Understanding Additive and Multiplicative Seasonal Decomposition in Time Series Analysis

Seasonal decomposition is a useful statistical technique for decomposing a time series into its underlying components: trend, seasonality, and residuals. By breaking down a time series into its component parts, seasonal decomposition can provide insights into the underlying patterns and trends in the data. There are two main types of seasonal decomposition: additive and multiplicative.

Additive Seasonal Decomposition: Additive seasonal decomposition involves using an additive model, where the trend, seasonality, and residuals are added together to produce the observed time series. This is useful when the magnitude of the trend and seasonality components does not change over time.

Examples of time series that may be well suited for additive seasonal decomposition include monthly retail sales data for a product that has a predictable seasonal demand, such as seasonal clothing, or quarterly financial data for a business that has a stable growth pattern.

For instance, consider the example of a retail store that sells a significant amount of goods during the holiday season, resulting in a consistent increase in sales during November and December, and a decrease in sales during the summer months of June, July, and August. The trend component of the time series may show an overall increase in sales over time, while the seasonality component displays the predictable fluctuations in sales due to the holiday season and summer months.

Multiplicative Seasonal Decomposition: Multiplicative seasonal decomposition involves using a multiplicative model, where the trend, seasonality, and residuals are multiplied together to produce the observed time series. This model is more useful when the magnitude of the trend and seasonality components changes over time.

For instance, electricity consumption data may exhibit a consistent increase in consumption during the summer months due to air conditioning, and a decrease in consumption during the winter months due to lower demand for heating. In this case, the trend component may…