Basically I measure the dominant cycle period ( using either the above linked sinewave indicator code or autocorrelation periodogram code ) and use the vector of measured dominant cycle periods as input to the hmmestimate function. Using the output from this, the hmmgenerate function is then used to generate a new period vector, these periods are converted to a slowly, periodically varying sine wave, and additive white Gaussian noise is added to the signal to produce a final signal upon which Monte Carlo testing of my proposed indicator can be conducted. A typical plot of the varying, dominant cycle periods looks like

whilst the noisy sine wave signal derived from this looks like this.

The relevant Octave code for all this is shown in the two code boxes below

```
clear all ;
pkg load statistics ;
% load all datafile names from Oanda
cd /home/dekalog/Documents/octave/oanda_data/daily ;
oanda_files_d = glob( "*_ohlc_daily" ) ; % cell with filenames matching *_ohlc_daily, e.g. eur_usd_ohlc_daily
all_transprobest = zeros( 75 , 75 ) ;
for ii = 1 : 124
filename = oanda_files_d{ ii } ;
current_data_d = load( "-binary" , filename ) ;
data = getfield( current_data_d , filename ) ;
midprice = ( data( : , 3 ) .+ data( : , 4 ) ) ./ 2 ;
period = autocorrelation_periodogram_2_5( midprice ) ;
period(1:49) = [] ;
min_val = min( period ) ; max_val = max( period ) ;
hmm_periods = period .- ( min_val - 1 ) ; hmm_states = hmm_periods ;
[ transprobest , outprobest ] = hmmestimate( hmm_periods , hmm_states ) ;
all_transprobest( min_val : max_val , min_val : max_val ) = all_transprobest( min_val : max_val , min_val : max_val ) .+ transprobest ;
endfor
all_transprobest = all_transprobest ./ 124 ;
[ i , j ] = find( all_transprobest ) ;
if ( min(i) == min(j) && max(i) == max(j) )
transprobest = all_transprobest( min(i):max(i) , min(j):max(j) ) ;
outprobest = eye( size(transprobest,1) ) ;
hmm_min_period_add = min(i) - 1 ;
endif
cd /home/dekalog/Documents/octave/period/hmm_period ;
save all_hmm_periods_daily transprobest outprobest hmm_min_period_add ;
```

and```
clear all ;
pkg load statistics ;
cd /home/dekalog/Documents/octave/snr ;
load all_snr ;
cd /home/dekalog/Documents/octave/period/hmm_period ;
load all_hmm_periods_daily ;
[ gen_period , gen_states ] = hmmgenerate( 2500 , transprobest , outprobest ) ;
gen_period = gen_period .+ hmm_min_period_add ;
gen_sine = sind( cumsum( 360 ./ gen_period ) ) ;
noise_val = mean( [ all_snr(:,1) ; all_snr(:,2) ] ) ;
noisy_sine = awgn( gen_sine , noise_val ) ;
[s,s1,s2,s3] = sinewave_indicator( noisy_sine ) ; s2(1:50) = s1(1:50) ;
figure(1) ; plot( gen_period , 'k' , 'linewidth' , 2 ) ;
figure(2) ; plot( gen_sine , 'k' , 'linewidth' , 2 , noisy_sine , 'b' , 'linewidth' , 2 , s , 'r' , 'linewidth' , 2 , ...
s1 , 'g' , 'linewidth' , 2 , s2 , 'm' , 'linewidth' , 2 ) ;
legend( "Gen Sine" , "Noisy Sine" , "Sine Ind" , "Sine Ind lead1" , "Sine Ind Lead2" ) ;
```

I hope readers find this useful if they need to generate synthetic, cyclic data for their own development/testing purposes too.
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