You can define a fiscal year that begins on any month of the year. When you do so, any yearly or quarterly preferences in Quicken are offset based on the first month of your fiscal year.
For example, if your fiscal year started in April 2016, and it's now January 2017, select April in the Start budget on field. Quicken then considers April 1, 2015, to March 31, 2016, as last year.
To base Quicken's yearly or quarterly budget options on January 1 to December 31, select January in the Start budget on field.