This exercise notebook refers to this lecture. Please use the lecture for explanations and sample code.
https://www.quantopian.com/lectures#Instability-of-Estimates
Part of the Quantopian Lecture Series:
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from statsmodels.stats.stattools import jarque_bera
# Set a seed so we can play with the data without generating new random numbers every time
Using the below normal distribution with mean 100 and standard deviation 50, find the means and standard deviations of samples of size 5, 25, 100, and 500.
POPULATION_MU = 100
POPULATION_SIGMA = 25
sample_sizes = [5, 25, 100, 500]
#Your code goes here
X = [ 31., 6., 21., 32., 41., 4., 48., 38., 43., 36., 50., 20., 46., 33., 8., 27., 17., 44., 16., 39., 3., 37.,
35., 13., 49., 2., 18., 42., 22., 25., 15., 24., 11., 19., 5., 40., 12., 10., 1., 45., 26., 29., 7., 30.,
14., 23., 28., 0., 34., 9., 47.]
Y = [ 15., 41., 33., 29., 3., 28., 28., 8., 15., 22., 39., 38., 22., 10., 39., 40., 24., 15., 21., 25., 17., 33.,
40., 32., 42., 5., 39., 8., 15., 25., 37., 33., 14., 25., 1., 31., 45., 5., 6., 19., 13., 39., 18., 49.,
13., 38., 8., 25., 32., 40., 17.]
Z = [ 38., 23., 16., 35., 48., 18., 48., 38., 24., 27., 24., 35., 37., 28., 11., 12., 31., -1., 9., 19., 20., 0.,
23., 33., 34., 24., 14., 28., 12., 25., 53., 19., 42., 21., 15., 36., 47., 20., 26., 41., 33., 50., 26., 22.,
-1., 35., 10., 25., 23., 24., 6.]
#Your code goes here
Use the jarque_bera function to conduct a Jarque-Bera test on $X$, $Y$, and $Z$ to determine whether their distributions are normal.
#Your code goes here
Create a histogram of the sample distributions of $X$, $Y$, and $Z$ along with the best estimate/mean based on the sample.
#Your code goes here
Just as in the lecture, find the mean and standard deviation of the running sharpe ratio for THO, this time testing for multiple window lengths: 300, 150, and 50. Restrict your mean and standard deviation calculation to pricing data up to 200 days away from the end.
def sharpe_ratio(asset, riskfree):
return np.mean(asset - riskfree)/np.std(asset - riskfree)
start = '2010-01-01'
end = '2015-01-01'
treasury_ret = get_pricing('BIL', fields='price', start_date=start, end_date=end).pct_change()[1:]
pricing = get_pricing('THO', fields='price', start_date=start, end_date=end)
returns = pricing.pct_change()[1:]
#Your code goes here
Plot the running sharpe ratio of all three window lengths, as well as their in-sample mean and standard deviation bars.
#Your code goes here
b15_df = pd.DataFrame([ 29., 22., 19., 17., 19., 19., 15., 16., 18., 25., 21.,
25., 29., 27., 36., 38., 40., 44., 49., 50., 58., 61.,
67., 69., 74., 72., 76., 81., 81., 80., 83., 82., 80.,
79., 79., 80., 74., 72., 68., 68., 65., 61., 57., 50.,
46., 42., 41., 35., 30., 27., 28., 28.],
columns = ['Weekly Avg Temp'],
index = pd.date_range('1/1/2012', periods=52, freq='W') )
#Your code goes here
Find the mean and standard deviation of Palo Alto weekly average temperature data for the year of 2015 stored in p15_df.
p15_df = pd.DataFrame([ 49., 53., 51., 47., 50., 46., 49., 51., 49., 45., 52.,
54., 54., 55., 55., 57., 56., 56., 57., 63., 63., 65.,
65., 69., 67., 70., 67., 67., 68., 68., 70., 72., 72.,
70., 72., 70., 66., 66., 68., 68., 65., 66., 62., 61.,
63., 57., 55., 55., 55., 55., 55., 48.],
columns = ['Weekly Avg Temp'],
index = pd.date_range('1/1/2012', periods=52, freq='W'))
#Your code goes here
Use the means you found in parts a and b to attempt to predict 2016 temperature data for both cities. Do this by creating two histograms for the 2016 temperature data in b16_df and p16_df with a vertical line where the 2015 means were to represent your prediction.
b16_df = pd.DataFrame([ 26., 22., 20., 19., 18., 19., 17., 17., 19., 20., 23., 22., 28., 28., 35., 38., 42., 47., 49., 56., 59., 61.,
61., 70., 73., 73., 73., 77., 78., 82., 80., 80., 81., 78., 82., 78., 76., 71., 69., 66., 60., 63., 56., 50.,
44., 43., 34., 33., 31., 28., 27., 20.],
columns = ['Weekly Avg Temp'],
index = pd.date_range('1/1/2012', periods=52, freq='W'))
p16_df = pd.DataFrame([ 50., 50., 51., 48., 48., 49., 50., 45., 52., 50., 51., 52., 50., 56., 58., 55., 61., 56., 61., 62., 62., 64.,
64., 69., 71., 66., 69., 70., 68., 71., 70., 69., 72., 71., 66., 69., 70., 70., 66., 67., 64., 64., 65., 61.,
61., 59., 56., 53., 55., 52., 52., 51.],
columns = ['Weekly Avg Temp'],
index = pd.date_range('1/1/2012', periods=52, freq='W'))
#Your code goes here
Congratulations on completing the instability of parameter estimates exercises!
As you learn more about writing trading models and the Quantopian platform, enter a daily Quantopian Contest. Your strategy will be evaluated for a cash prize every day.
Start by going through the Writing a Contest Algorithm tutorial.
This presentation is for informational purposes only and does not constitute an offer to sell, a solic itation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. ("Quantopian"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.