Трендовый или средний возврат с помощью statsmodels.tsa.stattools

Question

Большая часть кода ниже была "собрана" из разных источников. конечная цель состоит в том, чтобы определить цену закрытия акции как означающую возврат или тенденцию на как можно более короткие сроки. надежда состоит в том, что этот вопрос и ответ (ы) могут служить всеобъемлющим взглядом на предмет. к сожалению, вывод меня сбивает с толку / противоречив.

раздел 1: на основе значения p это выглядит как тенденция. исходя из критических значений, это выглядит как возвращение.

Раздел 2: все тренды, за исключением отставания в 50. Почему это означает возврат?

Раздел 3: все тренды. эти р-значения повсюду. как узнать, какой "тип" использовать? Нужно ли анализировать исходные данные, чтобы увидеть тренды? не в этом ли смысл СКАЗАТЬ нам, если это имеет тенденцию?

раздел 4: все тренды, кроме (лаг, автолаг) = (20, т-стат), (30, т-стат), (40, т-стат), (50, AIC). Зачем?

раздел 5: сильно значит возвращаться. все тесты выглядят близко.

Раздел 6: почему существуют множественные значения периода полураспада? какой из них прав?

Благодарю.

вход:

import pandas as pd
import numpy as np
import statsmodels.tsa.stattools as ts # time series library
from statsmodels.tsa.stattools import adfuller
import pandas_datareader.data as wb
import statsmodels.api as sm
from numpy import cumsum, log, polyfit, sqrt, std, subtract
from numpy.random import randn

#............................
df = wb.DataReader('GE','google', '2003, 5, 1', '2003, 12, 15')

print ('\n....... section 1 - adf statistic ......................')
name = pd.Series (df['Close'].values)
result = adfuller (name)

print('close - adf statistic: %f' % result[0] + ', p value: %f' % result[1])

if result[1] > 0.05:
    print ('trending based on p value > 0.05')
else:
    print ('mean reverting based on p value < 0.05')

print('critical values:')

for key, value in result[4].items():
    print('\t%s: %.3f' % (key, value))
    print ('if adf statistic > % test statistic, then trending at that %')

print ('\n..... section 2 - different lag times ...................')

lag_list = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60]

for lag in lag_list:
    name = pd.Series (df['Close'].values)
    result = adfuller (name, maxlag = lag)
    if result[1] > 0.05:
        print ('p-value: %f' % result[1] + ' trending based on lag = ' + str(lag))
    else:
        print ('p-value: %f' % result[1] + ' mean reverting based on lag = ' + str(lag))

print ('\n..... section 3 - different regression types ..........')
regress_list = ['c','ct','ctt','nc']

for regress in regress_list:
    name = pd.Series (df['Close'].values)
    result = adfuller (name, regression = regress)

    if regress == 'c':
        print ('regression for close with ' + regress + ' = constant only, p-value: %f' % result[1])
    if regress == 'ct':
        print ('\nregression for close with ' + regress + ' = constant and trend, p-value: %f' % result[1])
    if regress == 'ctt':
        print ('\nregression for close with ' + regress + ' = constant and linear and quadratic trend, p-value: %f' % result[1])
    if regress == 'nc':
        print ('\nregression for close with ' + regress + ' = no constant, no trend, p-value: %f' % result[1])    

    if result[1] > 0.05:
        print ('trending based on p value > 0.05')
    else:
        print ('mean reverting based on p value < 0.05')

print ('\n......... section 4 - different lag types')

alag_list = ['AIC', 'BIC', 't-stat'] 

for lag in lag_list:
    for alag in alag_list:
        name = pd.Series (df['Close'].values)
        result = adfuller (name, maxlag = lag, autolag = alag)
        print ('\nlag = ' + str(lag) + ', autolag = ' + alag + ', p-value = %f' % result[1])
        if result[1] > 0.05:
            print ('trending based on p value > 0.05')
        else:
            print ('mean reverting based on p value < 0.05')

print ('\n........ section 5 - hurst..........................')
def hurst(ts): # Returns the Hurst Exponent of the time series vector ts
    lags = range(2, 100) # Create the range of lag values

    # Calculate the array of the variances of the lagged differences
    tau = [sqrt(std(subtract(ts[lag:], ts[:-lag]))) for lag in lags]

    poly = polyfit(log(lags), log(tau), 1) # Use a linear fit to estimate the Hurst Exponent
    return poly[0]*2.0 # Return the Hurst exponent from the polyfit output

gbm = log(cumsum(randn(100000))+1000) # geometric brownian motion
mr = log(randn(100000)+1000) # mean reverting
tr = log(cumsum(randn(100000)+1)+1000) # trending

# Output the Hurst Exponent for each of the above series and the price of the ticker's close for the ADF test 
print ("hurst - geometric brownian motion - random walk - should be around 0.50:   %s" % hurst(gbm))
print ("hurst - mean reverting - should be around 0.00):    %s" % hurst(mr))
print ("hurst - trending - should be around 1.00):    %s" % hurst(tr))
print ("hurst:  %s" % hurst(df['Close']))

print ('\n.......  section 6 - half life ..........................')

def get_halflife(s):
    s_lag = s.shift(1)
    s_lag.ix[0] = s_lag.ix[1]

    s_ret = s - s_lag
    s_ret.ix[0] = s_ret.ix[1]

    s_lag2 = sm.add_constant(s_lag)

    model = sm.OLS(s_ret,s_lag2)
    res = model.fit()

    halflife = round(-np.log(2) / res.params[1],0)
    print ('half life = ' + str(halflife))
    return halflife

df.apply(get_halflife)
print ('\nprogram complete')

выход:

.................... section 1 - adf statistic ......................
close - adf statistic: -1.959732, p value: 0.304504
trending based on p value > 0.05
critical values:
    5%: -2.880
if adf statistic > % test statistic, then trending at that %
    10%: -2.577
if adf statistic > % test statistic, then trending at that %
    1%: -3.472
if adf statistic > % test statistic, then trending at that %

.................. section 2 - different lag times ...................
p-value: 0.304504 trending based on lag = 1
p-value: 0.304504 trending based on lag = 2
p-value: 0.304504 trending based on lag = 3
p-value: 0.304504 trending based on lag = 4
p-value: 0.304504 trending based on lag = 5
p-value: 0.304504 trending based on lag = 6
p-value: 0.304504 trending based on lag = 7
p-value: 0.304504 trending based on lag = 8
p-value: 0.304504 trending based on lag = 9
p-value: 0.304504 trending based on lag = 10
p-value: 0.304504 trending based on lag = 20
p-value: 0.304504 trending based on lag = 30
p-value: 0.304504 trending based on lag = 40
p-value: 0.009252 mean reverting based on lag = 50
p-value: 0.304504 trending based on lag = 60

.......... section 3 - different regression types ....................
regression for close with c = constant only, p-value: 0.304504
trending based on p value > 0.05

regression for close with ct = constant and trend, p-value: 0.588526
trending based on p value > 0.05

regression for close with ctt = constant and linear and quadratic trend, p-
value: 0.817117
trending based on p value > 0.05

regression for close with nc = no constant, no trend, p-value: 0.739828
trending based on p value > 0.05

........................ section 4 - different lag types

lag = 1, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 1, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 1, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 2, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 2, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 2, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 3, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 3, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 3, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 4, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 4, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 4, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 5, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 5, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 5, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 6, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 6, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 6, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 7, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 7, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 7, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 8, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 8, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 8, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 9, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 9, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 9, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 10, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 10, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 10, autolag = t-stat, p-value = 0.304504
trending based on p value > 0.05

lag = 20, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 20, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 20, autolag = t-stat, p-value = 0.046194
mean reverting based on p value < 0.05

lag = 30, autolag = AIC, p-value = 0.304504  
trending based on p value > 0.05

lag = 30, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 30, autolag = t-stat, p-value = 0.009252
mean reverting based on p value < 0.05

lag = 40, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 40, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 40, autolag = t-stat, p-value = 0.009252
mean reverting based on p value < 0.05

lag = 50, autolag = AIC, p-value = 0.009252
mean reverting based on p value < 0.05

lag = 50, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 50, autolag = t-stat, p-value = 0.335375
trending based on p value > 0.05

lag = 60, autolag = AIC, p-value = 0.304504
trending based on p value > 0.05

lag = 60, autolag = BIC, p-value = 0.304504
trending based on p value > 0.05

lag = 60, autolag = t-stat, p-value = 0.335375
trending based on p value > 0.05

................ section 5 - hurst..........................
hurst - geometric brownian motion - random walk - should be around 0.50:   0.50270119846
hurst - mean reverting - should be around 0.00):    0.000107190651568
hurst - trending - should be around 1.00):    0.95085392982 
hurst:  0.114851328923

..................  section 6 - half life ..........................
half life = 15.0
half life = 11.0
half life = 10.0
half life = 14.0
half life = 1.0

program complete