From 10faaa1b8c097d11bc202063a8c86836de2a9b1f Mon Sep 17 00:00:00 2001 From: Andrew Bannerman Date: Fri, 3 Aug 2018 20:32:46 -0500 Subject: [PATCH] runtests up to Euation 8-4 Autocorrelation Reversals --- src/MarketCycles.jl | 2 +- src/ehlers_cycles.jl | 733 +- test/runtests.jl | 73 +- test/test_7-4_Modified_Stochastic.csv | 68076 ++++++++++++++++++ test/test_7-5_Modified_RSI.csv | 68076 ++++++++++++++++++ test/test_8-3_Autocorrelation_Indicator.csv | 68076 ++++++++++++++++++ test/test_8-4_Autocorrelation_Reversals.csv | 68011 +++++++++++++++++ 7 files changed, 272856 insertions(+), 191 deletions(-) create mode 100644 test/test_7-4_Modified_Stochastic.csv create mode 100644 test/test_7-5_Modified_RSI.csv create mode 100644 test/test_8-3_Autocorrelation_Indicator.csv create mode 100644 test/test_8-4_Autocorrelation_Reversals.csv diff --git a/src/MarketCycles.jl b/src/MarketCycles.jl index 1cda104..af4214f 100644 --- a/src/MarketCycles.jl +++ b/src/MarketCycles.jl @@ -6,7 +6,7 @@ export SuperSmoother, Decycler, Decycle_OSC, BandPassFilter, DominantCycle, HurstCoefficient, HPLPRoofingFilter, ZeroMeanRoofingFilterK0, ZeroMeanRoofingFilterK1, RoofingFilterIndicator, ModifiedStochastic, ModifiedRSI, AutoCorrelationIndicator, SingleLagAutoCorrelationIndicator, AutoCorrelationPeriodogram, - AutoCorrelationReversals + AutoCorrelationReversals, DFT, AdaptiveRSI, AdaptiveStochastic include("ehlers_cycles.jl") diff --git a/src/ehlers_cycles.jl b/src/ehlers_cycles.jl index dda7c4a..ea29f2d 100644 --- a/src/ehlers_cycles.jl +++ b/src/ehlers_cycles.jl @@ -42,14 +42,14 @@ function Decycler(x::Array{Float64}; n::Int64=60)::Array{Float64} end """ - Decycle_OSC(x::Array{Float64}; n1::Int64=30, n2::Int64=60)::Array{Float64} + Decycle_OSC(x::Array{Float64}; LPPeriod::Int64=30, HPPeriod::Int64=60)::Array{Float64} Decycle Oscillator - Equation 4-2 """ -function Decycle_OSC(x::Array{Float64}; n1::Int64=30, n2::Int64=60)::Array{Float64} - @assert n20 "Argument n out of bounds." - alpha1 = (cosd(.707*360 / n1) + sind(.707*360 / n1) - 1) / cosd(.707*360 / n1) - alpha2 = (cosd(.707*360 / n2) + sind(.707*360 / n2) - 1) / cosd(.707*360 / n2) +function Decycle_OSC(x::Array{Float64}; LPPeriod::Int64=30, HPPeriod::Int64=60)::Array{Float64} + @assert HPPeriod0 "Argument HPPeriod out of bounds." + alpha1 = (cosd(.707*360 / LPPeriod) + sind(.707*360 / LPPeriod) - 1) / cosd(.707*360 / LPPeriod) + alpha2 = (cosd(.707*360 / HPPeriod) + sind(.707*360 / HPPeriod) - 1) / cosd(.707*360 / HPPeriod) HP1 = zeros(x) HP2 = zeros(x) Decycle_OSC = zeros(x) @@ -75,8 +75,8 @@ function BandPassFilter(x::Array{Float64}; n::Int64=30, bandwidth::Float64=.3):: HP = zeros(x) BP = zeros(x) @inbounds for i in 3:length(x) - HP[i] = (1 + alpha2 / 2)*(x[i] - x[i-1]) + (1- alpha2)*HP[i-1] - BP[i] = .5*(1 - alpha1)*(HP[i] - HP[i-2]) + beta1*(1 + alpha1)*BP[i-1] - alpha1*BP[i-2] + HP[i] = (1 + alpha2 / 2)*(x[i] - x[i-1]) + (1- alpha2)*HP[i-1] + BP[i] = .5*(1 - alpha1)*(HP[i] - HP[i-2]) + beta1*(1 + alpha1)*BP[i-1] - alpha1*BP[i-2] end # Signal Signal = zeros(x) @@ -85,45 +85,52 @@ function BandPassFilter(x::Array{Float64}; n::Int64=30, bandwidth::Float64=.3):: Peak[i] = .991*Peak[i-1] if abs(BP[i]) > Peak[i] Peak[i] = abs(BP[i]) - if Peak[i] != 0 - Signal[i] = BP[i] / Peak[i] - end - else + if Peak[i] != 0 Signal[i] = BP[i] / Peak[i] end + else + Signal[i] = BP[i] / Peak[i] + end end # Replace Nan to 0 @inbounds for i in 1:length(Signal) - if isnan(Signal[i]) == 1 - Signal[i] = 0.0 - else - Signal[i] = Signal[i] - end + if isnan(Signal[i]) == 1 + Signal[i] = 0.0 + else + Signal[i] = Signal[i] + end end # Trigger alpha2 = (cosd(1.5*bandwidth*360 / n) + sind(1.5*bandwidth*360 / n) - 1) / cosd(1.5*bandwidth*360 /n) BP_Trigger = zeros(x) - i = 1 + i=1 @inbounds for i = 2:length(x) BP_Trigger[i] = (1 + alpha2 / 2)*(Signal[i] - Signal[i-1]) +(1 -alpha2)*BP_Trigger[i-1] end return BP_Trigger end +#=""" + TO DO - Help Wanted - DC Portion of Calculation + +Zero Crossings of the Band-Pass Filter - Equation 5-2 """ - HurstCoefficient(x::Array{Float64}; n::Int64=30, Smooth::Int64=20)::Array{Float64} +=# + +""" + HurstCoefficient(x::Array{Float64}; n::Int64=30, LPPeriod::Int64=20)::Array{Float64} Hurst Coefficient - Equation 6-1 """ -function HurstCoefficient(x::Array{Float64}; n::Int64=30, Smooth::Int64=20)::Array{Float64} +function HurstCoefficient(x::Array{Float64}; n::Int64=30, LPPeriod::Int64=20)::Array{Float64} @assert n0 "Argument n out of bounds." @assert iseven(n) "n must be an even number." # Smooth with a Super Smoother Filter from equation 3-3 half_n = Int64(n/2) - a1 = exp(-1.414*3.14159 / Smooth) - b1 = 2*a1*cosd(1.414*180 / Smooth) + a1 = exp(-1.414*3.14159 / LPPeriod) + b1 = 2*a1*cosd(1.414*180 / LPPeriod) c2 = b1 c3 = -a1*a1 c1 = 1 - c2 - c3 @@ -132,18 +139,18 @@ function HurstCoefficient(x::Array{Float64}; n::Int64=30, Smooth::Int64=20)::Arr LL = zeros(x) N3 = zeros(x) @inbounds for i = n:size(x,1) - HH[i] = maximum(x[i-n+1:i]) - LL[i] = minimum(x[i-n+1:i]) - N3[i] = (HH[i] - LL[i]) / n + HH[i] = maximum(x[i-n+1:i]) + LL[i] = minimum(x[i-n+1:i]) + N3[i] = (HH[i] - LL[i]) / n end # Rolling min and max half of n HH = zeros(x) LL = zeros(x) N1 = zeros(x) @inbounds for i = half_n:size(x,1) - HH[i] = maximum(x[i-half_n+1:i]) - LL[i] = minimum(x[i-half_n+1:i]) - N1[i] = (HH[i] - LL[i]) / half_n + HH[i] = maximum(x[i-half_n+1:i]) + LL[i] = minimum(x[i-half_n+1:i]) + N1[i] = (HH[i] - LL[i]) / half_n end # Set trailing close half of n HH = [fill(0,half_n); x[1:length(x)-half_n]] @@ -152,40 +159,40 @@ function HurstCoefficient(x::Array{Float64}; n::Int64=30, Smooth::Int64=20)::Arr LL_out = zeros(x) N2 = zeros(x) @inbounds for i = half_n:size(x,1) - HH_out[i] = maximum(HH[i-half_n+1:i]) - LL_out[i] = minimum(LL[i-half_n+1:i]) - N2[i] = (HH_out[i] - LL_out[i])/(half_n) + HH_out[i] = maximum(HH[i-half_n+1:i]) + LL_out[i] = minimum(LL[i-half_n+1:i]) + N2[i] = (HH_out[i] - LL_out[i])/(half_n) end # Hurst Dimen = zeros(x) Hurst = zeros(x) SmoothHurst = zeros(x) @inbounds for i = 3:size(x,1) - if N1[i] > 0 && N2[i] > 0 && N3[i] > 0 - Dimen[i] = .5*((log(N1[i]+ N2[i]) - log(N3[i])) / log(2) + Dimen[i-1]) - Hurst[i] = 2 - Dimen[i] - SmoothHurst[i] = c1*(Hurst[i] + Hurst[i-1]) / 2 + c2*SmoothHurst[i-1]+ c3*SmoothHurst[i-2]; - end + if N1[i] > 0 && N2[i] > 0 && N3[i] > 0 + Dimen[i] = .5*((log(N1[i]+ N2[i]) - log(N3[i])) / log(2) + Dimen[i-1]) + Hurst[i] = 2 - Dimen[i] + SmoothHurst[i] = c1*(Hurst[i] + Hurst[i-1]) / 2 + c2*SmoothHurst[i-1]+ c3*SmoothHurst[i-2]; + end end return SmoothHurst end """ - HPLPRoofingFilter(x::Array{Float64}; HPPeriod::Int64=48, Smooth::Int64=10)::Array{Float64} + HPLPRoofingFilter(x::Array{Float64}; HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} HP LP Roofing Filter - Equation 7-1 """ -function HPLPRoofingFilter(x::Array{Float64}; HPPeriod::Int64=48, Smooth::Int64=10)::Array{Float64} - @assert HPPeriod0 "Argument n out of bounds." +function HPLPRoofingFilter(x::Array{Float64}; HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} + @assert HPPeriod0 "Argument HPPeriod out of bounds." # Highpass filter cyclic components whose periods are shorter than 48 bars alpha1 = (cosd(360 / HPPeriod) + sind(360 / HPPeriod) - 1) / cosd(360 / HPPeriod) HP = zeros(x) @inbounds for i = 2:size(x,1) - HP[i] = (1 - alpha1 / 2)*(x[i] - x[i-1]) + (1 - alpha1)*HP[i-1] + HP[i] = (1 - alpha1 / 2)*(x[i] - x[i-1]) + (1 - alpha1)*HP[i-1] end # Smooth with a Super Smoother Filter from equation 3-3 - a1 = exp(-1.414*3.14159 / Smooth) # may wish to make this an argument in function - b1 = 2*a1*cosd(1.414*180 / Smooth) # may wish to make this an argument in function + a1 = exp(-1.414*3.14159 / LPPeriod) # may wish to make this an argument in function + b1 = 2*a1*cosd(1.414*180 / LPPeriod) # may wish to make this an argument in function c2 = b1 c3 = -a1*a1 c1 = 1 - c2 - c3 @@ -205,7 +212,7 @@ K0 = Lag 0 # Ehlers describes using Lag 0 and Lag 1 cross overs/unders as a signal trigger for buying / selling """ function ZeroMeanRoofingFilterK0(x::Array{Float64}; HPPeriod::Int64=48, Smooth::Int64=10)::Array{Float64} - @assert HPPeriod0 "Argument n out of bounds." + @assert HPPeriod0 "Argument HPPeriod out of bounds." # Highpass filter cyclic components whose periods are shorter than 48 bars alpha1 = (cosd(360 / HPPeriod) + sind(360 / HPPeriod) - 1) /cosd(360 / HPPeriod) HP = zeros(x) @@ -234,7 +241,7 @@ Zero Mean Roofing Filter - Lag 1 - Equation 7-2 K1 = Lag 1 """ function ZeroMeanRoofingFilterK1(x::Array{Float64}; HPPeriod::Int64=48, Smooth::Int64=10)::Array{Float64} - @assert HPPeriod0 "Argument n out of bounds." + @assert HPPeriod0 "Argument HPPeriod out of bounds." # Highpass filter cyclic components whose periods are shorter than 48 bars alpha1 = (cosd(360 / HPPeriod) + sind(360 / HPPeriod) - 1) /cosd(360 / HPPeriod) HP = zeros(x) @@ -257,19 +264,17 @@ function ZeroMeanRoofingFilterK1(x::Array{Float64}; HPPeriod::Int64=48, Smooth:: end """ - RoofingFilterIndicator(x::Array{Float64}; n1::Int64=40,n2::Int64=80)::Array{Float64} + RoofingFilterIndicator(x::Array{Float64}; LPPeriod::Int64=40,HPPeriod::Int64=80)::Array{Float64} Roofing Filter As Indicator - Equation 7-3 """ -function RoofingFilterIndicator(x::Array{Float64}; n1::Int64=40,n2::Int64=80)::Array{Float64} - @assert n10 "Argument n out of bounds." +function RoofingFilterIndicator(x::Array{Float64}; LPPeriod::Int64=40,HPPeriod::Int64=80)::Array{Float64} + @assert HPPeriod0 "Argument HPPeriod out of bounds." # Highpass filter cyclic components whose periods are shorter than 48 (n) bars - LPPeriod = n1 - HPPeriod = n2 alpha1 = (cosd(.707*360 / HPPeriod) + sind(.707*360 /HPPeriod) - 1) / cosd(.707*360 / HPPeriod) HP = zeros(x) @inbounds for i = 3:length(x) - HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] + x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] + HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] + x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] end #Smooth with a Super Smoother Filter from equation 3-3 a1 = exp(-1.414*3.14159 / LPPeriod) @@ -285,21 +290,21 @@ function RoofingFilterIndicator(x::Array{Float64}; n1::Int64=40,n2::Int64=80)::A end """ - ModifiedStochastic(x::Array{Float64}; n::Int64=20)::Array{Float64} + ModifiedStochastic(x::Array{Float64}; n::Int64=20, HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} Modified Stochastic - Equation 7-4 """ -function ModifiedStochastic(x::Array{Float64}; n::Int64=20)::Array{Float64} +function ModifiedStochastic(x::Array{Float64}; n::Int64=20, HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} @assert n0 "Argument n out of bounds." #Highpass filter cyclic components whose periods are shorter than 48 bars - alpha1 = (cosd(.707*360 / 48) + sind(.707*360 / 48) - 1) /cosd(.707*360 / 48) + alpha1 = (cosd(.707*360 / HPPeriod) + sind(.707*360 / HPPeriod) - 1) /cosd(.707*360 / HPPeriod) HP = zeros(x) @inbounds for i = 3:size(x,1) HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1]+ x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 -alpha1)*HP[i-2] end # Smooth with a Super Smoother Filter from equation 3-3 - a1 = exp(-1.414*3.14159 / 10) - b1 = 2*a1*cosd(1.414*180 / 10) + a1 = exp(-1.414*3.14159 / LPPeriod) + b1 = 2*a1*cosd(1.414*180 / LPPeriod) c2 = b1 c3 = -a1*a1 c1 = 1 - c2 - c3 @@ -313,29 +318,30 @@ function ModifiedStochastic(x::Array{Float64}; n::Int64=20)::Array{Float64} Stoc = zeros(x) MyStochastic = zeros(x) @inbounds for i = n:size(x,1) - HighestC[i] = maximum(Filt[i-n+1:i]) - LowestC[i] = minimum(Filt[i-n+1:i]) - Stoc[i] = (Filt[i] - LowestC[i]) / (HighestC[i] - LowestC[i]) - MyStochastic[i] = c1*(Stoc[i] + Stoc[i-1]) / 2 + c2*MyStochastic[i-1] + c3*MyStochastic[i-2] + HighestC[i] = maximum(Filt[i-n+1:i]) + LowestC[i] = minimum(Filt[i-n+1:i]) + Stoc[i] = (Filt[i] - LowestC[i]) / (HighestC[i] - LowestC[i]) + MyStochastic[i] = c1*(Stoc[i] + Stoc[i-1]) / 2 + c2*MyStochastic[i-1] + c3*MyStochastic[i-2] end return MyStochastic end -@doc """ +""" + ModifiedRSI(x::Array{Float64}; n::Int64=10, HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} + Modified RSI - Equation 7-5 -`ModifiedRSI(x::Array{Float64}; n::Int64=20)::Array{Float64}` """ -function ModifiedRSI(x::Array{Float64}; n::Int64=10)::Array{Float64} +function ModifiedRSI(x::Array{Float64}; n::Int64=10, HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} @assert n0 "Argument n out of bounds." - #Highpass filter cyclic components whose periods areshorter than 48 bars - alpha1 = (cosd(.707*360 / 48) + sind(.707*360 / 48) - 1) /cosd(.707*360 / 48) + # Highpass filter cyclic components whose periods areshorter than 48 bars + alpha1 = (cosd(.707*360 / HPPeriod) + sind(.707*360 / HPPeriod) - 1) /cosd(.707*360 / HPPeriod) HP = zeros(x) @inbounds for i =3:size(x,1) HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] +x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 -alpha1)*HP[i-2] end - #Smooth with a Super Smoother Filter from equation 3-3 - a1 = exp(-1.414*3.14159 / 10) - b1 = 2*a1*cosd(1.414*180 / 10) + # Smooth with a Super Smoother Filter from equation 3-3 + a1 = exp(-1.414*3.14159 / LPPeriod) + b1 = 2*a1*cosd(1.414*180 / LPPeriod) c2 = b1 c3 = -a1*a1 c1 = 1 - c2 - c3 @@ -356,46 +362,44 @@ function ModifiedRSI(x::Array{Float64}; n::Int64=10)::Array{Float64} posDiff[i] = filtdiff[i] elseif filtdiff[i] < 0 negDiff[i] = abs(filtdiff[i]) + end end - end - - # Running Sums of Filt - posSum = zeros(x) - negSum = zeros(x) - denom = zeros(x) - rsi= zeros(x) - @inbounds for i = n:size(x,1) - posSum[i] = sum(posDiff[i-n+1:i]) - negSum[i] = sum(negDiff[i-n+1:i]) - denom[i] = posSum[i]+negSum[i] - end - - # RSI - MyRSI = zeros(x) - @inbounds for i = 3:size(x,1) - if denom != 0 && denom[i-1] != 0 - MyRSI[i] = c1*(posSum[i] /denom[i] + posSum[i-1] / denom[i-1]) / 2 + c2*MyRSI[i-1] +c3*MyRSI[i-2] + # Running Sums of Filt + posSum = zeros(x) + negSum = zeros(x) + denom = zeros(x) + rsi = zeros(x) + @inbounds for i = n:size(x,1) + posSum[i] = sum(posDiff[i-n+1:i]) + negSum[i] = sum(negDiff[i-n+1:i]) + denom[i] = posSum[i]+negSum[i] end - end - return MyRSI + # RSI + MyRSI = zeros(x) + @inbounds for i = 3:size(x,1) + if denom != 0 && denom[i-1] != 0 + MyRSI[i] = c1*(posSum[i] /denom[i] + posSum[i-1] / denom[i-1]) / 2 + c2*MyRSI[i-1] +c3*MyRSI[i-2] + end + end + return MyRSI end -@doc """ -Autocorrelation - Equation 8-2 -Computes Matrix for all min_lag:max_lag -`AutoCorrelationIndicator(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48)::Array{Float64}` """ -function AutoCorrelationIndicator(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48)::Array{Float64} - @assert n0 "Argument n out of bounds." - #Highpass filter cyclic components whose periods areshorter than 48 bars - alpha1 = (cosd(.707*360 / 48) + sind(.707*360 / 48) - 1) / cosd(.707*360 / 48) + AutoCorrelationIndicator(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48, HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} + +Autocorrelation Indicator - Equation 8-2 +""" +function AutoCorrelationIndicator(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48, HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} + @assert max_lag0 "Argument max_lag out of bounds." + # Highpass filter cyclic components whose periods areshorter than 48 bars + alpha1 = (cosd(.707*360 / HPPeriod) + sind(.707*360 / HPPeriod) - 1) / cosd(.707*360 / HPPeriod) HP = zeros(x) @inbounds for i = 3:size(x,1) HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] +x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] end - #Smooth with a Super Smoother Filter from equation 3-3 - a1 = exp(-1.414*3.14159 / 10) - b1 = 2*a1*cosd(1.414*180 / 10) + # Smooth with a Super Smoother Filter from equation 3-3 + a1 = exp(-1.414*3.14159 / LPPeriod) + b1 = 2*a1*cosd(1.414*180 / LPPeriod) c2 = b1 c3 = -a1*a1 c1 = 1 - c2 - c3 @@ -407,34 +411,34 @@ function AutoCorrelationIndicator(x::Array{Float64}; min_lag::Int64=1, max_lag:: lags = min_lag:max_lag AutoCorrOut = zeros(size(x,1), max_lag) @inbounds for j = lags - # Lag series + # Lag series lagged = [fill(0,j); Filt[1:length(Filt)-j]] - # Roll correlation width of lag and lagged version of itself - @inbounds for i = 96:size(x,1) - AutoCorrOut[i,j] = cor(lagged[i-j+1:i], Filt[i-j+1:i]) - #//Scale each correlation to range between 0 and 1 - AutoCorrOut[i,j]= .5*(AutoCorrOut[i,j] + 1) + # Roll correlation width of lag and lagged version of itself + @inbounds for i = 96:size(x,1) + AutoCorrOut[i,j] = cor(lagged[i-j+1:i], Filt[i-j+1:i]) + # Scale each correlation to range between 0 and 1 + AutoCorrOut[i,j]= .5*(AutoCorrOut[i,j] + 1) end end return AutoCorrOut end -@doc """ -Single Lag Autocorrelation - Equation 8-3 -Extract A Single Lag Autocorrelation To Use as Standalone Indicator -`SingleLagAutoCorrelationIndicator(x::Array{Float64}; lag::Int64=10)::Array{Float64}` """ -function SingleLagAutoCorrelationIndicator(x::Array{Float64}; lag::Int64=10)::Array{Float64} - @assert n0 "Argument n out of bounds." - #Highpass filter cyclic components whose periods areshorter than 48 bars - alpha1 = (cosd(.707*360 / 48) + sind(.707*360 / 48) - 1) / cosd(.707*360 / 48) + SingleLagAutoCorrelationIndicator(x::Array{Float64}; lag::Int64=10, HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} + +Single Lag Autocorrelation Indicator - Equation 8-2 +""" +function SingleLagAutoCorrelationIndicator(x::Array{Float64}; lag::Int64=10, HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} + @assert lag0 "Argument n out of bounds." + # Highpass filter cyclic components whose periods areshorter than 48 bars + alpha1 = (cosd(.707*360 / HPPeriod) + sind(.707*360 / HPPeriod) - 1) / cosd(.707*360 / HPPeriod) HP = zeros(x) @inbounds for i = 3:size(x,1) HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] +x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] end - #Smooth with a Super Smoother Filter from equation 3-3 - a1 = exp(-1.414*3.14159 / 10) - b1 = 2*a1*cosd(1.414*180 / 10) + # Smooth with a Super Smoother Filter from equation 3-3 + a1 = exp(-1.414*3.14159 / LPPeriod) + b1 = 2*a1*cosd(1.414*180 / LPPeriod) c2 = b1 c3 = -a1*a1 c1 = 1 - c2 - c3 @@ -442,35 +446,146 @@ function SingleLagAutoCorrelationIndicator(x::Array{Float64}; lag::Int64=10)::Ar @inbounds for i = 3:size(x,1) Filt[i] = c1*(HP[i] + HP[i-1]) / 2 + c2*Filt[i-1] + c3*Filt[i-2] end - #Pearson correlation for specified lag + # Pearson correlation for specified lag AutoCorrOut = zeros(size(x,1)) # Lag series - lagged = [fill(0,lag); Filt[1:length(Filt)-lag]] + lagged = [fill(0,lag); Filt[1:length(Filt)-lag]] # Roll correlation width of lag and lagged version of itself @inbounds for i = lag:size(x,1) AutoCorrOut[i] = cor(lagged[i-lag+1:i], Filt[i-lag+1:i]) #Scale each correlation to range between 0 and 1 AutoCorrOut[i]= .5*(AutoCorrOut[i] + 1) - end + end return AutoCorrOut end -@doc """ +""" + AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48,HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} + Autocorrelation Periodogram- Equation 8-3 -Computes Matrix for all min_lag:max_lag - # //////////// note from normalization down did not reproduce TS results - reuires revisit - Help wanted -`AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48)::Array{Float64}` """ -function AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48)::Array{Float64} +function AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48,HPPeriod::Int64=48, LPPeriod::Int64=10)::Array{Float64} + @assert max_lag0 "Argument max_lag out of bounds." + alpha1 = (cosd(.707*360 / 48) + sind(.707*360 / 48) - 1) / cosd(.707*360 / 48) + HP = zeros(x) + @inbounds for i = 3:size(x,1) + HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] +x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] + end + # Smooth with a Super Smoother Filter from equation 3-3 + a1 = exp(-1.414*3.14159 / 10) + b1 = 2*a1*cosd(1.414*180 / 10) + c2 = b1 + c3 = -a1*a1 + c1 = 1 - c2 - c3 + Filt = zeros(x) + @inbounds for i = 3:size(x,1) + Filt[i] = c1*(HP[i] + HP[i-1]) / 2 + c2*Filt[i-1] + c3*Filt[i-2] + end + # Pearson correlation for each value of lag + # Initialize correlation sums + lags = min_lag:max_lag + avglength = 3 + temp = zeros(size(x,1)) + Avg_Corr_Out = zeros(size(x,1), max_lag) + @inbounds for j = lags + # Lag series + lagged = [fill(0,j); Filt[1:length(Filt)-j]] + # Roll correlation width of lag and lagged version of itself + @inbounds for i = 96:size(x,1) + Avg_Corr_Out[i,j] = cor(lagged[i-avglength+1:i], Filt[i-avglength+1:i]) + end + end + # Calcualte sine and cosine part + cosinePart = Array{Float64}(length(x),max_lag) + sinePart = Array{Float64}(length(x),max_lag) + sqSum = Array{Float64}(length(x),max_lag) + @inbounds for j = min_lag:max_lag + for k = 3:48 + cosinePart[:,j] .= cosinePart[:,j] .+ Avg_Corr_Out[:,k] .* cosd(370 * k / j) + sinePart[:,j] .= sinePart[:,j] .+ Avg_Corr_Out[:,k] .* sind(370 * k / j) + sqSum[:,j] .= cosinePart[:,j].^2 .+ sinePart[:,j].^2 + end + end + # Iterate over every i in j and smooth R by the .2 and .8 factors + R = Array{Float64}(length(x),max_lag) + @inbounds for j = min_lag:max_lag + @inbounds for i = 2:size(x,1) + R[i,j] = (.2*sqSum[i,j]) * (sqSum[i,j]) + (.8 *R[i-1,j]) + end + end +#### validated against TS above ^^^^^ ############### +## although followed logic for normalization as below could not reproduce same result = revisit. + + # Find Maximum Power Level for Normalization + # need to validate this and below! + MaxPwr = Array{Float64}(length(x),max_lag) + #MaxPwr = 0 + @inbounds for j = min_lag:max_lag + @inbounds for i = 2:size(x,1) + MaxPwr[i,j] = .995*MaxPwr[i-1,j] + if R[i,j] > MaxPwr[i,j] + MaxPwr[i,j]= R[i,j] + end + end + end + + Pwr = Array{Float64}(length(x),max_lag) + @inbounds for j = min_lag:max_lag + @inbounds for i = 1:size(x,1) + Pwr[i,j] = R[i,j] / MaxPwr[i,j] + end + end + + # Replace Nan to 0 + @inbounds for j = 1:max_lag + @inbounds for i = 1:size(x,1) + if isnan(Pwr[i,j]) == 1 + Pwr[i,j] = 0.0 + else + Pwr[i,j] = Pwr[i,j] + end + end + end + + # Compute the dominant cycle using the CG of the spectrum + Spx = zeros(size(x,1)) + Sp = zeros(size(x,1)) + for j = 10:48 + Spx .= ifelse.(Pwr[:,j] .>= 0.5, Spx .+ j .* Pwr[:,j],Spx) + Sp .= ifelse.(Pwr[:,j] .>= 0.5,Sp .+ Pwr[:,j],Sp) + end + + DominantCycle = zeros(x) + for i = 1:size(x,1) + if Sp[i] != 0 + DominantCycle[i] = Spx[i] / Sp[i] + end + end + return DominantCycle +end + +""" + AutoCorrelationReversals(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48, LPPeriod::Int64=10, HPPeriod::Int64=48, AvgLength::Int64=3)::Array{Float64} + +Autocorrelation Reversals - Equation 8-4 + +The indicated reversals are very sensitive to the smoothing of the price data. +LPLength is made available as an indicator input to decrease or increase the number of indicated reversals as desired. +The AvgLength parameter is also made available as an indicator because this averaging also impacts the number of indicated reversals. +Care should be taken when increasing the value of this input because the lag of the indicator increases in direct proportion to the increase of the value of the AvgLength. +Typical delay of the indicator will be about three bars when the AvgLength parameter is set to a value of 3. +""" +function AutoCorrelationReversals(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48, LPPeriod::Int64=10, HPPeriod::Int64=48, AvgLength::Int64=3)::Array{Float64} @assert max_lag0 "Argument n out of bounds." - alpha1 = (cosd(.707*360 / 48) + sind(.707*360 / 48) - 1) / cosd(.707*360 / 48) + # Highpass filter cyclic components whose periods are shorter than 48 bars + alpha1 = (cosd(.707*360 / HPPeriod) + sind(.707*360 / HPPeriod) - 1) / cosd(.707*360 / HPPeriod) HP = zeros(x) @inbounds for i = 3:size(x,1) HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] +x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] end - #Smooth with a Super Smoother Filter from equation 3-3 - a1 = exp(-1.414*3.14159 / 10) - b1 = 2*a1*cosd(1.414*180 / 10) + # Smooth with a Super Smoother Filter from equation 3-3 + a1 = exp(-1.414*3.14159 / LPPeriod) + b1 = 2*a1*cosd(1.414*180 / LPPeriod) c2 = b1 c3 = -a1*a1 c1 = 1 - c2 - c3 @@ -478,32 +593,174 @@ function AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag @inbounds for i = 3:size(x,1) Filt[i] = c1*(HP[i] + HP[i-1]) / 2 + c2*Filt[i-1] + c3*Filt[i-2] end - #//Pearson correlation for each value of lag - #//Initialize correlation sums + # Pearson correlation for each value of lag lags = min_lag:max_lag - avglength = 3 - temp = zeros(size(x,1)) - Avg_Corr_Out = zeros(size(x,1), max_lag) + Avg_Corr_Rev_Out = zeros(size(x,1), max_lag) @inbounds for j = lags - # Lag series + # Lag series lagged = [fill(0,j); Filt[1:length(Filt)-j]] - # Roll correlation width of lag and lagged version of itself + # Roll correlation width of lag and lagged version of itself + @inbounds for i = 96:size(x,1) + Avg_Corr_Rev_Out[i,j] = cor(lagged[i-AvgLength+1:i], Filt[i-AvgLength+1:i]) + # Scale each correlation to range between 0 and 1 + Avg_Corr_Rev_Out[i,j] = .5*(Avg_Corr_Rev_Out[i,j] + 1) + end + end + + # mark all > .5 and <.5 crossings + SumDeltas = zeros(size(x,1), max_lag) + @inbounds for j = lags @inbounds for i = 96:size(x,1) - Avg_Corr_Out[i,j] = cor(lagged[i-avglength+1:i], Filt[i-avglength+1:i]) + if (Avg_Corr_Rev_Out[i,j] > 0.5) && (Avg_Corr_Rev_Out[i-1,j] < 0.5) || (Avg_Corr_Rev_Out[i,j] < 0.5) && (Avg_Corr_Rev_Out[i-1,j] > 0.5) + SumDeltas[i,j] = 1.0 + else + SumDeltas[i,j] = 0.0 + end + end + end + + # Sum across the matrix of all correlation 0.5 crossings + Reversal = zeros(size(x,1)) + test_sum = zeros(size(x,1)) + @inbounds for i = 1:size(x,1) + test_sum[i] = sum(SumDeltas[i,:]) + if sum(SumDeltas[i,:]) > 24 + Reversal[i] = 1 + else Reversal[i] = 0 + end + end + return Reversal +end + +""" + DFT(x::Array{Float64}; LPLength::Int64=10, HPLength::Int64=48)::Array{Float64} + +Discrete Fourier Transform Sprectral Estimate - Equation 9-1 +""" +function DFT(x::Array{Float64}; LPLength::Int64=10, HPLength::Int64=48)::Array{Float64} + @assert HPLength0 "Argument n out of bounds." +# Highpass filter cyclic components whose periods are shorter than 48 bars + alpha1 = (cosd(.707*360 / HPLength) + sind(.707*360 / HPLength) - 1) / cosd(.707*360 / HPLength) + HP = zeros(x) + @inbounds for i = 3:size(x,1) + HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] +x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] + end + # Smooth with a Super Smoother Filter from equation 3-3 + a1 = exp(-1.414*3.14159 / LPLength) + b1 = 2*a1*cosd(1.414*180 / LPLength) + c2 = b1 + c3 = -a1*a1 + c1 = 1 - c2 - c3 + Filt = zeros(x) + @inbounds for i = 3:size(x,1) + Filt[i] = c1*(HP[i] + HP[i-1]) / 2 + c2*Filt[i-1] + c3*Filt[i-2] + end + + # Initialize matrix + CosinePart = zeros(size(x,1), HPLength) + SinePart = zeros(size(x,1), HPLength) + Pwr = zeros(size(x,1), HPLength) + # This is the DFT + @inbounds for j = 10:48 + @inbounds for k = 0:47 + lagged_filt = [fill(0,k); Filt[1:length(Filt)-k]] + CosinePart[:,j] .= CosinePart[:,j] .+ lagged_filt .* cosd(360 * k / j) / j + SinePart[:,j] .= SinePart[:,j] .+ lagged_filt .* sind(360 * k / j) / j + Pwr[:,j] .= CosinePart[:,j] .* CosinePart[:,j] .+ SinePart[:,j] .* SinePart[:,j] + end + end + # Find Maximum Power Level for Normalization + # Note difers from TS output + MaxPwr = Array{Float64}(length(x),max_lag) + @inbounds for j = 8:48 + @inbounds for i = 2:size(x,1) + MaxPwr[i,j] = .995*MaxPwr[i-1,j] + if Pwr[i,j] > MaxPwr[i,j] + MaxPwr[i,j] = Pwr[i,j] end end + end +#+_+_+_+_+_+_+_+_+_+_+_+_ unable to validate the below against TS + #Normalize Power Levels and Convert to Decibels + @inbounds for j = 10:48 + @inbounds for i = 1:size(x,1) + if MaxPwr[i,j] != 0 + Pwr[i,j] = Pwr[i,j] / MaxPwr[i,j] + end + end + end - cosinePart = Array{Float64}(length(x),max_lag) - sinePart = Array{Float64}(length(x),max_lag) - sqSum = Array{Float64}(length(x),max_lag) + # Compute the dominant cycle using the CG of the spectrum + Spx = zeros(size(x,1)) + Sp = zeros(size(x,1)) + for j = 10:48 + Spx .= ifelse.(Pwr[:,j] .>= 0.5, Spx .+ j .* Pwr[:,j],Spx) + Sp .= ifelse.(Pwr[:,j] .>= 0.5,Sp .+ Pwr[:,j],Sp) + end + + DominantCycle = zeros(x) + for i = 2:size(x,1) + if Sp[i] != 0 + DominantCycle[i] = Spx[i] / Sp[i] + else + DominantCycle[i] = DominantCycle[i-1] # if its zero carry forwrd previous value + end + end + return DominantCycle +end + +#=""" + TO DO + +Comb Filter Spectral Estimate - Equation 10-1 +This spectral estimate may be used to adust other indicators such as RSI, Stochastic and CCI +For example of how the indicator adjustments are made see Adaptive Indicators in equation 11-* +""" +=# +""" + AdaptiveRSI(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48,LPLength::Int64=10, HPLength::Int64=48, AvgLength::Int64=3)::Array{Float64} + +Adaptive RSI - Equation 11-1 +Adjust the RSI by a lookback period half the length of the dominant cycle +""" +function AdaptiveRSI(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48,LPLength::Int64=10, HPLength::Int64=48, AvgLength::Int64=3)::Array{Float64} + @assert max_lag0 "Argument n out of bounds." + alpha1 = (cosd(.707*360 / HPLength) + sind(.707*360 / HPLength) - 1) / cosd(.707*360 / HPLength) + HP = zeros(x) + @inbounds for i = 3:size(x,1) + HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] +x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] + end + # Smooth with a Super Smoother Filter from equation 3-3 + a1 = exp(-1.414*3.14159 / LPLength) + b1 = 2*a1*cosd(1.414*180 / LPLength) + c2 = b1 + c3 = -a1*a1 + c1 = 1 - c2 - c3 + Filt = zeros(x) + @inbounds for i = 3:size(x,1) + Filt[i] = c1*(HP[i] + HP[i-1]) / 2 + c2*Filt[i-1] + c3*Filt[i-2] + end + # Pearson correlation for each value of lag + # Initialize correlation sums + lags = min_lag:max_lag + temp = zeros(size(x,1)) + Avg_Corr_Out = zeros(size(x,1), max_lag) + @inbounds for j = lags + # Lag series + lagged = [fill(0,j); Filt[1:length(Filt)-j]] + # Roll correlation width of lag and lagged version of itself + @inbounds for i = 96:size(x,1) + Avg_Corr_Out[i,j] = cor(lagged[i-AvgLength+1:i], Filt[i-AvgLength+1:i]) + end + end # Calcualte sine and cosine part cosinePart = Array{Float64}(length(x),max_lag) sinePart = Array{Float64}(length(x),max_lag) sqSum = Array{Float64}(length(x),max_lag) @inbounds for j = min_lag:max_lag - for k = 3:48 + @inbounds for k = 3:48 cosinePart[:,j] .= cosinePart[:,j] .+ Avg_Corr_Out[:,k] .* cosd(370 * k / j) sinePart[:,j] .= sinePart[:,j] .+ Avg_Corr_Out[:,k] .* sind(370 * k / j) sqSum[:,j] .= cosinePart[:,j].^2 .+ sinePart[:,j].^2 @@ -517,9 +774,7 @@ function AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag R[i,j] = (.2*sqSum[i,j]) * (sqSum[i,j]) + (.8 *R[i-1,j]) end end - #### validated against TS above ^^^^^ ############### - ## although followed logic for normalization could not reproduce same result = revisit. - + #### validated ^^^^^ ############### # Find Maximum Power Level for Normalization # need to validate this and below! MaxPwr = Array{Float64}(length(x),max_lag) @@ -527,12 +782,11 @@ function AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag @inbounds for j = min_lag:max_lag @inbounds for i = 2:size(x,1) MaxPwr[i,j] = .995*MaxPwr[i-1,j] - if R[i,j] > MaxPwr[i,j] - MaxPwr[i,j]= R[i,j] + if R[i,j] > MaxPwr[i,j] + MaxPwr[i,j]= R[i,j] end end end - Pwr = Array{Float64}(length(x),max_lag) @inbounds for j = min_lag:max_lag @inbounds for i = 1:size(x,1) @@ -543,12 +797,12 @@ function AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag # Replace Nan to 0 @inbounds for j = 1:max_lag @inbounds for i = 1:size(x,1) - if isnan(Pwr[i,j]) == 1 - Pwr[i,j] = 0.0 - else - Pwr[i,j] = Pwr[i,j] - end - end + if isnan(Pwr[i,j]) == 1 + Pwr[i,j] = 0.0 + else + Pwr[i,j] = Pwr[i,j] + end + end end # Compute the dominant cycle using the CG of the spectrum @@ -564,28 +818,71 @@ function AutoCorrelationPeriodogram(x::Array{Float64}; min_lag::Int64=1, max_lag if Sp[i] != 0 DominantCycle[i] = Spx[i] / Sp[i] end + if DominantCycle[i] < 10 + DominantCycle[i] = 10 end - return DominantCycle + if DominantCycle[i] > 48 + DominantCycle[i] = 48 + end + end + + # Adaptive RSI starts here, using half the measured dominant + ClosesUp = zeros(x) + ClosesDn = zeros(x) + filtdiff = zeros(x) + posDiff= zeros(x) + negDiff= zeros(x) + # pos and neg diffs + @inbounds for i = 2:size(x,1) + # difference + filtdiff[i] = Filt[i] - Filt[i-1] + if filtdiff[i] > 0 + posDiff[i] = filtdiff[i] + elseif filtdiff[i] < 0 + negDiff[i] = abs(filtdiff[i]) + end + end + + # Running Sums of Filt + posSum = zeros(x) + negSum = zeros(x) + denom = zeros(x) + rsi= zeros(x) + # Set width of look back 50% of the dominant cycle + n = round.(DominantCycle ./ 2) + n = Int64.(n) + i=1 + @inbounds for i = n[1]:size(x,1) + k = n[i] + posSum[i] = sum(posDiff[i-k+1:i]) + negSum[i] = sum(negDiff[i-k+1:i]) + denom[i] = posSum[i]+negSum[i] + end + + # RSI + MyRSI = zeros(x) + @inbounds for i = 3:size(x,1) + if denom != 0 && denom[i-1] != 0 + MyRSI[i] = c1*(posSum[i] /denom[i] + posSum[i-1] / denom[i-1]) / 2 + c2*MyRSI[i-1] +c3*MyRSI[i-2] + end + end + return MyRSI end -@doc """ -Autocorrelation Reversals - Equation 8-3 -# The indicated reversals are very sensitive to the smoothing of the price data. -# LPLength is made available as an indicator input to decrease or increase the number of indicated reversals as desired. -# The AvgLength parameter is also made available as an indicator because this averaging also impacts the number of indicated reversals. -# Care should be taken when increasing the value of this input because the lag of the indicator increases in direct proportion to the increase of the value of the AvgLength. -# Typical delay of the indicator will be about three bars when the AvgLength parameter is set to a value of 3. -`AutoCorrelationReversals(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48, LPLength::Int64=10, HPLength::Int64=48, AvgLength::Int64=3)::Array{Float64}` """ -function AutoCorrelationReversals(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48, LPLength::Int64=10, HPLength::Int64=48, AvgLength::Int64=3)::Array{Float64} + AdaptiveStochastic(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48,LPLength::Int64=10, HPLength::Int64=48, AvgLength::Int64=3)::Array{Float64} + +Adaptive Stochastic - Equation 11-2 +Adjust the stochastic lookback period by the same value as the dominant cycle +""" +function AdaptiveStochastic(x::Array{Float64}; min_lag::Int64=1, max_lag::Int64=48,LPLength::Int64=10, HPLength::Int64=48, AvgLength::Int64=3)::Array{Float64} @assert max_lag0 "Argument n out of bounds." - # Highpass filter cyclic components whose periods are shorter than 48 bars alpha1 = (cosd(.707*360 / HPLength) + sind(.707*360 / HPLength) - 1) / cosd(.707*360 / HPLength) HP = zeros(x) @inbounds for i = 3:size(x,1) HP[i] = (1 - alpha1 / 2)*(1 - alpha1 / 2)*(x[i] - 2*x[i-1] +x[i-2]) + 2*(1 - alpha1)*HP[i-1] - (1 - alpha1)*(1 - alpha1)*HP[i-2] end - #Smooth with a Super Smoother Filter from equation 3-3 + # Smooth with a Super Smoother Filter from equation 3-3 a1 = exp(-1.414*3.14159 / LPLength) b1 = 2*a1*cosd(1.414*180 / LPLength) c2 = b1 @@ -595,46 +892,108 @@ function AutoCorrelationReversals(x::Array{Float64}; min_lag::Int64=1, max_lag:: @inbounds for i = 3:size(x,1) Filt[i] = c1*(HP[i] + HP[i-1]) / 2 + c2*Filt[i-1] + c3*Filt[i-2] end - #Pearson correlation for each value of lag + # Pearson correlation for each value of lag + # Initialize correlation sums lags = min_lag:max_lag - Avg_Corr_Rev_Out = zeros(size(x,1), max_lag) + temp = zeros(size(x,1)) + Avg_Corr_Out = zeros(size(x,1), max_lag) @inbounds for j = lags - # Lag series + # Lag series lagged = [fill(0,j); Filt[1:length(Filt)-j]] # Roll correlation width of lag and lagged version of itself - @inbounds for i = 96:size(x,1) - Avg_Corr_Rev_Out[i,j] = cor(lagged[i-AvgLength+1:i], Filt[i-AvgLength+1:i]) - # Scale each correlation to range between 0 and 1 - Avg_Corr_Rev_Out[i,j] = .5*(Avg_Corr_Rev_Out[i,j] + 1) + @inbounds for i = 96:size(x,1) + Avg_Corr_Out[i,j] = cor(lagged[i-AvgLength+1:i], Filt[i-AvgLength+1:i]) end end - # mark all > .5 and <.5 crossings - SumDeltas = zeros(size(x,1), max_lag) - @inbounds for j = lags - @inbounds for i = 96:size(x,1) - if (Avg_Corr_Rev_Out[i,j] > 0.5) && (Avg_Corr_Rev_Out[i-1,j] < 0.5) || (Avg_Corr_Rev_Out[i,j] < 0.5) && (Avg_Corr_Rev_Out[i-1,j] > 0.5) - SumDeltas[i,j] = 1.0 - else - SumDeltas[i,j] = 0.0 + # Calcualte sine and cosine part + cosinePart = Array{Float64}(length(x),max_lag) + sinePart = Array{Float64}(length(x),max_lag) + sqSum = Array{Float64}(length(x),max_lag) + @inbounds for j = min_lag:max_lag + @inbounds for k = 3:48 + cosinePart[:,j] .= cosinePart[:,j] .+ Avg_Corr_Out[:,k] .* cosd(370 * k / j) + sinePart[:,j] .= sinePart[:,j] .+ Avg_Corr_Out[:,k] .* sind(370 * k / j) + sqSum[:,j] .= cosinePart[:,j].^2 .+ sinePart[:,j].^2 + end + end + + # Iterate over every i in j and smooth R by the .2 and .8 factors + R = Array{Float64}(length(x),max_lag) + @inbounds for j = min_lag:max_lag + @inbounds for i = 2:size(x,1) + R[i,j] = (.2*sqSum[i,j]) * (sqSum[i,j]) + (.8 *R[i-1,j]) + end + end + #### validated ^^^^^ ############### + # Find Maximum Power Level for Normalization + # need to validate this and below! + MaxPwr = Array{Float64}(length(x),max_lag) + #MaxPwr = 0 + @inbounds for j = min_lag:max_lag + @inbounds for i = 2:size(x,1) + MaxPwr[i,j] = .995*MaxPwr[i-1,j] + if R[i,j] > MaxPwr[i,j] + MaxPwr[i,j]= R[i,j] end end end + Pwr = Array{Float64}(length(x),max_lag) + @inbounds for j = min_lag:max_lag + @inbounds for i = 1:size(x,1) + Pwr[i,j] = R[i,j] / MaxPwr[i,j] + end + end - # Sum across the matrix of all correlation 0.5 crossings - Reversal = zeros(size(x,1)) - test_sum = zeros(size(x,1)) - @inbounds for i = 1:size(x,1) - test_sum[i] = sum(SumDeltas[i,:]) - if sum(SumDeltas[i,:]) > 24 - Reversal[i] = 1 - else - Reversal[i] = 0 + # Replace Nan to 0 + @inbounds for j = 1:max_lag + @inbounds for i = 1:size(x,1) + if isnan(Pwr[i,j]) == 1 + Pwr[i,j] = 0.0 + else + Pwr[i,j] = Pwr[i,j] + end + end + end + + # Compute the dominant cycle using the CG of the spectrum + Spx = zeros(size(x,1)) + Sp = zeros(size(x,1)) + for j = 10:48 + Spx .= ifelse.(Pwr[:,j] .>= 0.5, Spx .+ j .* Pwr[:,j],Spx) + Sp .= ifelse.(Pwr[:,j] .>= 0.5,Sp .+ Pwr[:,j],Sp) + end + + DominantCycle = zeros(x) + for i = 1:size(x,1) + if Sp[i] != 0 + DominantCycle[i] = Spx[i] / Sp[i] end + if DominantCycle[i] < 10 + DominantCycle[i] = 10 + end + if DominantCycle[i] > 48 + DominantCycle[i] = 48 + end + end + # Stochastic Computation starts here + # Highest and lowest filt over same period as dominant cycle + HighestC = zeros(x) + LowestC = zeros(x) + Stoc = zeros(x) + AdaptiveStochastic = zeros(x) + n = Int64.(round.(DominantCycle)) + @inbounds for i = n[1]:size(x,1) + k = n[i] + HighestC[i] = maximum(Filt[i-k+1:i]) + LowestC[i] = minimum(Filt[i-k+1:i]) + Stoc[i] = (Filt[i] - LowestC[i]) / (HighestC[i] - LowestC[i]) + AdaptiveStochastic[i] = c1*(Stoc[i] + Stoc[i-1]) / 2 + c2*AdaptiveStochastic[i-1] + c3*AdaptiveStochastic[i-2] end - return Reversal + return AdaptiveStochastic end + # Help Wanted ##### DC portion needs to be completed correctly ### ## Data validation vs TS passes with exception of DC diff --git a/test/runtests.jl b/test/runtests.jl index 76e10fc..978e14b 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -9,7 +9,7 @@ end ###################################################################### # Validate against John Ehlers Original TradeStation Easylanguage code -# Run against dummy data loaded in Tradestation +# Run against dummy data loaded in Tradestation ###################################################################### # Note - for some tests irratic results for the lead in period # @@ -45,7 +45,7 @@ end test = CSV.read( filename) dat = Float64.(test[:x]) decycler_osc_benchmark = Float64.(test[:thirty_sixty_decycle_osc]) - decycler_osc = Decycle_OSC(dat, n1=30,n2=60) + decycler_osc = Decycle_OSC(dat, LPPeriod=30,HPPeriod=60) decycler_osc = round.(decycler_osc,2) # round same as tradestation output valid = ifelse.(decycler_osc .== decycler_osc_benchmark,1,0) @test sum(valid) == length(valid)-148 # minus lead in @@ -108,7 +108,7 @@ end @testset "Roofing Filter Indicator Equation 7-3" begin filename = joinpath(dirname(@__FILE__), "test_7-3_Roofing_Filter_Indicator.csv") - test = CSV.read( filename) + test = CSV.read(filename) dat = Float64.(test[:x]) Roofing_Filter_Indicator_benchmark = Float64.(test[:Filt]) Roofing_Filter_Indicator = RoofingFilterIndicator(dat) @@ -117,4 +117,71 @@ end @test sum(valid) == length(valid)-213 # 213 bar lead in period end + @testset "Modified Stochastic - Equation 7-4" begin + filename = joinpath(dirname(@__FILE__), "test_7-4_Modified_Stochastic.csv") + test = CSV.read(filename) + dat = Float64.(test[:x]) + Modified_stochastic_benchmark = Float64.(test[:Modified_stochasitc]) + Modified_stochastic = ModifiedStochastic(dat,n=20) + Modified_stochastic = round.(Modified_stochastic,2) # round same as tradestation output + valid = ifelse.(Modified_stochastic .== Modified_stochastic_benchmark,1,0) + @test sum(valid) == length(valid)-72 # 72 bar lead in period + end + + @testset "Modified RSI - Equation 7-5" begin + filename = joinpath(dirname(@__FILE__), "test_7-5_Modified_RSI.csv") + test = CSV.read(filename) + dat = Float64.(test[:x]) + Modified_RSI_benchmark = Float64.(test[:mod_rsi]) + Modified_RSI = ModifiedRSI(dat,n=10) + Modified_RSI = round.(Modified_RSI,2) # round same as tradestation output + valid = ifelse.(Modified_RSI .== Modified_RSI_benchmark,1,0) + @test sum(valid) == length(valid)-96 # 96 bar lead in period + end + + @testset "Autocorrelation Indicator - Equation 8-2" begin + filename = joinpath(dirname(@__FILE__), "test_8-3_Autocorrelation_Indicator.csv") + test = CSV.read(filename) + dat = Float64.(test[:x]) + Autocor_p48_benchmark = Float64.(test[:cor_48]) + Autocor_p10_benchmark = Float64.(test[:cor_10]) + Autocor_ind_out = AutoCorrelationIndicator(dat) + autocorr_p48 = Autocor_ind_out[:,48] + autocorr_p10 = Autocor_ind_out[:,10] + autocorr_p48 = round.(autocorr_p48,4) # round same as tradestation output + autocorr_p10 = round.(autocorr_p10,4) # round same as tradestation output + valid = ifelse.(autocorr_p10 .== Autocor_p10_benchmark,1,0) + @test sum(valid) == length(valid)-124 # 124 bar lead in period + valid = ifelse.(autocorr_p48 .== Autocor_p48_benchmark,1,0) + @test sum(valid) == length(valid)-185 # 185 bar lead in period + end + + @testset "Single Lag Autocorrelation - Equation 8-3" begin + filename = joinpath(dirname(@__FILE__), "test_8-3_Autocorrelation_Indicator.csv") + test = CSV.read(filename) + dat = Float64.(test[:x]) + Autocor_p10_benchmark = Float64.(test[:cor_10]) + Autocor_ind_out = AutoCorrelationIndicator(dat) + autocorr_p10 = Autocor_ind_out[:,10] + autocorr_p10 = round.(autocorr_p10,4) # round same as tradestation output + valid = ifelse.(autocorr_p10 .== Autocor_p10_benchmark,1,0) + @test sum(valid) == length(valid)-124 # 124 bar lead in period + end + + # to do - fix MaxPwr calculation for Autocorrelation Peeriodogram 8-3 + + @testset "Autocorrelation Reversals - Equation 8-4" begin + filename = joinpath(dirname(@__FILE__), "test_8-4_Autocorrelation_Reversals.csv") + test = CSV.read(filename) + dat = Float64.(test[:x]) + Autocor_reversals_benchmark = Float64.(test[:autocor_reversal]) + Autocor_reversals_out = AutoCorrelationReversals(dat) + valid = ifelse.(Autocor_reversals_out .== Autocor_reversals_benchmark,1,0) + @test sum(valid) == length(valid)-110 # 110 bar lead in period + end + + # TO DO- fix MaxPwr calculation for DFT Spectral Estimate + + # TO DO - Complete Comb Filter Spectral Estimate - Equation 10-1 + end diff --git a/test/test_7-4_Modified_Stochastic.csv b/test/test_7-4_Modified_Stochastic.csv new file mode 100644 index 0000000..89d7dcd --- /dev/null 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