Tuesday 8 November 2016

Preliminary Tests of Currency Strength Indicator

Since my last post on the currency strength indicator I have been conducting a series of basic randomisation tests to see if the indicator has better than random predictive ability. The first test was a random permutation test, as described in Aronson's Evidence Based Technical Analysis book, the code for which I have previously posted on my Data Snooping Tests Github page. These results were all disappointing in that the null hypothesis of no predictive ability cannot be rejected. However, looking at a typical chart ( repeated from the previous post but colour coded for signals )
it can be seen that there are a lot of green ( no signal ) bars which, during the randomisation test, can be selected and give equal or greater returns than the signal bars ( blue for longs, red for shorts ). The relative sparsity of the signal bars compared to non-signal bars gives the permutation test, in this instance, low power to detect significance, although I am not able to show that this is actually true in this case.

In the light of the above I decided to conduct a different test, the .m code for which is shown below.
clear all ;
load all_strengths_quad_smooth_21 ;

all_random_entry_distribution_results = zeros( 21 , 3 ) ;

tic();

for ii = 1 : 21

clear -x ii all_strengths_quad_smooth_21 all_random_entry_distribution_results ;

  if ii == 1
  load audcad_daily_bin_bars ;
  mid_price = ( audcad_daily_bars( : , 3 ) .+ audcad_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 6 ; term_ix = 7 ;
  end
  
  if ii == 2
  load audchf_daily_bin_bars ;
  mid_price = ( audchf_daily_bars( : , 3 ) .+ audchf_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 6 ; term_ix = 4 ;
  end

  if ii == 3
  load audjpy_daily_bin_bars ;
  mid_price = ( audjpy_daily_bars( : , 3 ) .+ audjpy_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 6 ; term_ix = 5 ;
  end
  
  if ii == 4
  load audusd_daily_bin_bars ;
  mid_price = ( audusd_daily_bars( : , 3 ) .+ audusd_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 6 ; term_ix = 1 ;
  end
  
  if ii == 5
  load cadchf_daily_bin_bars ;
  mid_price = ( cadchf_daily_bars( : , 3 ) .+ cadchf_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 7 ; term_ix = 4 ;
  end
  
  if ii == 6
  load cadjpy_daily_bin_bars ;
  mid_price = ( cadjpy_daily_bars( : , 3 ) .+ cadjpy_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 7 ; term_ix = 5 ;
  end
  
  if ii == 7
  load chfjpy_daily_bin_bars ;
  mid_price = ( chfjpy_daily_bars( : , 3 ) .+ chfjpy_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 4 ; term_ix = 5 ;
  end
  
  if ii == 8
  load euraud_daily_bin_bars ;
  mid_price = ( euraud_daily_bars( : , 3 ) .+ euraud_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 2 ; term_ix = 6 ;
  end
  
  if ii == 9
  load eurcad_daily_bin_bars ;
  mid_price = ( eurcad_daily_bars( : , 3 ) .+ eurcad_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 2 ; term_ix = 7 ;
  end
  
  if ii == 10
  load eurchf_daily_bin_bars ;
  mid_price = ( eurchf_daily_bars( : , 3 ) .+ eurchf_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 2 ; term_ix = 4 ;
  end
  
  if ii == 11
  load eurgbp_daily_bin_bars ;
  mid_price = ( eurgbp_daily_bars( : , 3 ) .+ eurgbp_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 2 ; term_ix = 3 ;
  end
  
  if ii == 12
  load eurjpy_daily_bin_bars ;
  mid_price = ( eurjpy_daily_bars( : , 3 ) .+ eurjpy_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 2 ; term_ix = 5 ;
  end
  
  if ii == 13
  load eurusd_daily_bin_bars ;
  mid_price = ( eurusd_daily_bars( : , 3 ) .+ eurusd_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 2 ; term_ix = 1 ;
  end
  
  if ii == 14
  load gbpaud_daily_bin_bars ;
  mid_price = ( gbpaud_daily_bars( : , 3 ) .+ gbpaud_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 3 ; term_ix = 6 ;
  end
  
  if ii == 15
  load gbpcad_daily_bin_bars ;
  mid_price = ( gbpcad_daily_bars( : , 3 ) .+ gbpcad_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 3 ; term_ix = 7 ;
  end
  
  if ii == 16
  load gbpchf_daily_bin_bars ;
  mid_price = ( gbpchf_daily_bars( : , 3 ) .+ gbpchf_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 3 ; term_ix = 4 ;
  end
  
  if ii == 17
  load gbpjpy_daily_bin_bars ;
  mid_price = ( gbpjpy_daily_bars( : , 3 ) .+ gbpjpy_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 3 ; term_ix = 5 ;
  end
  
  if ii == 18
  load gbpusd_daily_bin_bars ;
  mid_price = ( gbpusd_daily_bars( : , 3 ) .+ gbpusd_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 3 ; term_ix = 1 ;
  end
  
  if ii == 19
  load usdcad_daily_bin_bars ;
  mid_price = ( usdcad_daily_bars( : , 3 ) .+ usdcad_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 1 ; term_ix = 7 ;
  end
  
  if ii == 20
  load usdchf_daily_bin_bars ;
  mid_price = ( usdchf_daily_bars( : , 3 ) .+ usdchf_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 1 ; term_ix = 4 ;
  end
  
  if ii == 21
  load usdjpy_daily_bin_bars ;
  mid_price = ( usdjpy_daily_bars( : , 3 ) .+ usdjpy_daily_bars( : , 4 ) ) ./ 2 ; mid_price_rets = [ 0 ; diff( mid_price ) ] ;
  base_ix = 1 ; term_ix = 5 ;
  end
  
