Indicator Evaluation
Computational Investing
Chris Harris
11 Nov 2014
Chris Harris
11 Nov 2014
Introduction
Beyond price action, a second initiative builds on indicator development, with a goal to use indicator signals as a means to drive quantitative investment decisions. Although one could envision indicator values as triggers to buy or sell stocks, by modifying event.py, in the quantitative analysis routine, only the indicators themselves will receive attention here. When considering momentum signals, the commodity channel index, CCI, will serve as a baseline. To flatten or linearize bollinger bands:
bollinger feature = ( price - mean ) / standard deviation
yields a normalized, unitless quantity, a number of standard deviations above or below the mean. By producing a value relative to key reference areas: +2 standard deviations, mean, -2 standard deviations, it captures the behavior of bollinger bands. With the remarkable shape conformation between the bollinger feature and CCI, the bollinger bands depict a 2-D graphical illustration of momentum. When the bollinger bands contract to a narrow range, momentum indicator noise becomes apparent, as the weak bandwidth amplifies superficial momentum shifts.
Although John Bollinger promotes a 20 period moving average as a reference frame, a 40 period momentum profile dwells primarily above zero in an uptrend, and below zero in a downtrend. Conventional scientific techniques suggest a 40 sample population count represents a minimum threshold to ensure statistical significance. Hence, statistical knowledge may explain why institutional investors recognize the 50 period moving average as the boundary between buy and sell. A notable departure from this guideline includes the relative strength index, RSI, where a 14 period momentum value corresponds to a 40 period CCI. When comparing performance, put the indicators side by side to observe response times.
yields a normalized, unitless quantity, a number of standard deviations above or below the mean. By producing a value relative to key reference areas: +2 standard deviations, mean, -2 standard deviations, it captures the behavior of bollinger bands. With the remarkable shape conformation between the bollinger feature and CCI, the bollinger bands depict a 2-D graphical illustration of momentum. When the bollinger bands contract to a narrow range, momentum indicator noise becomes apparent, as the weak bandwidth amplifies superficial momentum shifts.
Although John Bollinger promotes a 20 period moving average as a reference frame, a 40 period momentum profile dwells primarily above zero in an uptrend, and below zero in a downtrend. Conventional scientific techniques suggest a 40 sample population count represents a minimum threshold to ensure statistical significance. Hence, statistical knowledge may explain why institutional investors recognize the 50 period moving average as the boundary between buy and sell. A notable departure from this guideline includes the relative strength index, RSI, where a 14 period momentum value corresponds to a 40 period CCI. When comparing performance, put the indicators side by side to observe response times.
Python Code
cci.py:
import os
import shutil
import math
import matplotlib as mpl
import matplotlib.pyplot as plt
# obtain market data
def acquire(sym,interval):
if not os.path.isfile("../data/%s.csv" %sym):
shutil.copy("../QSTK-0.2.8/QSTK/QSData/Yahoo/%s.csv" %sym, "../data")
data = open("../data/%s.csv" %sym,'r')
stream = data.read()
data.close()
field = 7
entry = ""
val = []
matrix = []
for ch in stream:
entry = entry + ch
if ch==',' or ch=='\n':
if len(entry)>1:
val.append(entry[:-1])
entry = ""
if len(val)>=field:
if interval[1] >= val[0] >= interval[0]:
matrix.append(val)
val = []
matrix.sort()
return matrix
def plot(label,matrix,mean,cci,delta,period):
x = []
y = [[]for l in range(2)]
Y = []
hd = 0
hs = [-100,100]
xl = [-10,period-delta+10]
mpl.rc('text', color='#C8A078')
mpl.rc('figure', facecolor='black', edgecolor='black')
mpl.rc('axes', edgecolor='#C6BDBA', labelcolor='#C8A078', facecolor='black', linewidth=2)
mpl.rc('xtick', color='#C8A078')
mpl.rc('ytick', color='#C8A078')
plt.tick_params(bottom=False, top=False, left=False, right=False)
plt.figure(1)
plt.subplot(211)
for i in range(delta-1,period):
x.append(float(i-delta+1))
y[0].append(mean[i])
y[1].append(cci[i])
Y.append(float(matrix[i][6]))
plt.plot(x, Y, color='#004040', linewidth=2)
plt.plot(x, y[0], color='#640064', linewidth=2)
plt.xlim(xl)
plt.title("%s Stockchart: Jan 2008 to Dec 2009" %label, fontsize=25)
plt.xticks(fontsize=20)
plt.yticks(fontsize=20)
plt.ylabel("Price", fontsize=25)
plt.subplot(212)
plt.hlines(hs, xl[0], xl[1], linestyles='solid', color='#F5A078', linewidth=1)
plt.hlines(hd, xl[0], xl[1], linestyles='dotted', color='#F5A078', linewidth=2)
plt.plot(x, y[1], color='#004000', linewidth=2)
plt.xlim(xl)
plt.xticks(fontsize=20)
plt.yticks(fontsize=20)
plt.xlabel("Trade days", fontsize=25)
plt.ylabel("CCI", fontsize=25)
plt.show()
def cci(symbol,delta,interval):
# input GOOGL info
matrix = acquire(symbol,interval)
period = len(matrix)
# evaluate statistical parameters over lookback period
# --------------------------------------------------------------------------------------------
#
# need extra month to accommodate stockchart
#
# --------------------------------------------------------------------------------------------
print("\n\t Date\t\t Index\t\tPrice\t\tMean\t\tAbDev\t\tCCI\n")
pt = [0.0 for p in range(period)]
med = [0.0 for q in range(period)]
mean = [0.0 for r in range(period)]
ad = [0.0 for s in range(period)]
cci = [0.0 for t in range(period)]
for i in range(delta-1,period):
sm = 0.0
sad = 0.0
init = False
for j in range(i-delta+1,i+1):
pt[j] = (float(matrix[j][2]) + float(matrix[j][3]) + float(matrix[j][4]))/3.0*float(matrix[j][6])/float(matrix[j][4])
sm = sm + pt[j]
if init:
if pt[j] > pth:
pth = pt[j]
if pt[j] < ptl:
ptl = pt[j]
else:
pth = pt[j]
ptl = pt[j]
init = True
med[i] = (pth + ptl)/2.0
mean[i] = sm/float(delta)
for j in range(i-delta+1,i+1):
d = abs(pt[j] - med[i])
sad = sad + d
ad[i] = sad/float(delta)
cci[i] = (pt[i] - mean[i])/ad[i]/0.015
print("\t%s\t\t%i\t\t%s\t\t%.4g\t\t%.4g\t\t%.4g" %(matrix[i][0],i,matrix[i][6],mean[i],ad[i],cci[i]))
# display results
print("\n # %i-period lookback cycles =\t%i\n" %(delta,period-delta))
plot(symbol,matrix,mean,cci,delta,period)
return cci
def main():
delta = 20
symbol = "GOOGL"
interval = ["2007-12-04","2009-12-31"]
cf = cci(symbol,delta,interval)
main()
Python Code
bollinger.py:
import os
import shutil
import math
import matplotlib as mpl
import matplotlib.pyplot as plt
# obtain market data
def acquire(sym,interval):
if not os.path.isfile("../data/%s.csv" %sym):
shutil.copy("../QSTK-0.2.8/QSTK/QSData/Yahoo/%s.csv" %sym, "../data")
data = open("../data/%s.csv" %sym,'r')
stream = data.read()
data.close()
field = 7
entry = ""
val = []
matrix = []
for ch in stream:
entry = entry + ch
if ch==',' or ch=='\n':
if len(entry)>1:
val.append(entry[:-1])
entry = ""
if len(val)>=field:
if interval[1] >= val[0] >= interval[0]:
matrix.append(val)
val = []
matrix.sort()
return matrix
def plot(label,matrix,mean,std,rat,delta,period):
x = []
y = [[]for l in range(4)]
Y = []
hd = 0
hs = [-2,2]
xl = [-10,period-delta+10]
mpl.rc('text', color='#C8A078')
mpl.rc('figure', facecolor='black', edgecolor='black')
mpl.rc('axes', edgecolor='#C6BDBA', labelcolor='#C8A078', facecolor='black', linewidth=2)
mpl.rc('xtick', color='#C8A078')
mpl.rc('ytick', color='#C8A078')
plt.tick_params(bottom=False, top=False, left=False, right=False)
plt.figure(1)
plt.subplot(211)
for i in range(delta-1,period):
x.append(float(i-delta+1))
y[0].append(mean[i])
y[1].append(mean[i] - std[i])
y[2].append(mean[i] + std[i])
y[3].append(rat[i])
Y.append(float(matrix[i][6]))
plt.plot(x, Y, color='#004040', linewidth=2)
plt.plot(x, y[0], color='#F5A078', linewidth=2)
plt.plot(x, y[1], color='#640064', linewidth=2)
plt.plot(x, y[2], color='#640064', linewidth=2)
plt.xlim(xl)
plt.title("%s Stockchart: Jan 2008 to Dec 2009" %label, fontsize=25)
plt.xticks(fontsize=20)
plt.yticks(fontsize=20)
plt.ylabel("Price", fontsize=25)
plt.subplot(212)
plt.hlines(hs, xl[0], xl[1], linestyles='solid', color='#F5A078', linewidth=1)
plt.hlines(hd, xl[0], xl[1], linestyles='dotted', color='#F5A078', linewidth=2)
plt.plot(x, y[3], color='#004000', linewidth=2)
plt.xlim(xl)
plt.xticks(fontsize=20)
plt.yticks(fontsize=20)
plt.xlabel("Trade days", fontsize=25)
plt.ylabel("Bollinger Feature", fontsize=25)
plt.show()
def bollinger(symbol,delta,interval):
# input GOOGL info
matrix = acquire(symbol,interval)
period = len(matrix)
# evaluate statistical parameters over lookback period
# --------------------------------------------------------------------------------------------
#
# need extra month to accommodate stockchart
#
# --------------------------------------------------------------------------------------------
print("\n\t Date\t\t Index\t\tPrice\t\tMean\t\tStDev\t\tFeature\n")
std = [0.0 for r in range(period)]
mean = [0.0 for s in range(period)]
rat = [0.0 for t in range(period)]
for i in range(delta-1,period):
sm = 0.0
sd2 = 0.0
for j in range(i-delta+1,i+1):
sm = sm + float(matrix[j][6])
mean[i] = sm/float(delta)
for j in range(i-delta+1,i+1):
d = float(matrix[j][6]) - mean[i]
sd2 = sd2 + d**2.0
std[i] = math.sqrt(sd2/float(delta))
rat[i] = (float(matrix[i][6]) - mean[i])/std[i]
print("\t%s\t\t%i\t\t%s\t\t%.4g\t\t%.4g\t\t%.4g" %(matrix[i][0],i,matrix[i][6],mean[i],std[i],rat[i]))
# display results
print("\n # %i-period lookback cycles =\t%i\n" %(delta,period-delta))
plot(symbol,matrix,mean,std,rat,delta,period)
return rat
def main():
delta = 20
symbol = "GOOGL"
interval = ["2007-12-04","2009-12-31"]
bf = bollinger(symbol,delta,interval)
main()
PowerLanguage .NET Code
Multichart bollinger feature with trailing 6 period moving average
Bollinger_Ratio_Triangle.pln:
using System;
using System.Drawing;
using PowerLanguage.Function;
namespace PowerLanguage.Indicator
{
[SameAsSymbol(true)]
public class Bollinger_Ratio_Triangle : IndicatorObject
{
private TriAverage m_triaverage1;
private TriAverage m_triaverage2;
private VariableSeries<Double> ratio;
private Function.NormGradientColor m_normgradientcolor1;
private int m_applicationtype;
private IPlotObject Plot1;
private IPlotObject Plot2;
private IPlotObject Plot3;
private IPlotObject Plot4;
private IPlotObject Plot5;
public Bollinger_Ratio_Triangle(object ctx) :
base(ctx){
axis = 0;
numdevsdn = -2;
numdevsup = 2;
avelength = 6;
bollength = 20;
gridforegroundcolor = Color.Black;
dncolor = Color.Red;
upcolor = Color.Yellow;
colornormlength = 14;
}
private ISeries<double> bollingerprice { get; set; }
[Input]
public int avelength { get; set; }
[Input]
public int bollength { get; set; }
[Input]
public double numdevsup { get; set; }
[Input]
public double numdevsdn { get; set; }
[Input]
public int axis { get; set; }
[Input]
public int colornormlength { get; set; }
[Input]
public Color upcolor { get; set; }
[Input]
public Color dncolor { get; set; }
[Input]
public Color gridforegroundcolor { get; set; }
protected override void Create(){
m_triaverage1 = new TriAverage(this);
m_triaverage2 = new TriAverage(this);
ratio = new VariableSeries<Double>(this);
m_normgradientcolor1 = new Function.NormGradientColor(this);
Plot1 = AddPlot(new PlotAttributes("Axis", 0, Color.Gray, Color.Empty, 0, 0, true));
Plot2 = AddPlot(new PlotAttributes("Low", 0, Color.Gray, Color.Empty, 0, 0, true));
Plot3 = AddPlot(new PlotAttributes("High", 0, Color.Gray, Color.Empty, 0, 0, true));
Plot4 = AddPlot(new PlotAttributes("Ratio", 0, Color.Cyan, Color.Empty, 0, 0, true));
Plot5 = AddPlot(new PlotAttributes("Ave", 0, Color.Blue, Color.Empty, 0, 0, true));
}
protected override void StartCalc(){
bollingerprice = Bars.Close;
m_triaverage1.price = bollingerprice;
m_triaverage1.length = bollength;
m_triaverage2.price = ratio;
m_triaverage2.length = avelength;
m_normgradientcolor1.dataseriesvalue = m_triaverage2;
m_normgradientcolor1.crosseszero = true;
m_normgradientcolor1.colornormlength = colornormlength;
m_normgradientcolor1.upcolor = upcolor;
m_normgradientcolor1.dncolor = dncolor;
m_applicationtype = (int) Environment.ApplicationCode;
}
protected override void CalcBar(){
var m_avg = m_triaverage1[0];
var m_sdev = bollingerprice.StandardDeviationCustom(bollength, 1);
if(m_sdev > 0.0) ratio.Value = (bollingerprice[0] - m_avg)/m_sdev;
else ratio.Value = 0.0;
Plot1.Set(0, axis);
Plot2.Set(0, numdevsdn);
Plot3.Set(0, numdevsup);
Plot4.Set(0, ratio[0]);
Plot5.Set(0, m_triaverage2[0]);
if (!upcolor.IsEmpty && !dncolor.IsEmpty){
var m_colorlevel = m_normgradientcolor1.Value;
if (m_applicationtype == 1){
Plot5.Colors[0] = m_colorlevel;
}
else{
if (m_applicationtype > 1){
Plot5.Colors[0] = gridforegroundcolor;
Plot5.BGColor = m_colorlevel;
}
}
}
}
}
}
Results
$ python cci.py
Date Index Price Mean AbDev CCI
2008-01-02 19 342.94 348.1 5.419 -53.97
2008-01-03 20 343.01 348.1 5.457 -76.75
2008-01-04 21 328.83 347.3 6.251 -158
2008-01-07 22 324.95 345.8 7.813 -176.4
2008-01-08 23 316.16 344 8.949 -172.8
2008-01-09 24 326.93 342.1 9.924 -135.9
2008-01-10 25 323.69 340.6 9.773 -111
2008-01-11 26 319.44 339.1 10.1 -126.1
2008-01-14 27 327.24 338.1 10.19 -76.45
2008-01-15 28 319.14 336.8 10.54 -102.1
...
2009-12-17 514 297.27 293.4 3.038 97.45
2009-12-18 515 298.51 294 3.052 101.9
2009-12-21 516 299.64 294.7 2.43 126.4
2009-12-22 517 300.86 295.2 2.591 137.7
2009-12-23 518 306.15 295.9 3.08 194.4
2009-12-24 519 309.55 296.7 4.065 196.9
2009-12-28 520 311.75 297.8 5.569 164.4
2009-12-29 521 310.01 298.8 6.139 129.7
2009-12-30 522 311.68 299.6 6.174 121.7
2009-12-31 523 310.30 300.4 6.248 114.8
# 20-period lookback cycles = 504
$ python bollinger.py
Date Index Price Mean StDev Feature
2008-01-02 19 342.94 348.1 6.618 -0.7855
2008-01-03 20 343.01 348.2 6.594 -0.7823
2008-01-04 21 328.83 347.1 7.81 -2.343
2008-01-07 22 324.95 345.5 8.773 -2.34
2008-01-08 23 316.16 343.4 10.39 -2.62
2008-01-09 24 326.93 341.8 10.29 -1.442
2008-01-10 25 323.69 340.5 10.82 -1.549
2008-01-11 26 319.44 338.9 11.5 -1.694
2008-01-14 27 327.24 337.9 11.6 -0.9205
2008-01-15 28 319.14 336.6 12.15 -1.437
...
2009-12-17 514 297.27 293.5 3.39 1.1
2009-12-18 515 298.51 294.1 3.177 1.379
2009-12-21 516 299.64 294.8 2.678 1.79
2009-12-22 517 300.86 295.3 2.862 1.937
2009-12-23 518 306.15 296 3.598 2.812
2009-12-24 519 309.55 296.9 4.582 2.771
2009-12-28 520 311.75 297.9 5.357 2.58
2009-12-29 521 310.01 298.8 5.769 1.936
2009-12-30 522 311.68 299.7 6.34 1.895
2009-12-31 523 310.30 300.5 6.604 1.488
# 20-period lookback cycles = 504
$ python cci.py
Date Index Price Mean AbDev CCI
2008-01-31 39 282.43 326.5 25.94 -122.3
2008-02-01 40 258.21 324.4 29.12 -145.9
2008-02-04 41 247.96 322 31.72 -150.5
2008-02-05 42 253.65 319.4 31.83 -143.3
2008-02-06 43 251.11 316.7 31.84 -135.4
2008-02-07 44 252.73 314.1 32.63 -125.6
2008-02-08 45 258.60 311.7 32.46 -111.3
2008-02-11 46 260.84 309.4 32.31 -102
2008-02-12 47 259.30 307.3 32.26 -96.53
2008-02-13 48 267.58 305.2 32.08 -83.6
...
2009-12-17 514 297.27 285.7 8.699 93.02
2009-12-18 515 298.51 286.3 8.912 92.88
2009-12-21 516 299.64 286.8 9.164 90.99
2009-12-22 517 300.86 287.4 9.212 95.23
2009-12-23 518 306.15 288.1 8.592 129.9
2009-12-24 519 309.55 289.1 8.208 159.4
2009-12-28 520 311.75 290 8.145 176.3
2009-12-29 521 310.01 291 8.204 160.3
2009-12-30 522 311.68 292.1 8.158 153.6
2009-12-31 523 310.30 293.2 7.685 156.3
# 40-period lookback cycles = 484
$ python bollinger.py
Date Index Price Mean StDev Feature
2008-01-31 39 282.43 326.3 27.03 -1.622
2008-02-01 40 258.21 324.2 28.9 -2.282
2008-02-04 41 247.96 321.6 30.95 -2.38
2008-02-05 42 253.65 319 32.14 -2.033
2008-02-06 43 251.11 316.3 33.22 -1.963
2008-02-07 44 252.73 313.7 33.93 -1.796
2008-02-08 45 258.60 311.4 34.48 -1.531
2008-02-11 46 260.84 309.2 34.79 -1.389
2008-02-12 47 259.30 306.9 35.09 -1.358
2008-02-13 48 267.58 305 35.06 -1.067
...
2009-12-17 514 297.27 285.9 9.432 1.205
2009-12-18 515 298.51 286.4 9.529 1.268
2009-12-21 516 299.64 287 9.627 1.314
2009-12-22 517 300.86 287.6 9.738 1.364
2009-12-23 518 306.15 288.4 9.925 1.791
2009-12-24 519 309.55 289.4 10.03 2.013
2009-12-28 520 311.75 290.3 10.38 2.07
2009-12-29 521 310.01 291.3 10.22 1.831
2009-12-30 522 311.68 292.4 9.961 1.935
2009-12-31 523 310.30 293.4 9.61 1.755
# 40-period lookback cycles = 484
Figure 1: GOOGL Stockchart; day, 20 period cci
Figure 1: GOOGL Stockchart; day, 20 period cci
Figure 2: GOOGL Stockchart; day, 20 period bf
Figure 2: GOOGL Stockchart; day, 20 period bf
Figure 3: GOOGL Stockchart; day, 40 period cci
Figure 3: GOOGL Stockchart; day, 40 period cci
Figure 4: GOOGL Stockchart; day, 40 period bf
Figure 4: GOOGL Stockchart; day, 40 period bf
Figure 5: YM Future Chart; 30 min, 20 period bf
Figure 5: YM Future Chart; 30 min, 20 period bf
Figure 6: YM Future Chart; 30 min, 40 period bf
Figure 6: YM Future Chart; 30 min, 40 period bf
Figure 7: YM Future Chart; 4096 tick, 20 period bf
Figure 7: YM Future Chart; 4096 tick, 20 period bf
Figure 8: YM Future Chart; 4096 tick, 40 period bf
Figure 8: YM Future Chart; 4096 tick, 40 period bf
