SineWaveIndv0.1
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The Instantaneous Trend Line is a sophisticated technical analysis tool designed to identify and visualize the underlying cycles of price movement. Unlike standard moving averages that simply smooth out price data, this script uses advanced trigonometry and signal processing to determine the "heartbeat" of the market—specifically, how fast it is currently oscillating.
How the Logic Works
1. Price Analysis and Component Breaking The script begins by analyzing the average price over a specific period. It breaks this raw movement down into two mathematical components: the In-Phase component (which represents the primary trend) and the Quadrature component (which represents the perpendicular movement). By splitting the data this way, the tool can more accurately track the "momentum" of price swings rather than just the price itself.
2. Detecting the Current Cycle (Instantaneous Period) The core intelligence of this script lies in its ability to calculate the Instantaneous Period. Instead of assuming a fixed cycle length (like a 50-day or 100-day wave), the logic calculates how long it takes for the market to complete one full rotation at any given moment. It does this by measuring the "Delta Phase"—the tiny shift in the price cycle from one candle to the next—and summing those shifts until they complete a full 360-degree circle.
3. Identifying the Dominant Trendline Once the script knows how long the current cycle is (e.g., it identifies that the market is currently moving in a 40-bar wave), it performs a calculation to find the "Dominant Cycle." It uses sine and cosine functions to project where the price should be based on that specific cycle length. This allows it to separate the meaningful trend from the "noise" of minor, temporary fluctuations.
4. Visual Outputs (Sine Waves) The final output is presented as two distinct lines in a separate window:
- The Sine Wave (Red): This represents the primary calculated trend based on the current cycle dynamics.
- The Lead Sine (Blue): This is an advanced projection that leads the primary wave by 45 degrees. This acts as a "look-ahead" indicator, helping traders anticipate where the cycle is heading next before the price actually makes the move.
Summary for the User
In simple terms, this script treats the market like a swinging pendulum. While most tools just tell you where the pendulum is right now, this script calculates how long the swing takes and which direction it is accelerating toward. This provides a clearer view of the cycle's rhythm, helping to identify when a trend is reaching its peak or exhaustion point based on the mathematical wave rather than just the raw price history.
//+------------------------------------------------------------------+
//| Instantaneous Trend Line by John Ehlers |
//| Copyright © 2004, Poul_Trade_Forum |
//| Aborigen |
//| http://forex.kbpauk.ru/ |
//+------------------------------------------------------------------+
#property copyright "Poul Trade Forum"
#property link "http://forex.kbpauk.ru/"
#property indicator_separate_window
#property indicator_buffers 2
#property indicator_color1 Red
#property indicator_color2 Blue
//---- buffers
extern int Len=40;
double SineWave[];
double LeadSine[];
double Value1[],Value2,Value3,Value4,Value5[2],Value11[2];
double RealPart,ImagPart,DCPhase;
double Pi = 3.1415926535;
double Price[],InPhase[2],Quadrature[2],Phase[2],DeltaPhase[],InstPeriod[2],Period_,Trendline;
double test[];
//+------------------------------------------------------------------+
//| Custom indicator initialization function |
//+------------------------------------------------------------------+
int init()
{
string short_name;
IndicatorBuffers(5);
//---- indicator line
SetIndexStyle(0,DRAW_LINE,EMPTY,2,Red);
SetIndexStyle(1,DRAW_LINE,EMPTY,2,Blue);
SetIndexBuffer(0,SineWave);
SetIndexBuffer(1,LeadSine);
SetIndexBuffer(2,Value1);
SetIndexBuffer(3,Price);
SetIndexBuffer(4,DeltaPhase);
SetIndexEmptyValue(0,0);
SetIndexEmptyValue(1,0);
//---- name for DataWindow and indicator subwindow label
short_name="Sine Wave Indicator";
IndicatorShortName(short_name);
SetIndexLabel(0,short_name);
//----
SetIndexDrawBegin(0,30);
SetIndexDrawBegin(1,30);
//----
return(0);
}
int deinit(){return(0);}
int start()
{
int counted_bars=IndicatorCounted(),i,shift,count;
if (counted_bars==0) counted_bars=100;
i=(Bars-counted_bars)-2;
for (shift=i; shift>=0;shift--)
{
InPhase[1] =InPhase[0]; Quadrature[1] =Quadrature[0];
Phase[1]=Phase[0]; InstPeriod[1] = InstPeriod[0];
Value5[1] =Value5[0];Value11[1] =Value11[0];
Price[shift]=(High[shift+1]+Low[shift+1])/2;
// {Compute InPhase and Quadrature components}
Value1[shift] = Price[shift] - Price[shift+6];
Value2 =Value1[shift+3];
Value3 =0.75*(Value1[shift] - Value1[shift+6]) + 0.25*(Value1[shift+2] - Value1[shift+4]);
InPhase[0] = 0.33*Value2 + 0.67*InPhase[1];
Quadrature[0] = 0.2*Value3 + 0.8*Quadrature[1];
// {Use ArcTangent to compute the current phase}
if (MathAbs(InPhase[0]+InPhase[1])>0) Phase[0]=MathArctan(MathAbs((Quadrature[0]+Quadrature[1])/(InPhase[0]+InPhase[1])));
// {Resolve the ArcTangent ambiguity}
if (InPhase[0] < 0 && Quadrature[0] > 0) Phase[0] = 180 - Phase[0];
if (InPhase[0] < 0 && Quadrature[0] < 0) Phase[0] = 180 + Phase[0];
if (InPhase[0] > 0 && Quadrature[0] < 0) Phase[0] = 360 - Phase[0];
// {Compute a differential phase, resolve phase wraparound, and limit delta phase errors}
DeltaPhase[shift] = Phase[1] - Phase[0];
if (Phase[1] < 90 && Phase[0] > 270) DeltaPhase[shift] = 360 + Phase[1] - Phase[0];
if (DeltaPhase[shift] < 1) DeltaPhase[shift] = 1;
if (DeltaPhase[shift] > 60) DeltaPhase[shift] = 60;
// {Sum DeltaPhases to reach 360 degrees. The sum is the instantaneous period.}
InstPeriod[0] = 0;
Value4 = 0;
for (count = 0;count<=Len;count++)
{
Value4 = Value4 + DeltaPhase[shift+count];
if (Value4 > 360 && InstPeriod[0] == 0) InstPeriod[0] = count;
}
// {Resolve Instantaneous Period errors and smooth}
if (InstPeriod[0] == 0) InstPeriod[0] = InstPeriod[1];
Value5[0] = 0.25*(InstPeriod[0]) + 0.75*Value5[1];
// {Compute Trendline as simple average over the measured dominant cycle period}
Period_ = MathCeil(Value5[0]); Trendline = 0;///Period_ = IntPortion(Value5)
RealPart=0.0;
ImagPart=0.0;
for (count = 0;count<=Period_ - 1;count++)
{ RealPart = RealPart + Price[shift+count]*MathSin(360*count/Period_*Pi/180);
ImagPart = ImagPart + Price[shift+count]*MathCos(360*count/Period_*Pi/180); }
if (MathAbs(ImagPart) > 0.001) DCPhase = 180/Pi*MathArctan(RealPart / ImagPart);
if (MathAbs(ImagPart) <= 0.001)
{
if (ImagPart>0) DCPhase = 90*RealPart;
else DCPhase = -90*RealPart;
}
DCPhase=DCPhase+90;
if (ImagPart < 0) DCPhase = DCPhase + 180;
if (DCPhase > 315) DCPhase = DCPhase - 360;
// if (Period_ > 0) Trendline = Trendline / (Period_ + 2);
// Value11[0] = 0.33*(Price[shift] + 0.5*(Price[shift] - Price[shift+3])) + 0.67*Value11[1];
SineWave[shift]=MathSin(DCPhase*Pi/180);
LeadSine[shift]=MathSin((DCPhase+45)*Pi/180);
//----
}
/*
Comment("Last Tick:",TimeToStr(CurTime(),TIME_DATE|TIME_SECONDS),"\n",
"Instant Trendline","\n",
"Red Trend: ",SineWave[0],"\n",
"Blue Trend: ",LeadSine[0]);*/
return(0);
}
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