Time series decomposition is a technique to split time series data into several components. These components include trend, seasonality, and residuals. Understanding these patterns is important for analysis and forecasting, and decomposition makes the data easier to study and model. In R, decomposition is done using specific functions, the most common of which are decompose() and stl().
In this article, you will learn how to perform time series decomposition in R.
What is Time Series Decomposition?
Time series data shows patterns like trends, seasonality, and random noise. Breaking down the data helps separate these parts for easier analysis. Decomposition is usually done on data that is collected over regular time periods. This helps to understand the different patterns in the data.
Time series decomposition involves splitting a time series into three main components:
- Trend: Represents the pattern in the data, such as an increasing or decreasing movement
- Seasonality: Identifies recurring patterns or cycles over a fixed period, such as weekly, monthly, or yearly fluctuations
- Residuals: The random fluctuations in the data that cannot be attributed to the trend or seasonality
Time series decomposition can be additive or multiplicative:
- Additive decomposition assumes that the components combine linearly: Y(t) = T(t) + S(t) + R(t)
- Multiplicative decomposition assumes that the components multiply together: Y(t) = T(t) × S(t) × R(t)
T(t) is the trend, S(t) is the seasonal component, and R(t) is the residual.
Additive models work when seasonal fluctuations stay the same regardless of the trend. Multiplicative models are best when seasonal fluctuations grow as the trend increases.
Time Series Decomposition
R provides multiple methods to decompose time series data. Two common methods are decompose() and stl().
Loading the Data
To begin, we need a time-series data. For illustration, we’ll use the built-in AirPassengers dataset. It contains the monthly number of airline passengers from 1949 to 1960.
# Load the data
data("AirPassengers")
Using the decompose() Function
The decompose() function in R performs classical decomposition of time series data. It can handle additive and multiplicative decomposition. The type argument specifies whether to use an additive or multiplicative model.
# Perform additive decomposition decomposed_data <- decompose(AirPassengers, type = "additive") # Plot the decomposition plot(decomposed_data)
Using the stl() Function
The stl() function in R is used for advanced time series decomposition. It stands for seasonal and trend decomposition using LOESS. LOESS is a method that smooths the data to find non-linear trends and irregular seasonality. The s.window = “periodic” argument specifies a periodic seasonal window. stl() is more flexible than decompose() and can handle complex seasonal patterns.
# Perform STL decomposition stl_decomposed_data <- stl(AirPassengers, s.window = "periodic") # Plot the decomposition plot(stl_decomposed_data)
Using the forecast() Function
The forecast() function helps predict future values using time series data. It looks at the trend, seasonal patterns, and random changes. The h = 12 argument specifies a forecast for the next 12 months. This method is useful for forecasting because it considers long-term trends and regular cycles. It makes predictions more accurate by using the patterns in the data.
# Load the necessary library
library(forecast)
# Load the AirPassengers dataset
data("AirPassengers")
# Perform STL decomposition
stl_decomposed_data <- stl(AirPassengers, s.window = "periodic")
# Forecast the next 12 months based on the decomposed data
forecasted_data <- forecast(stl_decomposed_data, h = 12)
# Plot the forecast
plot(forecasted_data)
Conclusion
Time series decomposition is a useful tool for analyzing time series data. It breaks the data into trend, seasonality, and residual components. Additive models work for stable patterns, while multiplicative models handle changing seasonal effects. In R, decompose() is suitable for simple decomposition. The stl() function provides more advanced and flexible decomposition. Using forecast(), you can predict future values accurately.
