pairs_trading/math_for_pairs_trading.mqh

<EFBFBD><EFBFBD>//
// <EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0g0O(uY0<EFBFBD>0pef[<EFBFBD>|n0<EFBFBD><EFBFBD>pe~0h0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0<EFBFBD>0
//

//+------------------------------------------------------------------+
//|  <EFBFBD>}b_<EFBFBD>V0^ f[<EFBFBD>
//+------------------------------------------------------------------+
vector LinearRegression(const vector &x, const vector &y)
{
  vector results = vector::Zeros(2);

//--- <EFBFBD>0<EFBFBD>0<EFBFBD>0L0U<EFBFBD>F0h0M0o00<EFBFBD>0ԏY0
  int size = (int)x.Size();
  if(size != y.Size()) {
    return results;
  }

  double x_mean = x.Mean();
  double y_mean = y.Mean();
  double numerator = 0.0, denominator = 0.0;

//--- g\<EFBFBD>NWN<EFBFBD>l
  for (int i = 0; i < size; i++) {
    numerator += (x[i] - x_mean) * (y[i] - y_mean);
    denominator += (x[i] - x_mean) * (x[i] - x_mean);
  }
  results[0] = numerator / denominator;
  results[1] = y_mean - results[0] * x_mean;

  return results;
}
//+------------------------------------------------------------------+
//| <EFBFBD>}b_<EFBFBD>V0^ <EFBFBD>N,n
//+------------------------------------------------------------------+
double LinearRegressionPredict(double x, const vector &results)
{
  return x * results[0] + results[1];
}
//+------------------------------------------------------------------+
//| <EFBFBD>}b_<EFBFBD>V0^ <EFBFBD>k<EFBFBD>]
//+------------------------------------------------------------------+
double LinearRegressionResidual(double x, double y, const vector &results)
{
  return y - (x * results[0] + results[1]);
}