Here's an indicator (Haar wavelet with lifting) which, similar to the other wavelet implementations I posted, can essentially break a time series down to constituent frequency components. However because this is implemented via lifting it reduces boundary effects To be more compliant with Daniel R.'s vision, this does not use numpy and all calculations are done internally with no libraries.

This can be used as a crossover indicator for someone who wants an off the shelf solution. For the more advanced user I've also implemented basic thresholding of the wavelet coefficients (threshlist), or you can pick out a wavelet level in isolation (coeffpick).

Further, it also has an incremental flag which although very computationally expensive (an inefficiency that I may refine later on) shows the current bar value without computing from future bars. I don't know that this really makes as much of a difference in practice as an indicator, however.

This is implemented in Python 3.

To call:

examplelwt = bbhaarlift(self.data, coefflev=9, coeffpick = 3, blnincremental = True, threshlist=[1, 1, 1, 1, 0, 0, 0, 0, 0])

Where coeffpick and threshlist are mutually exclusive use one or the other. If both are provided, coeffpick takes precedence. The above picks out the third wavelet level out of nine total.

Because this uses lifting, 2**n bars are needed for calculation. If coefflev isn't provided, the routine uses the next lowest power of 2 bars. Ie. all the bars it can given your input data length.

And here's the code:

```
'''
Author: B. Bradford adapted from information provided by
bearcave.com and Ian Kaplan.
MIT License
Copyright (c) B. Bradford
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
'''
import backtrader as bt
# input lengths must be a power of two for haar with lifting:
class bbhaarlift(bt.Indicator):
plotinfo = dict(subplot=False)
lines = ('haarlift', )
params = (('coefflev', None),
('coeffpick', None),
('blnincremental', False),
('threshlist', [1])) #2**coefflev data points required or 2**coefflev
@staticmethod
def next_power_of_2(x):
return 1 if x == 0 else 2 ** (x.bit_length() -1)
def once(self, start, end):
self.blnforward = 1
self.blninverse = 2
#create dummy line to manipulate and desired 2** data length (max or selected)
lstinputdata = self.data.array[:] #make a copy of the list/array
if self.params.coefflev is None: #max available data length
pow2padding = self.next_power_of_2(len(lstinputdata)) #input needs to be power of two data points
else: #selected 2** from coefflev
pow2padding = 2 ** self.params.coefflev
if self.next_power_of_2(len(lstinputdata)) < pow2padding: raise ValueError("COEFF LEVEL %s GREATER THAN MAX DATA LENGTH %s AVAILABLE" % (self.params.coefflev, self.next_power_of_2(len(lstinputdata))))
if self.params.coefflev is None:
self.params.coefflev = pow2padding.bit_length() - 1
# If specific coeffpick selected set it to one, and others to zero:
if self.params.coeffpick is not None:
self.params.threshlist = [1] * self.params.coeffpick + [0] * (
self.params.coefflev - self.params.coeffpick)
dpcnt = len(lstinputdata) - pow2padding #only do loop once at end of array if blnincremental not true
#Count backwards through line to leave most recent value in place if incremental:
while dpcnt > 0:
dpcnt -= 1 #decrement immediately as list slicing is zero-based
inlist = self.data.array[dpcnt:dpcnt + pow2padding]
ftresult = bbhaarlift.forwardtrans(self, vec=inlist) #forward transform
threshedresult = bbhaarlift.wvltthreshold(coeffary=ftresult, threshlist=self.params.threshlist)
itresult = bbhaarlift.inversetrans(self, vec=threshedresult) #inverse transform
dummyaryout = lstinputdata[:dpcnt] + itresult + lstinputdata[dpcnt + pow2padding:]
lstinputdata = dummyaryout # self.lines[0].array[pow2padding:] + itresult
#Only run once if not doing incremental:
if not self.params.blnincremental: break
self.lines[0].array = lstinputdata
def wvltthreshold(coeffary, threshlist):
print ("bbwaveletlifting: len(coeffary).bit_length()", len(coeffary).bit_length())
if len(coeffary).bit_length() < len(threshlist):
raise ValueError('WARNING: THRESHOLD LIST LENGTH IS SMALLER THAN NUMBER OF COEFF LEVELS.')
threshedresult = coeffary[:]
for i in range(1, len(threshlist)):
for x in range(2**i, 2**(i+1)):
print ("bbwaveletlifting: i, x, len(threshlist) ", i, x, len(threshlist))
threshedresult[x] = coeffary[x] * threshlist[i]
return threshedresult
def split(vec, N):
start = 1
end = N - 1
while (start < end):
#Could do this with list comprehension, but want to stick to the original java structure:
for i in range(start, end, 2):
tmp = vec[i]
vec[i] = vec [i + 1]
vec[i+1] = tmp
start += 1
end -= 1
return vec
def merge(self, vec, N):
half = N >> 1
start = half-1
end = half
while (start > 0):
for i in range(start, end, 2):
tmp = vec[i]
vec[i] = vec[i+1]
vec[i+1] = tmp
start -= 1
end += 1
def forwardtrans(self, vec):
'''
The result of forwardTrans is a set of wavelet coefficients
ordered by increasing frequency and an approximate average
of the input data set in vec[0]. The coefficient bands
follow this element in powers of two (e.g., 1, 2, 4, 8...).
'''
N = len(vec)
print ("forwardtrans N: ", N)
#set for counter:
n = N
print ("forwardtrans n: ", n)
while n > 1:
print ("forwardtrans split...")
vec = bbhaarlift.split(vec, n)
print("forwardtrans predict...")
vec = bbhaarlift.predict (self, vec, n, self.blnforward)
print("update split...")
vec = bbhaarlift.update (self, vec, n, self.blnforward)
n = n >> 1
return vec
def inversetrans(self, vec):
N = len(vec)
n = 2
while n <= N:
bbhaarlift.update(self, vec, n, self.blninverse)
bbhaarlift.predict (self, vec, n, self.blninverse)
bbhaarlift.merge(self, vec, n)
n = n << 1
return vec
def predict(self, vec, N, direction):
half = N >> 1
cnt = 0
for i in range (0, half, 1):
predictval = float(vec[i])
j = int(i+half)
if (direction == self.blnforward):
vec[j] = vec[j] - predictval
elif (direction == self.blninverse):
vec[j] = vec[j] + predictval
else:
debug.print("haar: predict: bad direction value")
return vec
def update(self, vec, N, direction):
half = N >> 1
for i in range (0, half, 1):
j = int(i + half)
updateVal = float(vec[j] / 2.0)
if (direction == self.blnforward):
vec[i] = vec[i] + updateVal
elif (direction == self.blninverse):
vec[i] = vec[i] - updateVal
else:
debug.print("haar update: bad direction value")
return vec
```