  % the returns vectors suitably alligned with position vector
  mid_price_rets = shift( mid_price_rets , -1 ) ;
  sma2 = sma( mid_price_rets , 2 ) ; sma2_rets = shift( sma2 , -2 ) ; sma3 = sma( mid_price_rets , 3 ) ; sma3_rets = shift( sma3 , -3 ) ;
  all_rets = [ mid_price_rets , sma2_rets , sma3_rets ] ;

  % delete burn in and 2016 data ( 2016 reserved for out of sample testing )
  all_rets( 7547 : end , : ) = [] ; all_rets( 1 : 50 , : ) = [] ;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% simple divergence strategy - be long the uptrending and short the downtrending currency. Uptrends and downtrends determined by crossovers
% of the strengths and their respective smooths
  smooth_base = smooth_2_5( all_strengths_quad_smooth_21(:,base_ix) ) ; smooth_term = smooth_2_5( all_strengths_quad_smooth_21(:,term_ix) ) ;
  test_matrix = ( all_strengths_quad_smooth_21(:,base_ix) > smooth_base ) .* ( all_strengths_quad_smooth_21(:,term_ix) < smooth_term) ; % +1 for longs
  short_vec = ( all_strengths_quad_smooth_21(:,base_ix) < smooth_base ) .* ( all_strengths_quad_smooth_21(:,term_ix) > smooth_term) ; short_vec = find( short_vec ) ;
  test_matrix( short_vec ) = -1 ; % -1 for shorts 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  % delete burn in and 2016 data
  test_matrix( 7547 : end , : ) = [] ; test_matrix( 1 : 50 , : ) = [] ;
  [ ix , jx , test_matrix_values ] = find( test_matrix ) ;
  no_of_signals = length( test_matrix_values ) ;
 
  % the actual returns performance
  real_results = mean( repmat( test_matrix_values , 1 , size( all_rets , 2 ) ) .* all_rets( ix , : ) ) ;
  
  % set up for randomisation test
  iters = 5000 ;
  imax = size( test_matrix , 1 ) ;
  rand_results_distribution_matrix = zeros( iters , size( real_results , 2 ) ) ;

    for jj = 1 : iters
      rand_idx = randi( imax , no_of_signals , 1 ) ; 
      rand_results_distribution_matrix( jj , : ) = mean( test_matrix_values .* all_rets( rand_idx , : ) ) ;
    endfor
    
  all_random_entry_distribution_results( ii , : ) = ( real_results .- mean( rand_results_distribution_matrix ) ) ./ ...
                                                    ( 2 .* std( rand_results_distribution_matrix ) ) ; 
  
endfor % end of ii loop

toc()

save -ascii all_random_entry_distribution_results all_random_entry_distribution_results ;

plot(all_random_entry_distribution_results(:,1),'k','linewidth',2,all_random_entry_distribution_results(:,2),'b','linewidth',2,...
all_random_entry_distribution_results(:,3),'r','linewidth',2) ; legend('1 day','2 day','3 day');
What the code basically does is construct null hypothesis distributions of 1, 2 and 3 day returns of n random entries, where n is the same number of signal bars -1 or +1 as the currency strength indicator signal. The signal returns are then plotted as a line chart of the distance between random return means and signal return means normalised by 2x the random return standard deviations. In this way values >1 approximately correspond to p values < 0.05. Two typical charts are shown below

The first chart shows the results of the unsmoothed currency strength indicator and the second the smoothed version. From this I surmise that the delay introduced by the smoothing is/will be detrimental to performance and so for the nearest future I shall be working on improving the smoothing algorithm used in the indicator calculations.

2 comments:

Unknown said...

nice work! im just having trouble interpreting the results from the second approach. can you elaborate more what the two charts are implying?

Dekalog said...

Hi Unknown, sorry for the late response to your comment.

The two charts are displays of a crude Monte Carlo permutation analysis whereby the position vector ( i.e. 1 for long, -1 for short, 0 for neutral ) is randomly permuted whilst preserving the ratio between long, short and neutral. These random position vectors are multiplied, element by element, with the real return vector to give a distribution of returns that could be expected from random trades that exactly mimic the "profile" of the real, signalled trades. This random distribution is assumed to be a normal/gaussian distribution, and so the mean and standard are calculated, and the real, signalled returns are compared to this distribution. Because of the scaling, any return > 1 is equivalent to a distance > two standard deviations away from the mean, i.e. a p-value of approximately 5%.

Hope this short description helps.