In [4]:
import pandas as pd
import numpy as np
import matplotlib.pylab as plt
%matplotlib inline
from matplotlib.pylab import rcParams
rcParams['figure.figsize'] = 15, 6
In [11]:
data = pd.read_csv('household_power_consumptions.csv')
print (data.head())
print ('\n Data Types:')
print (data.dtypes)
In [12]:
dateparse = lambda dates: pd.datetime.strptime(dates, '%d/%m/%Y %H:%M:%S')
data = pd.read_csv('household_power_consumptions.csv', parse_dates=['Time'], index_col='Time',date_parser=dateparse)
print (data.head())
In [13]:
#check datatype of index
data.index
Out[13]:
In [14]:
#convert to time series:
ts = data['Global_intensity']
ts.head(10)
Out[14]:
In [15]:
ts['2006-12-17']
Out[15]:
In [16]:
plt.plot(ts)
Out[16]:
In [17]:
from statsmodels.tsa.stattools import adfuller
def test_stationarity(timeseries):
#Determing rolling statistics
rolmean = pd.rolling_mean(timeseries, window=12)
rolstd = pd.rolling_std(timeseries, window=12)
#Plot rolling statistics:
orig = plt.plot(timeseries, color='blue',label='Original')
mean = plt.plot(rolmean, color='red', label='Rolling Mean')
std = plt.plot(rolstd, color='black', label = 'Rolling Std')
plt.legend(loc='best')
plt.title('Rolling Mean & Standard Deviation')
plt.show(block=False)
#Perform Dickey-Fuller test:
print ('Results of Dickey-Fuller Test:')
dftest = adfuller(timeseries, autolag='AIC')
dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])
for key,value in dftest[4].items():
dfoutput['Critical Value (%s)'%key] = value
print (dfoutput)
In [18]:
test_stationarity(ts)
In [19]:
ts_log = np.log(ts)
plt.plot(ts_log)
Out[19]:
In [20]:
moving_avg = pd.rolling_mean(ts_log,1440)
plt.plot(ts_log)
plt.plot(moving_avg, color='red')
Out[20]:
In [22]:
ts_log_moving_avg_diff = ts_log - moving_avg
ts_log_moving_avg_diff.head(1440)
Out[22]:
In [23]:
ts_log_moving_avg_diff.dropna(inplace=True)
ts_log_moving_avg_diff.head()
Out[23]:
In [25]:
test_stationarity(ts_log_moving_avg_diff)
In [26]:
#Take first difference:
ts_log_diff = ts_log - ts_log.shift()
plt.plot(ts_log_diff)
Out[26]:
In [27]:
ts_log_diff.dropna(inplace=True)
test_stationarity(ts_log_diff)
In [30]:
from statsmodels.tsa.arima_model import ARIMA
In [31]:
#ACF and PACF plots:
from statsmodels.tsa.stattools import acf, pacf
lag_acf = acf(ts_log_diff, nlags=20)
lag_pacf = pacf(ts_log_diff, nlags=20, method='ols')
#Plot ACF:
plt.subplot(121)
plt.plot(lag_acf)
plt.axhline(y=0,linestyle='--',color='gray')
plt.axhline(y=-1.96/np.sqrt(len(ts_log_diff)),linestyle='--',color='gray')
plt.axhline(y=1.96/np.sqrt(len(ts_log_diff)),linestyle='--',color='gray')
plt.title('Autocorrelation Function')
#Plot PACF:
plt.subplot(122)
plt.plot(lag_pacf)
plt.axhline(y=0,linestyle='--',color='gray')
plt.axhline(y=-1.96/np.sqrt(len(ts_log_diff)),linestyle='--',color='gray')
plt.axhline(y=1.96/np.sqrt(len(ts_log_diff)),linestyle='--',color='gray')
plt.title('Partial Autocorrelation Function')
plt.tight_layout()
In [32]:
model = ARIMA(ts_log, order=(2, 1, 0))
results_AR = model.fit(disp=-1)
plt.plot(ts_log_diff)
plt.plot(results_AR.fittedvalues, color='red')
plt.title('RSS: %.4f'% sum((results_AR.fittedvalues-ts_log_diff)**2))
Out[32]:
In [33]:
model = ARIMA(ts_log, order=(0, 1, 2))
results_MA = model.fit(disp=-1)
plt.plot(ts_log_diff)
plt.plot(results_MA.fittedvalues, color='red')
plt.title('RSS: %.4f'% sum((results_MA.fittedvalues-ts_log_diff)**2))
Out[33]:
In [34]:
model = ARIMA(ts_log, order=(2, 1, 2))
results_ARIMA = model.fit(disp=-1)
plt.plot(ts_log_diff)
plt.plot(results_ARIMA.fittedvalues, color='red')
plt.title('RSS: %.4f'% sum((results_ARIMA.fittedvalues-ts_log_diff)**2))
Out[34]:
In [35]:
predictions_ARIMA_diff = pd.Series(results_ARIMA.fittedvalues, copy=True)
print (predictions_ARIMA_diff.head())
In [36]:
predictions_ARIMA_diff_cumsum = predictions_ARIMA_diff.cumsum()
print (predictions_ARIMA_diff_cumsum.head())
In [37]:
predictions_ARIMA_log = pd.Series(ts_log.ix[0], index=ts_log.index)
predictions_ARIMA_log = predictions_ARIMA_log.add(predictions_ARIMA_diff_cumsum,fill_value=0)
predictions_ARIMA_log.head()
Out[37]:
In [38]:
predictions_ARIMA = np.exp(predictions_ARIMA_log)
plt.plot(ts)
plt.plot(predictions_ARIMA)
plt.title('RMSE: %.4f'% np.sqrt(sum((predictions_ARIMA-ts)**2)/len(ts)))
Out[38]:
In [ ]: