3. linear regression and std #211
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linear regression and std #211

  • B
    administrators

    From Issue #211

    Hi,

    Could you include in the next release both linear regression and standard deviation? I think these indicators help people to calculate ratios over the time series.

    S1= timeseries close
S2= timeseries close
rolling_beta = pd.ols(y=S1, x=S2, window_type='rolling', window=30)
spread = S2 - rolling_beta.beta['x'] * S1
std_30 = pd.Series.rolling(spread,window=30,center=False).std()

    Rgds,
    JJ

    0
  • B
    administrators

    Standard Deviation is already included (since many versions ago)

    1
  • J

    ok, thanks, i will wait up Standard Deviation. Congrats on the community!!!!

    1
  • B
    administrators

    There seem to be several linear regressions, including channels, slopes ...

    1
  • J

    This code could be adapted to use two timeseries backtrader:
    https://github.com/vikasrtr/pyLinearRegression/blob/master/models/LinearRegression.py
    https://github.com/vikasrtr/pyLinearRegression/blob/master/models/LinearRegressionGradientDescent.py

    1
  • J
     

    def linreg(X, Y):
    """

        Linear regression  y = ax + b

    """
    if len(X) != len(Y):  raise ValueError, 'unequal length'
    N = len(X)
    Sx = Sy = Sxx = Syy = Sxy = 0.0
    for x, y in map(None, X, Y):
        Sx = Sx + x
        Sy = Sy + y
        Sxx = Sxx + x*x
        Syy = Syy + y*y
        Sxy = Sxy + x*y
    det = Sxx * N - Sx * Sx
    a, b = (Sxy * N - Sy * Sx)/det, (Sxx * Sy - Sx * Sxy)/det
    meanerror = residual = 0.0
    for x, y in map(None, X, Y):
        meanerror = meanerror + (y - Sy/N)**2
        residual = residual + (y - a * x - b)**2
    RR = 1 - residual/meanerror
    ss = residual / (N-2)
    Var_a, Var_b = ss * N / det, ss * Sxx / det
    return a, b, RR
    1
  • J

    My idea is to use linear regression to test these posts:

    https://www.quantopian.com/posts/how-to-build-a-pairs-trading-strategy-on-quantopian

    https://www.quantstart.com/articles/Backtesting-An-Intraday-Mean-Reversion-Pairs-Strategy-Between-SPY-And-IWM

    https://www.quantinsti.com/blog/pair-trading-strategy-backtesting-using-quantstrat/

    1
  • J
     

    if X and Y are cointegrated:

calculate Beta between X and Y 

calculate spread as X - Beta * Y

calculate z-score of spread

# entering trade (spread is away from mean by two sigmas):
if z-score > 2:
    sell spread (sell 1000 of X, buy 1000 * Beta of Y)
if z-score < -2:
    buy spread (buy 1000 of X, sell 1000 * Beta of Y)

# exiting trade (spread converged close to mean):
if we're short spread and z-score < 1:
    close the trades
if we're long spread and z-score > -1:
    close the trades

loop: repeat above on each new bar, recalculating rolling Beta and spread etc.
    1
    R
     1 Reply
  • R

    hi guys,

    I am interested in that as well :D

    Remroc

    0
  • B
    administrators

    It seems that the beta is the important part here

    import pandas as pd
import backtrader as bt

class OLS_Beta(bt.indicators.PeriodN):
    _mindatas = 2  # ensure at least 2 data feeds are passed
    lines = (('beta'),)
    params = (('period', 30),)

    def next(self):
        y, x = (d.get(size=self.p.period) for d in (self.data0, self.data1))
        r_beta = pd.ols(y=y, x=x, window_type='rolling', window=self.p.period)
        self.lines.beta[0] = r_beta.beta['x']

    or the spread directly

    import pandas as pd
import backtrader as bt

class Spread(bt.indicators.PeriodN):
    _mindatas = 2  # ensure at least 2 data feeds are passed
    lines = (('spread'),)
    params = (('period', 30),)

    def next(self):
        y, x = (d.get(size=self.p.period) for d in (self.data0, self.data1))
        r_beta = pd.ols(y=y, x=x, window_type='rolling', window=self.p.period)
        self.lines.spread[0] = self.data1[0] - r_beta.beta['x'] * self.data0[0]

    Is this in line?

    1
  • J

    Yes, I think these classes are covering our requeriments

    0
  • R

    Awesome. I ll give it a try tonight...
    U rock as usual, thanks Dro :astonished:

    0
  • R

    Hello DRo,

    I was not able to run your proposition. I am receiving :

    TypeError: 'builtin_function_or_method' object is not iterable

    And, it seems pd.ols will be deprecated. I have tried with statsmodel.api :
    http://statsmodels.sourceforge.net/stable/examples/notebooks/generated/ols.html

    import statsmodels.api as sm


class OLS_Transformation(btind.PeriodN):
    _mindatas = 2  # ensure at least 2 data feeds are passed
    lines = (('slope'),('intercept'),('spread'),('spread_mean'),('spread_std'),('zscore'),)
    params = (('period', 10),)

    def next(self):
        #y, x = (d.get(size=self.p.period) for d in (self.data0, self.data1))
        p0 =  self.data0.get(size=self.p.period)
        p1 =  sm.add_constant(self.data1.get(size=self.p.period),prepend=True)
        slope, intercept = sm.OLS(p0,p1).fit().params
        #r_beta = pd.ols(y=p1, x=x, window_type='rolling', window=self.params.period)
        self.lines.slope[0] = slope
        self.lines.intercept[0] = intercept
        self.lines.spread[0] = self.data0.close[0] - (slope * self.data1.close[0] + intercept)
        self.lines.spread_mean[0] = btind.MovAv.SMA(self.lines.spread, period=self.p.period)
        self.lines.spread_std[0] = btind.StandardDeviation(self.lines.spread, period=self.p.period)
        self.lines.zscore[0] = (self.lines.spread[0] - self.lines.spread_mean[0])/self.lines.spread_std[0]

    Do you have any recommandations for this path ?

