Class: Array

Inherits:
Object
  • Object
show all
Defined in:
lib/moving_average/moving_average.rb

Instance Method Summary collapse

Instance Method Details

#exponential_moving_average(idx = nil, tail = nil) ⇒ Object Also known as: ema

Compute the exponential moving average (EMA) of the values of an Array.

Formally, the EMA can be computed as n / d, where

n = p_1 + (1 - alpha)p_2 + (1 - alpha)^2p_3 + ... + (1 - alpha)^zp_(z + 1)

and

d = 1 + (1 - alpha) + (1 - alpha)^2 + (1 - alpha)^3 + ... + (1 - alpha)^z

where

alpha = 2 / (z + 1)

Formula taken from en.wikipedia.org/wiki/Moving_average#Exponential_moving_average

Parameters

  • idx - Optional, the index of the last datum to consider.

  • tail - Optional, the number of data to consider.



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# File 'lib/moving_average/moving_average.rb', line 47

def exponential_moving_average(idx=nil, tail=nil)
  idx, tail = idx_and_tail_or_defaults(idx, tail)
  valid_for_ma(idx, tail)
  alpha = 2.0 / (tail + 1)
  n = (1..tail).to_a.map{|tidx| (1 - alpha) ** (tidx - 1) * self[idx - tidx + 1]}.sum
  d = (1..tail).to_a.map{|tidx| (1 - alpha) ** (tidx - 1)}.sum
  n / d
end

#simple_moving_average(idx = nil, tail = nil) ⇒ Object Also known as: sma

Compute the simple moving average (SMA) of the values of an Array.

Parameters

  • idx - Optional, the index of the last datum to consider.

  • tail - Optional, the number of data to consider.



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# File 'lib/moving_average/moving_average.rb', line 63

def simple_moving_average(idx=nil, tail=nil)
  idx, tail = idx_and_tail_or_defaults(idx, tail)
  valid_for_ma(idx, tail)
  self[idx-tail+1..idx].sum.to_f / tail
end

#smoothed_moving_average(idx = nil, tail = nil) ⇒ Object Also known as: smma

Compute the smoothed moving average of the values of an Array.

Formally, given that the first value for the SMMA is the SMA, subsequent values can be computed as

(sma – smma_i-1 + a[i])
-----------------------
          n

where

smma_i-1

is the smoothed moving average of the previous index.

Formula taken from mahifx.com/indicators/smoothed-moving-average-smma

Parameters

  • idx - Optional, the index of the last datum to consider.

  • tail - Optional, the number of data to consider.



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# File 'lib/moving_average/moving_average.rb', line 92

def smoothed_moving_average(idx=nil, tail=nil)
  # Set these manually here since we need the leading SMA.
  if tail.nil?
    idx = self.size - 1 if idx.nil?
    tail = idx / 2
    tail += 1 if idx.odd?
  end
  idx, tail = idx_and_tail_or_defaults(idx, tail)
  valid_for_ma(idx, tail)
  valid_for_ma(idx - tail, tail)
  smma1 = self[idx - 2 * tail + 1..idx - tail].sma
  (idx - tail + 1..idx).to_a.each do |tidx|
    prevsum = self[tidx - tail + 1..tidx].sum
    smma1 = (prevsum - smma1 + self[idx - (idx - tidx)]) / tail
  end
  smma1
end

#sum ⇒ Object

Compute the sum of the values of an Array.



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# File 'lib/moving_average/moving_average.rb', line 143

def sum
  inject(0){|s, n| s += n}
end

#weighted_moving_average(idx = nil, tail = nil) ⇒ Object Also known as: wma

Compute the weighted moving average of the values of an Array.

Formally, the WMA can be computed as n / d, where

n = zp_M + (z - 1)p_(M - 1) + (z - 2)p_(M - 3) + ...

and

d = z + (z - 1) + (z - 2) + ...

The denominator is a triangle number of the form

z(z + 1) / 2

Formula taken from en.wikipedia.org/wiki/Moving_average#Weighted_moving_average

Parameters

  • idx - Optional, the index of the last datum to consider.

  • tail - Optional, the number of data to consider.



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# File 'lib/moving_average/moving_average.rb', line 132

def weighted_moving_average(idx=nil, tail=nil)
  idx, tail = idx_and_tail_or_defaults(idx, tail)
  valid_for_ma(idx, tail)
  n = (0..tail-1).to_a.map{|tidx| (tail - tidx) * self[idx - tidx]}.sum
  d = (tail * (tail + 1)) / 2.0
  n / d
end