Should all (but one) seasonal dummies be included? I have a question concerning the significance of seasonal dummies in a simple lm regression for time series. 
I want to determine whether I should include dummy variables for months of the year or not. When I run a decomposition function like tbats or stl it states that there is a seasonal component in my time series. When I then run a linear regression with dummies for seasonality and I look a the p-values, I get the result that some month dummies are significant and others are not. 
Should I only include the significant month dummies into the model or am I missing something here? I have hundreds of time series so I'm looking for some kind of rule of thumb that I can apply to all of them at once.
 A: There is no general answer to this. When including predictors, you should always first think about if you may suspect some influence. What is your time series about? Does season play a role for your question or might it influence your data?
Examples:


*

*Your time-series is about the amount of energy used in a city for each day. Of course energy consumption during winter seasons (heating) or summer (air conditioning) would be higher than in other seasons. You should probably include season as a predictor in your model.

*You are modeling approval rate for presidential candidates over time. Unless you have a really good reason why approval rates should depend on the season, better leave it out.


In some examples, it may actually be better to figure out which factors mediate the effect of season, and then instead use those. For example, if you have a time series for energy consumption, it would probably be better to include the average temperature for each day as a predictor as this has a more direct influence on the energy consumption.
You can probably find more examples. In statistics, there is something called the "kitchen-sink model" (put everything in it, except the kitchen sink). This is a really bad approach to modeling because you are just trying instead of thinking about the question. 
In general, finding out which predictors should be included and which should be left out is one of the most fundamental questions in any modeling task and there is no rule of thumb for this.
