Comparing base year % change to a year-on-year % change I am analysing a dataset with annual data for roughly a 100-year time period. I am trying to analyse the changes over time. One method is to use a base year, and then compare every year to this base year. The other method is comparing year-on-year percentage changes. I wonder which method is more accurate in grasping the changes over time. I assume it is the first one.
 A: I believe there is an inherent danger in analyzing data without understanding the generating process of the underlying variables.  For example, if we're talking about tree growth and we know that there are periods/cycles of accelerated growth relating to favorable conditions as higher annual rainfall or elevated temperature, or conversely, other cycles relating to drought and cold temperatures which may hinder growth, ignoring these factors as explanatory inputs to normalize the data inherently makes meaningful inferences harder to assess, in my opinion.
So my recommendation, start by looking for rational (per the related science of the phenomena being explored) explanatory variables. Model the historical data with a constant term and with these explanatory variables values minus their associated mean (or median if you use least absolute deviation regression, LAD). If a time variable is employed as an explanatory variable,  it should be reported and justified.
Claim: The fitted values of such a model represent normalized (as in corrected for expected year specific factors) values of your annual historical data. Also, if the value of the correcting variables are small to zero, then the associated constant term is only marginally adjusted, which with standard regression is the sample mean of your historical data (or its median with LAD) as one measure to use as a base for historical comparative statements.
