Suppose I have the following problem - we are interested in modelling the number of animals that cross a certain point each year (e.g. swim across a river). Let's say that these animals typically migrate during the summer months (e.g. April - September), and in the winter months this number becomes almost becomes 0.

Suppose I have 10 years of data collected at the weekly level - this means that in the winter months, the number of animals that cross this point are basically 0. Thus, there are large natural "gaps" that occur within the data.

When such situations arise, is it generally better to fit a time series model (e.g. ARIMA) to the entire dataset and treat each year as a cycle - or is it better to construct cycles out of the "active months" that contain data?

E.g.

• Option 1 - Stack Rows from Each Subset on Top of Each Other to Create a Modified Dataset: (April 2010 - September 2010, April 2011 - September 2011, April 2012 - September 2012,etc.)
• Option 2 - Simply Model the Entire Dataset: April 2010 - April 2020

In general, is it better to fit time series models to datasets created from Option 1 or Option 2? Are some models (e.g. arima, ets, regime switch models) more suitable for this kind of problems(e.g. some models perhaps might make negative predictions or negative confidence intervals when the response variable is low)?