Mathematica periodic moving map

I am pleased to have MovingMap in Mathematica 10. But, today, I encountered the problem that needs MovingMap with a periodic boundary condition.

To be specific, Consider the following example.

MovingMap[ f, Range[3], {2} ]

will gives the result {f[{1, 2}], f[{2, 3}], f[{3, 4}]}. However, what I want to get is {f[{1, 2}], f[{2, 3}], f[{3, 4}], f[{4,1}]}.

One of the easiest and straightforward way would be calculating the last one and then join the lists together. But I want to know if there is more elegant way to do it. (I checked the optional arguments of MovingMap but I couldn't find a solution.)

Answer

"Reflected" padding works as desired but "Periodic" padding is missed. There is corresponding definition for "Reflected"

RandomProcesses`TemporalDataUtilitiesDump`toCannonicalPadding[

  RandomProcesses`TemporalDataUtilitiesDump`td_, "Reflected", 
  RandomProcesses`TemporalDataUtilitiesDump`w_, 
  RandomProcesses`TemporalDataUtilitiesDump`Caller_] := 
 Reverse[Rest[
   TemporalData`Utilities`TDResample[
     RandomProcesses`TemporalDataUtilitiesDump`td,
     RandomProcesses`TemporalDataUtilitiesDump`w, {}, 
     RandomProcesses`TemporalDataUtilitiesDump`Caller]["Values"]]]

So we can add a similar definition for "Periodic"

RandomProcesses`TemporalDataUtilitiesDump`toCannonicalPadding[
  RandomProcesses`TemporalDataUtilitiesDump`td_, "Periodic", 
  RandomProcesses`TemporalDataUtilitiesDump`w_, 
  RandomProcesses`TemporalDataUtilitiesDump`Caller_] := 
 TemporalData`Utilities`TDResample[
   RandomProcesses`TemporalDataUtilitiesDump`td, 
   RandomProcesses`TemporalDataUtilitiesDump`w, {}, 
   RandomProcesses`TemporalDataUtilitiesDump`Caller]["Values"]

Verification:

MovingMap[f, Range[3], {2}, "Periodic"]
(* {f[{3, 1}], f[{1, 2}], f[{2, 3}]} *)