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Long Term Trend Detector Crossover
//------------------------------------------------------------------------------
//
//  Formula Name:    Ehlers Instantaneous Trend
//  Author/Uploader: Not Too Swift 
//  E-mail:          
//  Date/Time Added: 2005-03-20 00:25:13
//  Origin:          
//  Keywords:        
//  Level:           medium
//  Flags:           indicator
//  Formula URL:     http://www.amibroker.com/library/formula.php?id=444
//  Details URL:     http://www.amibroker.com/library/detail.php?id=444
//
//------------------------------------------------------------------------------
//
//  This is a zero lag trend indicator with an interesting predictive trigger.
//
//------------------------------------------------------------------------------

SetBarsRequired(200, 0);

// Ehlers ITrend
// from Ehlers, John F. Cybernetic Analysis for Stocks and Futures. Wiley. 2004. 
// Chapter 3, p. 21. Code on p. 24.

function ITrend(array, alpha)
{
  // initialize early array values and declare as array
  it = array;
  //it = (array[2] - 2*array[1] + array[0])/4; This initialization takes a long time to converge.
  for(i = 2; i < BarCount; i++)
  {
    it[i] = (alpha - alpha*alpha/4)*array[i] + 
         .5*alpha*alpha*array[i-1] -
         (alpha - .75*alpha*alpha)*array[i-2] +
         2*(1 - alpha)*it[i-1] -
         (1 - alpha)*(1 - alpha)*it[i-2];
  }
  return it;
}

function ITrendTrigger(array)
{
  trigger = 2*array - Ref(array, -2);
  return trigger;
}

Med = (H+L)/2;

// Instantaneous Trend
Plot(Med, "", colorBlack, styleLine);
trend = ITrend(Med, .07);
Plot(trend, "ITrend", colorBlue, styleLine);
Plot(ITrendTrigger(trend), "", colorRed, styleLine);