CoCalc -- EQUITY MEAN REVERSION 2018-08-29-093828.ipynb

MEAN REVERSION HURST

Path: EQUITY MEAN REVERSION 2018-08-29-093828.ipynb

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Kernel: SageMath (stable)

Testing Mean Reversion Code

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from datetime import datetime

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from pandas_datareader import data

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import pandas as pd

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import numpy as np

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from numpy import log, polyfit, sqrt, std, subtract

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import statsmodels.tsa.stattools as ts

/ext/anaconda3/lib/python3.5/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.
  from pandas.core import datetools

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import statsmodels.api as sm

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import matplotlib.pyplot as plt

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import seaborn as sns

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import pprint

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symbList = ['GOOG','FB']

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start_date = '2008/01/01'

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end_date = '2018/01/01'

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# Fetching data and initializing the IV column
#here's the way to add a new column: Initialize it, ha!

dataAll = pd.read_csv("CompaniesSP.csv")
#create a new column and give value 0, just to do something new in the data file
dataAll['IV'] = 0

#take the first8 columns of the file, iterating name range
data=dataAll.loc[:, 'Date':'SBUX']

data.head()

	Date	SPX	AAPL	MSFT	GOOG	AMZN	FB	SBUX
0	2000-08-31	1517.680054	2.935255	25.539095	NaN	41.5000	NaN	3.735864
1	2000-09-01	1520.770020	3.055676	25.676279	NaN	41.5000	NaN	3.844242
2	2000-09-05	1507.079956	3.007508	25.653412	NaN	45.6875	NaN	3.837867
3	2000-09-06	1492.250000	2.814835	25.401903	NaN	45.8750	NaN	3.767739
4	2000-09-07	1502.510010	2.986434	25.630543	NaN	43.5000	NaN	3.837867

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tickers =  ['AAPL', 'MSFT']

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from pandas import read_csv
series = read_csv('CompaniesSP.csv', header=0, parse_dates=[0], index_col=0, squeeze=True)
print(type(series))
series.describe()

<class 'pandas.core.frame.DataFrame'>

	SPX	AAPL	MSFT	GOOG	AMZN	FB	SBUX	SPX_ret	AAPL_ret	MSFT_ret	...	AMZN_ret_HV21_vol_prem	FB_ret_HV21_vol_prem	SBUX_ret_HV21_vol_prem	SPX_ret_Vcorr	AAPL_ret_Vcorr	MSFT_ret_Vcorr	GOOG_ret_Vcorr	AMZN_ret_Vcorr	FB_ret_Vcorr	SBUX_ret_Vcorr
count	4442.000000	4442.000000	4442.000000	3448.000000	4442.000000	1496.000000	4442.000000	4441.000000	4441.000000	4441.000000	...	3723.000000	1136.000000	3723.000000	4.190000e+03	4190.000000	4190.000000	3196.000000	4190.000000	1244.000000	4190.000000
mean	1458.840833	41.359003	29.691175	406.808014	239.160950	90.675635	20.903147	0.000198	0.001241	0.000466	...	21.959204	19.149914	11.369873	1.000000e+00	0.535958	0.647527	0.573460	0.499291	0.473103	0.574429
std	466.505382	48.123965	16.563054	256.515001	309.531626	49.050331	18.269219	0.012050	0.025153	0.018710	...	9.674753	10.134565	7.060319	1.295721e-14	0.129706	0.121225	0.129951	0.092332	0.149839	0.106975
min	676.530029	0.631968	12.002091	49.681866	5.970000	17.730000	2.856087	-0.090350	-0.518691	-0.118155	...	4.831570	4.221414	-0.477096	1.000000e+00	0.193932	0.364624	0.086375	0.298710	0.082368	0.234126
25%	1131.440033	3.426210	20.062912	229.441452	38.905001	49.689999	6.667941	-0.004764	-0.010371	-0.008068	...	14.349202	11.526887	6.827820	1.000000e+00	0.434108	0.577042	0.505172	0.426852	0.442305	0.500515
50%	1309.825012	17.599251	22.606724	298.446395	89.005001	81.975003	12.474978	0.000538	0.000765	0.000117	...	21.428194	16.117665	9.167523	1.000000e+00	0.546415	0.665509	0.589889	0.487428	0.523660	0.571625
75%	1782.164978	66.533138	32.544173	555.451157	306.270004	125.405000	33.679004	0.005616	0.012922	0.008630	...	27.531779	32.496460	14.903605	1.000000e+00	0.651333	0.748857	0.659155	0.555657	0.564986	0.648543
max	2872.870117	181.021957	96.352371	1175.839966	1598.390015	193.089996	63.265320	0.115800	0.139050	0.195652	...	45.250383	38.788546	33.339979	1.000000e+00	0.750971	0.819369	0.825443	0.761214	0.673141	0.786925

8 rows × 35 columns

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# This line is necessary for the plot to appear in a Jupyter notebook (you don't need it if you're working in Rodeo)
%matplotlib inline
# Control the default size of figures in this Jupyter notebook (n/a if working in Rodeo)
%pylab inline
pylab.rcParams['figure.figsize'] = (15, 9)   # Change the size of plots

# Plot the adjusted closing price of AAPL
series.loc[:, 'AAPL':'SBUX'].plot(grid = True)

Populating the interactive namespace from numpy and matplotlib

/ext/anaconda3/lib/python3.5/site-packages/IPython/core/magics/pylab.py:160: UserWarning: pylab import has clobbered these variables: ['datetime']
`%matplotlib` prevents importing * from pylab and numpy
  "\n`%matplotlib` prevents importing * from pylab and numpy"

<matplotlib.axes._subplots.AxesSubplot at 0x7fb0b21b54e0>

WARNING: Some output was deleted.

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series.loc[:, 'AAPL'].plot(grid = True)

<matplotlib.axes._subplots.AxesSubplot at 0x7fb0b1de2320>

WARNING: Some output was deleted.

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#create changes and add the corresponding new columns
series['GOOG_Ret'] = series['GOOG'].pct_change().dropna()
series['SPX_Ret'] = series['SPX'].pct_change().dropna()
series['AAPL_Ret'] = series['AAPL'].pct_change().dropna()

#rolling correlation of google and sp500 of returns yearly (250 days)
series['GOOG_Ret'].rolling(252).corr(series['SPX_Ret']).plot(figsize=(15,4))

<matplotlib.axes._subplots.AxesSubplot at 0x7fb0b1ff3470>

WARNING: Some output was deleted.

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#create the historical 30day vol
series['SPX_HV21'] = series['SPX_Ret'].rolling(21).std() * np.sqrt(252) * 100
series['GOOG_HV21'] = series['GOOG_Ret'].rolling(21).std() * np.sqrt(252) * 100
series['AAPL_HV21'] = series['AAPL_Ret'].rolling(21).std() * np.sqrt(252) * 100

series[['GOOG_HV21','AAPL_HV21','SPX_HV21']].plot(figsize=(15,8), grid= True)

<matplotlib.axes._subplots.AxesSubplot at 0x7fb0b1f56908>

WARNING: Some output was deleted.

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AAPL_TS=series['AAPL_Ret']

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def hurst(AAPL_TS):
    # Create the range of lag values
    lags= range (2,100)
     # Calculate the array of variances of the lagged differences
    tau=[sqrt(std(subtract(AAPL_TS[lag:], AAPL_TS[-lag]))) for lag in lags]
     # Use a linear fit to estimate the hurst exponent
    poly = polyfit(log(lags), log(tau), 1)
     # Return the hurst exponent from the polyfit output
    return poly[0]*2.0

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hurst(AAPL_TS)

-0.029860508371503839

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series.loc[:, 'AAPL_Ret'].plot(grid = True)

<matplotlib.axes._subplots.AxesSubplot at 0x7fb0b1df9278>

WARNING: Some output was deleted.

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AAPL_Price=series['AAPL']

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def hurst(AAPL_Price):
    # Create the range of lag values
    lags= range (2,100)
     # Calculate the array of variances of the lagged differences
    tau=[sqrt(std(subtract(AAPL_Price[lag:], AAPL_Price[-lag]))) for lag in lags]
     # Use a linear fit to estimate the hurst exponent
    poly = polyfit(log(lags), log(tau), 1)
     # Return the hurst exponent from the polyfit output
    return poly[0]*2.0

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hurst(AAPL_Price)

0.0010023252339726358

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AAPL_Price2=series['2000-08-31':'2008-08-31']['AAPL']

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AAPL_Price2.head()

Date
2000-08-31    2.935255
2000-09-01    3.055676
2000-09-05    3.007508
2000-09-06    2.814835
2000-09-07    2.986434
Name: AAPL, dtype: float64

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AAPL_Price2.tail()

Date
2008-08-25    16.622875
2008-08-26    16.727882
2008-08-27    16.827114
2008-08-28    16.737513
2008-08-29    16.331944
Name: AAPL, dtype: float64

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hurst(AAPL_Price2)

0.00350593165566435

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AAPL_Price3=series['2008-08-31':'2018-04-30']['AAPL']

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hurst(AAPL_Price3)

-0.0052954428489820054

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AAPL_Price3=series['2008-08-31':'2018-04-30']['AAPL'].plot()

WARNING: Some output was deleted.

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AAPL_Price16=series['2008-08-31':'2016-04-30']['AAPL']

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hurst(AAPL_Price16)

-0.0067036462086532758

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