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
np.random.seed(123)

POPULATION_MU = 100
POPULATION_SIGMA = 25
sample_sizes = [5, 25, 100, 500]

#Your code goes here

for i in range(len(sample_sizes)):
    sample = np.random.normal(POPULATION_MU, POPULATION_SIGMA, sample_sizes[i])
    print 'Mean', (i+1),':', np.mean(sample),'Std',(i+1),':',np.std(sample)

print "\nAs sample size increases, the mean and standard deviation approach those of the population. However, even at the 500 sample level the sample mean is not the same as the population mean."

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

print "Mean X:", np.mean(X)
print "Mean Y:", np.mean(Y)
print "Mean Z:", np.mean(Z)

from statsmodels.stats.stattools import jarque_bera

print 'X jarque_bera:', jarque_bera(X)[1]
if jarque_bera(X)[1] < 0.05:
    print 'The distribution of X is likely normal. \n'
else:
    print 'The distribution of X is likely not normal. \n'

print 'Y jarque_bera:', jarque_bera(Y)[1]
if jarque_bera(Y)[1] < 0.05:
    print 'The distribution of Y is likely normal. \n'
else:
    print 'The distribution of Y is likely not normal. \n'

print 'Z jarque_bera:', jarque_bera(Z)[1]
if jarque_bera(Z)[1] < 0.05:
    print 'The distribution of Z is likely normal. \n'
else:
    print 'The distribution of Z is likely not normal. \n'

plt.hist([X, Y, Z], normed=1, histtype='bar', stacked=False, alpha = 0.7);
plt.ylabel('Frequency')
plt.xlabel('Value');

plt.axvline(np.mean(X));
plt.axvline(np.mean(Y), c='r');
plt.axvline(np.mean(Z), c='g');

print "All three datasets have a similar mean, but have very different distributions. Mean alone is very non-informative about what is going on in data, and should not be used alone as an estimator." 

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

def sharpe_ratio(asset, riskfree):
    return np.mean(asset - riskfree)/np.std(asset - riskfree)

for window in [50, 150, 300]:
    # Compute the running Sharpe ratio
    running_sharpe = [sharpe_ratio(returns[i-window+10:i], treasury_ret[i-window+10:i]) for i in range(window-10, len(returns))]

    # Compute the mean and std of the running Sharpe ratios up to 200 days before the end
    mean_rs = np.mean(running_sharpe[:-200])
    std_rs = np.std(running_sharpe[:-200])

    print (window),'Mean of running Sharpe ratio:', mean_rs
    print (window),'std of running Sharpe ratio: ', std_rs, '\n'

for window in [50, 150, 300]:
    running_sharpe = [sharpe_ratio(returns[i-window+10:i], treasury_ret[i-window+10:i]) for i in range(window-10, len(returns))]
    mean_rs = np.mean(running_sharpe[:-200])
    std_rs = np.std(running_sharpe[:-200])
    
    _, ax2 = plt.subplots()
    
    ax2.plot(range(window-10, len(returns)), running_sharpe)
    ticks = ax2.get_xticks()

    ax2.set_xticklabels([pricing.index[i].date() for i in ticks[:-1]])
    
    ax2.axhline(mean_rs)
    ax2.axhline(mean_rs + std_rs, linestyle='--')
    ax2.axhline(mean_rs - std_rs, linestyle='--')
    
    ax2.axvline(len(returns) - 200, color='pink');
    plt.title(window, fontsize = 20)
    plt.xlabel('Date')
    plt.ylabel('Sharpe Ratio')
    plt.legend(['Sharpe Ratio', 'Mean', '+/- 1 Standard Deviation'])

    
print "Despite the longer window Sharpe ratios having less variability, they are still unpredictable with repect to just the mean. But within the context of the standard deviation the mean has more predictive value, as we see that even in the out-of-sample periods the ratios of all window lengths stay mainly within 1 standard deviation of the mean."

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

b15_mean = np.mean(b15_df['Weekly Avg Temp'])
b15_std = np.std(b15_df['Weekly Avg Temp'])

print "Boston Weekly Temp Mean: ", b15_mean
print "Boston Weekly Temp Std:  ", b15_std

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

p15_mean = np.mean(p15_df['Weekly Avg Temp'])
p15_std = np.std(p15_df['Weekly Avg Temp'])

print "Palo Alto Weekly Temp Mean: ", p15_mean
print "Palo Alto Weekly Temp Std:  ", p15_std

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

b16_df.plot.hist(title = "Boston 2016 Temperature vs. Prediction");
plt.axvline(b15_mean);

p16_df.plot.hist(title = "Palo Alto 2016 Temperature vs. Prediction");
plt.axvline(p15_mean);

b_avg_error = np.mean(abs(b16_df['Weekly Avg Temp'] - b15_mean))
p_avg_error = np.mean(abs(p16_df['Weekly Avg Temp'] - p15_mean))

print "Avg of Absolute Value of Prediction Error in Boston:", b_avg_error
print "Avg of Absolute Value of Prediction Error in Palo Alto:", p_avg_error

print "\nWe know from parts a and b that the weather in Boston is much more variable than that of Palo Alto. As a result, we can predict that an estimate based on a sample mean in Boston will be less accurate than an estimate based on a sample from Palo Alto, which is confirmed by this test. The Palo Alto predictions had a much lower error than those of Boston. With mean alone we would not have been able to make any conclusions about the accuracy of our predictions."