Additive and multiplicative time series models are two key approaches used to analyze and forecast time series data. The main difference between these two models lies in how they combine various components of the data: additive models treat components individually, while multiplicative models combine them in a way that reflects their proportional relationship to each other.
In an additive time series model, the overall time series is expressed as the sum of its components: trend, seasonal, and irregular components. This means that each component contributes independently to the final values. For example, if a business had a consistent upward trend in sales over the years, along with consistent seasonal spikes during holiday months, the total sales figure could be represented by simply adding the individual contributions from the trend and seasonal effects. This type of model works best when the seasonal fluctuations remain constant in magnitude regardless of the trend—the effect of seasonality does not change as the trend increases or decreases.
On the other hand, a multiplicative time series model combines its components by multiplying them together. This approach assumes that the effect of each component influences the others proportionally. For example, if a company’s sales grow significantly during peak seasons, a multiplicative model would represent the relationship such that higher base sales during the trend period also lead to higher seasonal impacts. For instance, if sales in the holiday season increase 50% compared to other months, that percentage increase is multiplied by the base trend value. This kind of model is suitable when the seasonal fluctuations vary in proportion to the trend, as it captures the interaction between the growth and seasonal patterns more accurately. Thus, choosing between these models depends on the nature of the data being analyzed.