## Friday, 6 December 2013

### Brownian Oscillator

In my previous post I said I was thinking about an oscillator based on Brownian bands and the lower pane in the video below shows said oscillator in action. The upper pane simply shows the prices with super imposed Brownian bands. The oscillator ranges between 0 and 1 and is effectively a measurement of the randomness of price movement. The calculation is very simple: for consecutive look back periods of 1 to the dominant cycle period a counter is incremented by 1 for each look back length in which price is between the Brownian bands for that look back length, and the sum of this counter is then divided by the dominant cycle period. The logic should be easily discernible from the code given in the code box below. According to this logic the higher the oscillator value the more random price movement is, and the lower the value the higher the "trendiness" of the price series. The value of the oscillator could also be interpreted as the percentage of look back periods which indicate random movement. Nb. I have changed the calculation of the bands to use absolute price differences rather than log differences - I find that this change leads to better behaved bands.

I have not done any testing of this oscillator as an indicator but I think it might have some value as a filter for a trend following system, or as a way of switching between trend following and mean reversion types of systems. The fact that the oscillator values lie in the range 0 to 1 also makes it suitable as an input to a neural net.

The Octave .oct code
DEFUN_DLD ( brownian_oscillator, args, nargout,
"-*- texinfo -*-\n\
@deftypefn {Function File} {} brownian_oscillator (@var{price,period})\n\
This function takes price and period vector inputs and outputs a value\n\
normalised by the max look back period for the number of look back periods\n\
from 1 to max look back period inclusive for which the price is between\n\
Brownian bands.\n\
@end deftypefn" )

{
octave_value_list retval_list ;
int nargin = args.length () ;

// check the input arguments
if ( nargin != 2 )
{
error ( "Invalid arguments. Type help to see usage." ) ;
return retval_list ;
}

if ( args(0).length () < 50 ) // check length of price vector input
{
error ( "Invalid arguments. Type help to see usage." ) ;
return retval_list ;
}

if ( args(1).length () != args(0).length () ) // lookback period length argument
{
error ( "Invalid arguments. Type help to see usage." ) ;
return retval_list ;
}

if ( error_state )
{
error ( "Invalid arguments. Type help to see usage." ) ;
return retval_list ;
}
// end of input checking

ColumnVector price = args(0).column_vector_value () ;
ColumnVector period = args(1).column_vector_value () ;
ColumnVector abs_price_diff = args(0).column_vector_value () ;
ColumnVector osc = args(0).column_vector_value () ; osc(0) = 0.0 ;
double sum ;
double osc_sum ;
double up_bb ;
double low_bb ;
int jj ;

for ( octave_idx_type ii (1) ; ii < 50 ; ii++ ) // initialising loop
{
abs_price_diff(ii) = fabs( price(ii) - price(ii-1) ) ;
osc(ii) = 0.0 ;
}

for ( octave_idx_type ii (50) ; ii < args(0).length () ; ii++ ) // main loop
{
// initialise calculation values
sum = 0.0 ;
osc_sum = 0.0 ;
up_bb = 0.0 ;
low_bb = 0.0 ;

for ( jj = 1 ; jj < period(ii) + 1 ; jj++ ) // nested jj loop
{

abs_price_diff(ii) = fabs( price(ii) - price(ii-1) ) ;
sum += abs_price_diff(ii-jj+1) ;
up_bb = price(ii-jj) + (sum/double(jj)) * sqrt(double(jj)) ;
low_bb = price(ii-jj) - (sum/double(jj)) * sqrt(double(jj)) ;

if ( price(ii) <= up_bb && price(ii) >= low_bb )
{
osc_sum += 1.0 ;
}

} // end of nested jj loop

osc(ii) = osc_sum / period(ii) ;

} // end of main loop

retval_list(0) = osc ;

return retval_list ;

} // end of function