    Many thanks...

    remroc

    0
  • B
    administrators

    Those were typed snippets no actual tested code. The actual line which produced the error would be helpful in understanding what part of the snippet is trying to iterate a builtin_function_or_method

    0
  • R

    Hello DRo,

    Below is the received error by using the snippet.

    For info, in code I am using only Class OLS_Beta and have initiated a self.beta signal in the Strategy's init through :

             self.beta = OLS_Beta(self.data0, self.data1)

    The window parameter of pd.ols is window and not windows...

    Many thanks for your insights :D

    C:\Dev\Anaconda2\python.exe C:/Trading/backtrader-master-1.9.8.99-David/samples/pair-trading/pair-trading.py
C:/Trading/backtrader-master-1.9.8.99-David/samples/pair-trading/pair-trading.py:48: FutureWarning: The pandas.stats.ols module is deprecated and will be removed in a future version. We refer to external packages like statsmodels, see some examples here: http://statsmodels.sourceforge.net/stable/regression.html
  r_beta = pd.ols(y=y, x=x, window_type='rolling', window=self.p.period)
Traceback (most recent call last):
  File "C:/Trading/backtrader-master-1.9.8.99-David/samples/pair-trading/pair-trading.py", line 329, in <module>
    runstrategy()
  File "C:/Trading/backtrader-master-1.9.8.99-David/samples/pair-trading/pair-trading.py", line 272, in runstrategy
    oldsync=args.oldsync)
  File "C:\Dev\Anaconda2\lib\site-packages\backtrader\cerebro.py", line 809, in run
    runstrat = self.runstrategies(iterstrat)
  File "C:\Dev\Anaconda2\lib\site-packages\backtrader\cerebro.py", line 926, in runstrategies
    self._runonce(runstrats)
  File "C:\Dev\Anaconda2\lib\site-packages\backtrader\cerebro.py", line 1245, in _runonce
    strat._once()
  File "C:\Dev\Anaconda2\lib\site-packages\backtrader\lineiterator.py", line 274, in _once
    indicator._once()
  File "C:\Dev\Anaconda2\lib\site-packages\backtrader\lineiterator.py", line 294, in _once
    self.oncestart(self._minperiod - 1, self._minperiod)
  File "C:\Dev\Anaconda2\lib\site-packages\backtrader\indicator.py", line 124, in oncestart_via_nextstart
    self.nextstart()
  File "C:\Dev\Anaconda2\lib\site-packages\backtrader\lineiterator.py", line 324, in nextstart
    self.next()
  File "C:/Trading/backtrader-master-1.9.8.99-David/samples/pair-trading/pair-trading.py", line 48, in next
    r_beta = pd.ols(y=y, x=x, window_type='rolling', window=self.p.period)
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\stats\interface.py", line 143, in ols
    return klass(**kwargs)
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\stats\ols.py", line 642, in __init__
    OLS.__init__(self, y=y, x=x, weights=weights, **self._args)
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\stats\ols.py", line 70, in __init__
    self._index, self._time_has_obs) = self._prepare_data()
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\stats\ols.py", line 102, in _prepare_data
    self._weights_orig)
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\stats\ols.py", line 1298, in _filter_data
    lhs = Series(lhs, index=rhs.index)
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\core\series.py", line 137, in __init__
    index = _ensure_index(index)
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\indexes\base.py", line 3409, in _ensure_index
    return Index(index_like)
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\indexes\base.py", line 287, in __new__
    subarr = com._asarray_tuplesafe(data, dtype=object)
  File "C:\Dev\Anaconda2\lib\site-packages\pandas\core\common.py", line 1384, in _asarray_tuplesafe
    values = list(values)
TypeError: 'builtin_function_or_method' object is not iterable

Process finished with exit code 1
    0
  • B
    administrators

    The problem with the snippet being that pd.ols chokes on regular Python array-like structures (array.array, list, etc) needing pandas specific structures.

    The adapted and working code

    class OLS_Beta(bt.indicators.PeriodN):
    _mindatas = 2  # ensure at least 2 data feeds are passed
    lines = (('beta'),)
    params = (('period', 30),)

    def next(self):
        y, x = (pd.Series(d.get(size=self.p.period)) for d in self.datas)
        r_beta = pd.ols(y=y, x=x, window_type='full_sample')
        self.lines.beta[0] = r_beta.beta['x']

    In which the values from the dataX feeds is put into a pd.Series instance. There is, imho, no need to use a rolling operation because pd.ols only receives the needed data each time (the latest available data).

    The same concept can be applied other pandas operations and I guess to the code ported over to statsmodel

    1
    R
     1 Reply
  • R

    @backtrader thanks DRo !

    I will try this tomorrow...

    0
  • R

    Hello DRo,

    Thanks, it is working. Pair Trading is operational...

    I have implemented the statsmodel as well and seems to retrieve the same beta and spread...

    Quick question, how to :

    • show 2 data.lines in the same subplot (ie PEP and KO in the same subplot) ?
    • increase the height of the indicator's subplot ?
    • plot only 1 line of a multi-lines indicator in a dedicated subplot ?

    Many thanks,

    RemRoc

    0
  • B
    administrators

    Plotting options are detailed here: https://www.backtrader.com/docu/plotting/plotting.html

    0
    R
     1 Reply
  • R

    @backtrader thanks,

    Is it possible to contribute to backtrader by sharing the pair trading strategy as a sample of the distribution ?

    If yes, please let me know how to do it ?

    Thanks

    Remroc

    0
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