In [1]:

    

from __future__ import print_function
import os
import pandas as pd
import numpy as np
from pandas.tools.plotting import autocorrelation_plot
from statsmodels.tsa import stattools
%matplotlib inline
from matplotlib import pyplot as plt


    

In [3]:

    

#Read data from Excel file
daily_temp = pd.read_excel('datasets/mean-daily-temperature-fisher-river.xlsx')


    

In [4]:

    

#Display first 20 rows of the DataFrame
daily_temp.head(10)


    

    
Out[4]:






  

    

      

      
Date
      
Mean_Temperature
    
  
  

    

      
0
      
1988-01-01
      
-23.00
    
    

      
1
      
1988-01-02
      
-20.50
    
    

      
2
      
1988-01-03
      
-22.00
    
    

      
3
      
1988-01-04
      
-30.50
    
    

      
4
      
1988-01-05
      
-31.00
    
    

      
5
      
1988-01-06
      
-27.50
    
    

      
6
      
1988-01-07
      
-26.25
    
    

      
7
      
1988-01-08
      
-26.50
    
    

      
8
      
1988-01-09
      
-23.00
    
    

      
9
      
1988-01-10
      
-23.50
    
  

In [5]:

    

#Make formatted date as the row index of the dataset and drop the Date column
daily_temp.index = daily_temp['Date'].map(lambda date: pd.to_datetime(date, '%Y-%m-%d'))
daily_temp.drop('Date', axis=1, inplace=True)


    

In [6]:

    

#Re-display the first 10 rows of the modified DataFrame
daily_temp.head(10)


    

    
Out[6]:






  

    

      

      
Mean_Temperature
    
    

      
Date
      

    
  
  

    

      
1988-01-01
      
-23.00
    
    

      
1988-01-02
      
-20.50
    
    

      
1988-01-03
      
-22.00
    
    

      
1988-01-04
      
-30.50
    
    

      
1988-01-05
      
-31.00
    
    

      
1988-01-06
      
-27.50
    
    

      
1988-01-07
      
-26.25
    
    

      
1988-01-08
      
-26.50
    
    

      
1988-01-09
      
-23.00
    
    

      
1988-01-10
      
-23.50
    
  

In [7]:

    

fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
ax.set_title('Daily temperatures of Fisher River, TX, US')
daily_temp.plot(ax=ax)
plt.savefig('plots/ch2/B07887_02_08.png', format='png', dpi=300)


    

In [8]:

    

#Calculate monthly mean temperature
montly_resample = daily_temp['Mean_Temperature'].resample('M')
monthly_mean_temp = montly_resample.mean()
print('Shape of monthly mean temperature dataset:', monthly_mean_temp.shape)
monthly_mean_temp.head(10)


    

    




Shape of monthly mean temperature dataset: (48,)






    
Out[8]:





Date
1988-01-31   -22.137097
1988-02-29   -19.025862
1988-03-31    -8.258065
1988-04-30     2.641667
1988-05-31    11.290323
1988-06-30    19.291667
1988-07-31    19.048387
1988-08-31    17.379032
1988-09-30    10.675000
1988-10-31     2.467742
Freq: M, Name: Mean_Temperature, dtype: float64

In [9]:

    

#Plot the monthly mean temparature
fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
ax.set_title('Monthly mean temperatures of Fisher River, TX, US')
monthly_mean_temp.plot(ax=ax)
plt.savefig('plots/ch2/B07887_02_09.png', format='png', dpi=300)


    

In [10]:

    

#Plot ACF of the monthly mean temparature using pandas.tools.plotting.autocorrelation_plot
fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
ax.set_title('ACF of monthly mean temperatures of Fisher River, TX, US')
autocorrelation_plot(monthly_mean_temp, ax=ax)
plt.savefig('plots/ch2/B07887_02_10.png', format='png', dpi=300)


    

In [11]:

    

#Take seasonal differences with a period of 12 months on monthly mean temperatures
seasonal_diff = monthly_mean_temp.diff(12)
seasonal_diff = seasonal_diff[12:]


    

In [12]:

    

#Plot the seasonal differences
fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
ax.set_title('Seasonal differences')
seasonal_diff.plot(ax=ax)
plt.savefig('plots/ch2/B07887_02_11.png', format='png', dpi=300)


    

In [13]:

    

#Plot the seasonal differences
fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
ax.set_title('ACF of Seasonal differences')
autocorrelation_plot(seasonal_diff, ax=ax)
plt.savefig('plots/ch2/B07887_02_12.png', format='png', dpi=300)


    

In [14]:

    

#Perform Ljung-Box test on monthly mean temperature to get the p-values
#We will use lags of upto 10
_, _, _, pval_monthly_mean = stattools.acf(monthly_mean_temp, unbiased=True,
                                           nlags=10, qstat=True, alpha=0.05)
print('Null hypothesis is rejected for lags:', np.where(pval_monthly_mean<=0.05))


    

    




Null hypothesis is rejected for lags: (array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),)

In [15]:

    

#Perform Ljung-Box test on monthly mean temperature to get the p-values
#We will use lags of upto 10
_, _, _, pval_seasonal_diff = stattools.acf(seasonal_diff, unbiased=True,
                                            nlags=10, qstat=True, alpha=0.05)
print('Null hypothesis is rejected for lags:', np.where(pval_seasonal_diff<=0.05))


    

    




Null hypothesis is rejected for lags: (array([], dtype=int32),)