What is the term for a time series with seasonal effects removed by dividing each observation by a seasonal index?

The term for a time series with seasonal effects removed by dividing each observation by a seasonal index is "deseasonalized time series." This process involves calculating a seasonal index, which represents the average effect of seasonal variations for each time period in the data. By dividing the original observations by these indices, one effectively removes the predictable seasonal fluctuations, allowing for a clearer analysis of the underlying trends and patterns in the data. This approach is essential in time series analysis for businesses and researchers who aim to understand long-term trends without the noise introduced by seasonal effects.

In contrast, an adjusted time series typically refers to a more general adjustment that could include other corrections beyond just seasonal effects. A seasonal time series refers to the original data that exhibits seasonality without any modifications. Normalized time series usually implies scaling data to fit a certain range or distribution, which does not specifically address the removal of seasonal effects. Therefore, based on the definitions and the procedure described, "deseasonalized time series" is the most accurate term for the situation presented.