Decomposing Time Series | Time Series Analysis

Introduction

Time series analysis involves understanding patterns in data points collected or recorded at specific time intervals. Decomposing a time series helps us to separate these patterns into distinct components: trend, seasonality, and noise. This tutorial will guide you through the process of decomposing time series data using R programming.

Components of Time Series

A time series can generally be broken down into three main components:

Trend: The long-term progression of the series. It indicates a general direction in which the data is moving over time.
Seasonality: Patterns that repeat at regular intervals, such as sales spikes during holidays.
Noise: The random variation in the data that cannot be attributed to the trend or seasonality.

Decomposition Methods

There are two primary methods for decomposing time series data:

Additive Decomposition: Suitable for time series where the seasonal variations are roughly constant over time.
Multiplicative Decomposition: Suitable for time series where the seasonal variations change proportionally with the level of the series.

Implementing Decomposition in R

In R, the stats package provides a convenient function called decompose for additive decomposition and stl for seasonal and trend decomposition using loess (STL).

Example: Additive Decomposition

Let's assume we have a time series object called my_ts:

my_ts <- ts(data = c(...), frequency = 12, start = c(2020, 1))

Now we can decompose it:

decomposed <- decompose(my_ts)

To visualize the components:

plot(decomposed)

Interpreting the Results

After running the decomposition, you will receive a plot with four components:

Original: The initial time series data.
Trend: The long-term direction of the data.
Seasonal: The repeating seasonal patterns.
Random: The residual noise left after removing the trend and seasonality.

Understanding these components can help in forecasting future values and identifying anomalies in the data.

Conclusion

Decomposing time series data is fundamental to understanding its underlying patterns. By separating trend, seasonality, and noise, analysts can make more informed decisions based on historical data. R provides robust tools for such analyses, making it accessible for data scientists and statisticians.