In time series analysis, whether to use a multiplicative model or an additive model depends on the characteristics of the underlying data. Here are some considerations that might make the multiplicative model more appropriate:
Proportional Seasonal Variation: If the seasonal patterns in the data exhibit proportional changes relative to the level of the series, then a multiplicative model is more suitable. In other words, if the amplitude of the seasonal variation increases or decreases as the level of the series changes, a multiplicative model is preferred.
Varying Volatility: When the variability of the data increases or decreases with the level of the series, a multiplicative model may be more appropriate. For example, if the percentage fluctuations in the data increase with the level of the series, a multiplicative model is often more accurate.
Non-Constant Growth: If the trend in the time series exhibits a non-constant growth rate, the multiplicative model is more suitable. In such cases, the growth rate is proportional to the level of the series.
Seasonal Patterns Expressed as Percentage of the Mean: If the seasonal patterns are more appropriately expressed as a percentage of the mean, a multiplicative model may be preferred. This is common when the amplitude of seasonal fluctuations varies with the overall level of the series.
In contrast, an additive model is more appropriate when the seasonal variations and other components are consistent in magnitude regardless of the level of the series. The choice between a multiplicative and additive model is not always clear-cut, and sometimes experimentation with both models is necessary to determine which one provides a better fit to the data. Additionally, the nature of the data and the specific characteristics of the time series should guide the choice of the appropriate model.