can also perform time series forecasting. For this, we need the pmdarima library:

from pmdarima.arima import auto_arima

# Perform time series forecasting
model = auto_arima(data, seasonal=True, m=12, suppress_warnings=True)
forecast = model.predict(n_periods=12)

# Visualize the forecasted values
plt.plot(data.index, data.values, label='Actual')
plt.plot(data.index[-12:], forecast, label='Forecast')
plt.title('Air Passengers Forecast')
plt.xlabel('Year')
plt.ylabel('Number of Passengers')
plt.legend()
plt.show()

Final Note

Time series analysis is an essential skill for data scientists, analysts, and researchers, and Python provides a powerful and flexible environment for time series analysis and modeling.

In a next article, I’ll cover a real example of time series analysis, so be sure to follow me if you don’t want to miss it!

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