YearToDate (YTD) Previous Year (also QTD, MTD, WTD)

This is simple is you combine ParallelPeriod with the YTD functionality:

WITH
MEMBER [Measures].[Sales Amount YearToDate]
AS
    SUM(YTD( [Date].[Calendar].CurrentMember),[Measures].[Sales Amount])

MEMBER [Measures].[Sales Amount Previous Year]
AS
    SUM(ParallelPeriod( [Date].[Calendar].[Calendar Year], 1,[Date].[Calendar].CurrentMember),[Measures].[Sales Amount])

MEMBER [Measures].[Sales Amount YearToDate Previous Year]
AS
    SUM(YTD( ParallelPeriod( [Date].[Calendar].[Calendar Year], 1,[Date].[Calendar].CurrentMember)),[Measures].[Sales Amount])

Percentage difference from previous parallel period

Let’s start by getting the parallel period:

WITH MEMBER [Measures].[Sales Amount PY]
AS
(
    [Measures].[Sales Amount]
    , ParallelPeriod
        ([Date].[Calendar].[Calendar Year] // Level
        , 1 // number of periods back
        , [Date].[Calendar].CurrentMember) // Start member
)
, format_string = "Currency"

ParallelPeriod

The ParallelPeriod functionality is closely related to the Cousin functionality. The main difference is that the ParallelPeriod function expects a hierarchy of the type Time.
It will get you the value of a measure based given top-level.

Cousin

The Cousin functionality will get you the member on same position as the starting based on a new toplevel member. Most of the time you use it in the same way you use ParallelPeriod.

If you look at a date or calendar dimension is might look like this: All ==> Year ==> Semester ==> Quarter ==> Month ==> Date.

If you use a query like this:

MDX using member

The member function in MDX is comparable with the MS-SQL CTE functionality. It allows you to define a member before you use it in your query and thus keeping your query more readable.
An example:
WITH MEMBER [Measures].[Prior Year Sales] AS
    SUM(     
        ParallelPeriod
            (
                [Date].[Calendar].[Calendar Year],
                1,
                [Date].[Calendar].CurrentMember
            )
            ,
            [Measures].[Sales Amount]
       )
This calculates the SUM of the Sales Amount for the previous year using the ParallelPeriod functionality in combination with CurrentMember.