octave time-series vectorization moving-average

Perform a vectorized exponential moving average in octave

In GNU Octave, would like to calculate an n-day exponential moving average of a vector without using a for-loop.

I am able to do this with a for loop but it is inefficient. I would like to use the filter function, however I am unsure how to get this to work correctly.

Solution

Reinventing the wheel on octave exponential moving average for a vector is silly. Just copy and paste movavg.m function defined in the octave financial package here: https://octave.sourceforge.io/financial:

function [varargout] = movavg(asset, lead, lag, alpha = 0) 
  if nargin < 3 || nargin > 4 
    print_usage (); 
  endif 
  if lead > lag 
    error ("lead must be <= lag") 
  elseif ischar (alpha) 
    if ! strcmpi (alpha, "e") 
      error ("alpha must be 'e' if it is a char"); 
    endif 
  elseif ! isnumeric (alpha) 
    error ("alpha must be numeric or 'e'") 
  endif 
  ## Compute the weights 
  if ischar (alpha) 
    lead = exp(1:lead); 
    lag  = exp(1:lag); 
  else 
    lead = (1:lead).^alpha; 
    lag  = (1:lag).^alpha; 
  endif 
  ## Adjust the weights to equal 1 
  lead = lead / sum (lead); 
  lag  = lag / sum (lag); 
  short = asset; 
  long  = asset; 
  for i = 1:length (asset) 
    if i < length (lead) 
      ## Compute the run-in period 
      r        = length (lead) - i + 1:length(lead); 
      short(i) = dot (asset(1:i), lead(r))./sum (lead(r)); 
    else 
      short(i) = dot (asset(i - length(lead) + 1:i), lead); 
    endif 
    if i < length (lag) 
      r       = length (lag) - i + 1:length(lag); 
      long(i) = dot (asset(1:i), lag(r))./sum (lag(r)); 
    else 
      long(i) = dot (asset(i - length(lag) + 1:i), lag); 
    endif 
  endfor 
  if nargout > 0 
    varargout{1} = short; 
  else 
    plot((1:length(asset))', [asset(:), long(:), short(:)]); 
  endif 
  if nargout > 1 
    varargout{2} = long; 
  endif 
endfunction

And invoke thustly:

foo = [NaN; 1;4;8;10;-3;3;4;0;0;3;4;5;6;7;8;9];     
lead = 7 
lag = 7
alpha = 'e' 
movavg(foo, lead, lag, 'e')

Which prints: