Time for action – drawing trend lines

Perform the following steps to draw trend lines:

  1. First, we need to determine the pivot points. We shall pretend they are equal to the arithmetic mean of the high, low, and close price.
    h, l, c = np.loadtxt('data.csv', delimiter=',', usecols=(4, 5, 6), unpack=True)

pivots = (h + l + c) / 3
print "Pivots", pivots

    From the pivots, we can deduce the so-called resistance and support levels. The support level is the lowest level at which the price rebounds. The resistance level is the highest level at which the price bounces back. These are not natural phenomena; mind you, they are merely estimates. Based on these estimates, it is possible to draw support and resistance trend lines. We will define the daily spread to be the difference between the high and low price.

  2. Define a function to fit line to data to a line where y = at + b. The function should return a and b. This is another opportunity to apply the lstsq function of the NumPy linalg package. Rewrite the line equation to y = Ax, where A = [t 1] and x = [a b]. Form A with the NumPy ones and vstack functions.
    def fit_line(t, y):
    A = np.vstack([t, np.ones_like(t)])]).T
    return np.linalg.lstsq(A, y)[0]
  3. Assuming that support levels are one daily spread below the pivots, and that resistance levels are one daily spread above the pivots, fit the support and resistance trend lines.
    t = np.arange(len(c))
sa, sb = fit_line(t, pivots - (h - l)) 
ra, rb = fit_line(t, pivots + (h - l))
support = sa * t + sb
resistance = ra * t + rb
  4. At this juncture, we have all the necessary information to draw the trend lines, however, it is wise to check how many points fall between the support and resistance levels. Obviously, if only a small percentage of the data is between the trend lines, this setup is of no use to us. Make up a condition for points between the bands and select the where function based on that condition.
    condition = (c > support) & (c < resistance)
print "Condition", condition
between_bands = np.where(condition)

    The following are the condition values:

    Condition [False False  True  True  True  True  True False False  True False False
 False False False  True False False False  True  True  True  True False False  True  True  True False  True]

    Double-check the values:

    print support[between_bands]
print c[between_bands]
print resistance[between_bands]

    The array returned by the where function has rank 2, so call the ravel function before calling the len function.

    between_bands = len(np.ravel(between_bands))
print "Number points between bands", between_bands
print "Ratio between bands", float(between_bands)/len(c)

    You will get the following result:

    Number points between bands 15
Ratio between bands 0.5

    As an extra bonus, we gained a predictive model. Extrapolate the next day resistance and support levels.

    print "Tomorrows support", sa * (t[-1] + 1) + sb
print "Tomorrows resistance", ra * (t[-1] + 1) + rb

    This results in the following:

    Tomorrows support 349.389157088
Tomorrows resistance 360.749340996

    Another approach to figure out how many points are between the support and resistance estimates is to use [] and intersect1d. Define selection criteria in the [] operator and intersect the results with the intersect1d function.

    a1 = c[c > support]
a2 = c[c < resistance]
print "Number of points between bands 2nd approach" ,len(np.intersect1d(a1, a2))

    Not surprisingly, we get the following:

    Number of points between bands 2nd approach 15
  5. Once more, we will plot the results, as follows:
    plot(t, c)
plot(t, support)
plot(t, resistance)
show()

    We will get the following plot in which we have the price data and the corresponding support and resistance lines:

    Time for action – drawing trend lines

What just happened?

We drew trend lines without having to mess around with rulers, pencils, and paper charts. We defined a function that can fit data to a line with the NumPy vstack, ones, and lstsq functions. We fit the data in order to define support and resistance trend lines. Then we figured out how many points are within the support and resistance range. We did this using two separate methods that produced the same result.

The first method used the where function with a Boolean condition. The second method made use of the [] operator and the intersect1d function. The intersect1d function returns an array of common elements from two arrays (see trendline.py).

import numpy as np
from matplotlib.pyplot import plot
from matplotlib.pyplot import show

def fit_line(t, y):
    A = np.vstack([t, np.ones_like(t)]).T

    return np.linalg.lstsq(A, y)[0]

h, l, c = np.loadtxt('data.csv', delimiter=',', usecols=(4, 5, 6), unpack=True)

pivots = (h + l + c) / 3
print "Pivots", pivots

t = np.arange(len(c))
sa, sb = fit_line(t, pivots - (h - l)) 
ra, rb = fit_line(t, pivots + (h - l))

support = sa * t + sb
resistance = ra * t + rb 
condition = (c > support) & (c < resistance)
print "Condition", condition
between_bands = np.where(condition) 
print support[between_bands]
print c[between_bands]
print resistance[between_bands]
between_bands = len(np.ravel(between_bands))
print "Number points between bands", between_bands
print "Ratio between bands", float(between_bands)/len(c) 

print "Tomorrows support", sa * (t[-1] + 1) + sb
print "Tomorrows resistance", ra * (t[-1] + 1) + rb

a1 = c[c > support]
a2 = c[c < resistance]
print "Number of points between bands 2nd approach" ,len(np.intersect1d(a1, a2))

plot(t, c)
plot(t, support)
plot(t, resistance)
show()
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