//+------------------------------------------------------------------+
//| ParMA_BB.mq4 |
//| Copyright © 2006, MetaQuotes Software Corp. |
//| http://www.metaquotes.net |
//+------------------------------------------------------------------+
#property copyright "Copyright © 2006, MetaQuotes Software Corp."
#property link "http://www.metaquotes.net"
#property indicator_chart_window
#property indicator_buffers 3
#property indicator_color1 BlueViolet // main line
#property indicator_color2 DodgerBlue // upper band
#property indicator_color3 DodgerBlue // lower band
//---- input parameters
extern int ParMA_Period = 30;
extern bool BandsEnabled = false;
extern double BandsDev = 1.0;
//---- buffers
double ParMABuffer[];
double UpperBandBuffer[];
double LowerBandBuffer[];
//+------------------------------------------------------------------+
//| Custom indicator initialization function |
//+------------------------------------------------------------------+
int init()
{
if (ParMA_Period <= 1) // fool-proof & to prevent zero divide error
{ ParMA_Period = 3; }
//---- indicators
IndicatorDigits(Digits);
//
SetIndexStyle(0, DRAW_LINE);
SetIndexBuffer(0, ParMABuffer);
SetIndexLabel(0, "ParMA Line");
SetIndexDrawBegin(0, ParMA_Period);
//
if (BandsEnabled == true) // initialize Bollinger Bands buffers, if allowed
{
SetIndexStyle(1, DRAW_LINE);
SetIndexBuffer(1, UpperBandBuffer);
SetIndexLabel(1, "ParMA Upper Band");
SetIndexDrawBegin(1, ParMA_Period);
//
SetIndexStyle(2, DRAW_LINE);
SetIndexBuffer(2, LowerBandBuffer);
SetIndexLabel(2, "ParMA Lower Band");
SetIndexDrawBegin(2, ParMA_Period);
}
//----
return(0);
}
//+------------------------------------------------------------------+
//| Custom indicator deinitialization function |
//+------------------------------------------------------------------+
int deinit()
{
//----
Comment(""); // remove comment when finished; see notes below
//----
return(0);
}
//+------------------------------------------------------------------+
//| Custom indicator iteration function |
//+------------------------------------------------------------------+
int start()
{
int counted_bars = IndicatorCounted();
int Limit, cnt, i, k;
double old_val, new_val, sum, std_dev;
//----
if (counted_bars < 0) { return(-1); } // to prevent possible erors
Limit = Bars - counted_bars;
//
if (Limit > ParMA_Period) // run once when getting started
{ cnt = Limit - ParMA_Period; }
else // run elsewhere
{ cnt = Limit; }
// calculate ParMA - one step on time-serie bars array
for (i=cnt; i>=0; i--)
{ ParMABuffer[i] = GetParMA(i, ParMA_Period); }
//
if (BandsEnabled == true) // draw Bollinger Bands, if allowed
{
// calculate standard deviation
i = Bars - ParMA_Period;
if (counted_bars > (ParMA_Period - 1))
{ i = Bars - counted_bars - 1; }
while (i >= 0)
{
sum = 0.0;
k = i + ParMA_Period - 1;
old_val = ParMABuffer[i];
while (k >= i)
{
new_val = Close[k] - old_val;
sum += new_val * new_val;
k--;
}
std_dev = MathSqrt(sum / ParMA_Period);
// complete BB's buffers
UpperBandBuffer[i] = old_val + BandsDev * std_dev;
LowerBandBuffer[i] = old_val - BandsDev * std_dev;
i--;
}
// optional - may be deleted without hesitations
// if you did it, remove 'Comment("");' from deinit() procedure too
Comment("ParMA = ", NormalizeDouble(ParMABuffer[0], Digits), "\n",
"UpperBand = ", NormalizeDouble(UpperBandBuffer[0], Digits), "\n",
"LowerBand = ", NormalizeDouble(LowerBandBuffer[0], Digits));
}
// optional - may be deleted without hesitations
// if you did it, remove 'Comment("");' from deinit() procedure too
if (BandsEnabled != true)
{ Comment("ParMA = ", NormalizeDouble(ParMABuffer[0], Digits)); }
//----
return(0);
}
//+------------------------------------------------------------------+
/*
Parabolic approximation: y(x) = b0 + b1 * x + b2 * x^2;
To obtain coefficients b0, b1, b2 we have to solve a linear system:
b0 * N + b1 * Sum(x,N) + b2 * Sum(x^2,N) = Sum(y,N);
b0 * Sum(x,N) + b1 * Sum(x^2,N) + b2 * Sum(x^3,N) = Sum((x*y),N);
b0 * Sum(x^2,N) + b1 * Sum(x^3,N) + b2 * Sum(x^4,N) = Sum(((x^2)*y),N);
that can easily be done explicitly by hands.
*/
//+------------------------------------------------------------------+
double GetParMA(int shift, int ma_period)
{
static int ro_cnt = 1; // run-once counter
static double sum_x = 0.0, sum_x2 = 0.0, sum_x3 = 0.0, sum_x4 = 0.0;
int i, loop_begin; // counters
double sum_y, sum_xy, sum_x2y, var_tmp;
double A, B, C, D, E, F, K, L, M, P, Q, R, S; // intermediates
double B0, B1, B2; // parabolic regression coefficients
double ret_val; // value to be returned - parabolic MA
//----
// initial accumulation - run once when getting started
while (ro_cnt <= ma_period)
{
var_tmp = ro_cnt;
sum_x += var_tmp; // sum(x)
var_tmp *= ro_cnt;
sum_x2 += var_tmp; // sum(x^2)
var_tmp *= ro_cnt;
sum_x3 += var_tmp; // sum(x^3)
var_tmp *= ro_cnt;
sum_x4 += var_tmp; // sum(x^4)
ro_cnt++;
}
// main calculation loop
loop_begin = shift + ma_period - 1;
sum_y = 0.0;
sum_xy = 0.0;
sum_x2y = 0.0;
for (i = 1; i<=ma_period; i++)
{
var_tmp = Close[loop_begin-i+1];
sum_y += var_tmp;
sum_xy += i * var_tmp; // sum(x*y)
sum_x2y += i * i * var_tmp; // sum((x^2)*y)
}
// initialization
A = ma_period;
B = sum_x; C = sum_x2; F = sum_x3;
M = sum_x4; P = sum_y; R = sum_xy; S = sum_x2y;
// intermediates
D = B; E = C; K = C; L = F;
Q = D / A; E = E - Q * B; F = F - Q * C;
R = R - Q * P; Q = K / A; L = L - Q * B;
M = M - Q * C; S = S - Q * P; Q = L / E;
// calculate regression coefficients
B2 = (S - R * Q) / (M - F * Q);
B1 = (R - F * B2) / E;
B0 = (P - B * B1 - C * B2) / A;
// value to be returned - parabolic MA
ret_val = B0 + (B1 + B2 * A) * A;
//----
return(ret_val);
}
//+------------------------------------------------------------------+
Sample
Analysis
Market Information Used:
Series array that contains close prices for each bar
Indicator Curves created:
Implements a curve of type DRAW_LINE
Indicators Used:
Custom Indicators Used:
Order Management characteristics:
Other Features: