Moving Average Indicator: 20 in 1
This indicator is a collection of moving averages.
1. MVA - Simple Moving Average
MVA=(Price+Price[i-1]+…+Price[i-N])/N, where N-period
2. EMA - Exponential Moving Average
EMA=EMA[i-1]+2*(Price-EMA[i-1])/(1+N)
3. Wilder - Wilder Exponential Moving Average
Wilder=Wilder[i-1]+(Price-Wilder[i-1])/N
4. LWMA - Linear Weighted Moving Average
LWMA=Sum/Weight, where
Sum=Price*N+Price[i-1]*(N-1)+…+Price[i-N+1]*(1),
Weight=N+(N-1)+…+1=N*(N+1)/2.
5. SineWMA - Sine Weighted Moving Average
SineWMA=Sum/Weight, where
Sum=Price[i-N+1]*sin(PI*(N)/(N+1))+Price[i-N+2]*sin(PI*(N-1)/(N+1))+…+Price*sin(PI*1/(N+1))
Weight= sin(PI*(N)/(N+1))+ sin(PI*(N-1)/(N+1))+…+ sin(PI*1/(N+1)).
6. TriMA - Triangular Moving Average
TriMA[i]=(MVA(i,len)+MVA(i-1,len)+…+MVA(i-len+1,len))/len, where
MVA(i,N) – Simple Moving Average,
len=(N+1)/2.
7. LSMA - Least Square Moving Average
LSMA[i]=Sum/(N*(N+1)), where
Sum=(1-(N+1)/3)*Price[i-N+1]+(2-(N+1)/3)*Price[i-N+2]+…+(N-(N+1)/3)*Price[1].
8. SMMA - Smoothed Moving Average
SMMA[i]=(Sum-SMMA[i-1]+Price[i])/N, where
Sum=Price[i-1]+Price[i-2]+…+Price[i-N].
9. HMA - Hull Moving Average by Alan Hull
HMA[i]=LWMA(i,len,(2*LWMA(i,N/2,Price)-LWMA(i,N,Price))), where
len=Sqrt(N),
LWMA(i,N,Price) - Linear Weighted Moving Average
10. ZeroLagEMA - Zero-Lag Exponential Moving Average
ZeroLagEMA[i]=Alpha*(2*Price[i]-Price[i-lag])+(1-Alpha)* ZeroLagEMA[i-1], where
Alpha=2/(N+1),
Lag=(N-1)/2.
11. DEMA - Double Exponential Moving Average by Patrick Mulloy
DEMA[i]=2*D1[i]-D2[i], where
D1[i]=D1[i-1]+2*(Price[i]-D1[i-1])/(1+N),
D2[i]=D2[i-1]+2*(D1[i]-D2[i-1])/(1+N).
12. T3 - T3 by T.Tillson
T3[i]=DEMA(i,DEMA2), where
DEMA2[i]=DEMA(i,DEMA1),
DEMA1[i]=DEMA(i,Price),
DEMA - Double Exponential Moving Average
13. ITrend - Instantaneous Trendline by J.Ehlers
ITrend[i]=(Price[i]+2*Price[i-1]+Price[i-2])/4 for i<=7,
ITrend[i]=(Alpha-0.25*Alpha*Alpha)*Price[i]+0.5*Alpha*Alpha*Price[i-1]-(Alpha-0.75*Alpha*Alpha)*Price[i-2]+2*(1-Alpha)*ITrend[i-1]-(1-Alpha)*(1-Alpha)*ITrend[i-2] for i>7, where
Alpha=2/(N+1)
14. Median - Moving Median
Set of the prices (Price[i], Price[i-1], …, Price[i-N]) is sorted (on increase or decrease) and take value from of the set (N/2).
15. GeoMean - Geometric Mean
GeoMean[i]=Price[i]^(1/N)*Price[i-1]^(1/N)*…*Price[i-N+1]^(1/N).
16. REMA - Regularized EMA by Chris Satchwell
REMA[i]=(REMA[i-1]*(1+2*Lambda)+Alpha*(Price[i]-REMA[i-1])-Lambda*REMA[i-2])/(1+Lambda), where
Alpha=2/(N+1),
Lambda=0.5.
17. ILRS - Integral of Linear Regression Slope
ILRS[i]=(N*Sum1-Sum*Sumy)/(Sum*Sum-N*Sum2)+MVA(I,N), where
Sum=N*(N-1)*0.5,
Sum2=N*(N-1)*(2*N-1)/6,
Sum1=1*Price[i-1]+2*Price[i-2]+…+(N-1)*Price[i-N+1],
Sumy=Price[i]+Price[i-1]+…+Price[i-N+1],
MVA(i,N) – Simple Moving Average.
18. IE/2 - Combination of LSMA and ILRS
IE/2=(ILRS+LSMA)/2
19. TriMAgen - Triangular Moving Average generalized by J.Ehlers
TriMAgen[i]=Sum/(len+1), where
Sum=MVA(i,len)+MVA(i-1,len)+…+MVA(i-len,len), where
MVA(i,N) – Simple Moving Average,
len=(N+1)/2.
20. JSmooth - Smoothing by Mark Jurik
