Time Series forecasting

# -*- coding: utf-8 -*-
"""
Created on Tue Jan 22 11:17:01 2019
https://www.analyticsvidhya.com/blog/2016/02/time-series-forecasting-cod...
@author: K
"""

from statsmodels.tsa.stattools import adfuller
import pandas as pd
import numpy as np
import matplotlib.pylab as plt

from matplotlib.pylab import rcParams
rcParams['figure.figsize'] = 15, 6

dateparse = lambda dates: pd.datetime.strptime(dates, '%Y-%m')
data = pd.read_csv('AirPassengers.csv', parse_dates=['Month'], index_col='Month',date_parser=dateparse)
ts = data['#Passengers']

def test_stationarity(timeseries):
    
    #Determing rolling statistics
    #rolmean = pd.rolling_mean(timeseries, window=12)
    rolmean = timeseries.rolling(window=12).mean()
    #rolstd = pd.rolling_std(timeseries, window=12)
    rolstd = timeseries.rolling(window=12).std()

    #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='yellow', 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)

#test_stationarity(ts)

#plt.plot(ts, color='blue',label='Original')
descrip = ts.describe()

ts_log = np.log(ts)
#plt.plot(ts_log, color='green',label='Original')
'''
descrip = ts.describe()
print(" moyenne :",descrip['mean'])
'''
#ts_log = np.log(ts)
moving_avg = ts_log.rolling(window=12).mean()
#plt.plot(ts_log, color='blue',label='ts_log Original')
#plt.plot(moving_avg, color='red')

ts_log_moving_avg_diff = ts_log - moving_avg

ts_log_moving_avg_diff.dropna(inplace=True)
#plt.plot(ts_log_moving_avg_diff, color='red')
#test_stationarity(ts_log_moving_avg_diff)
'''
# exponentially weighted moving average
expwighted_avg = ts_log.ewm(com=12).mean()
plt.plot(ts_log)
plt.plot(expwighted_avg, color='red')

ts_log_ewma_diff = ts_log - expwighted_avg
test_stationarity(ts_log_ewma_diff)
'''
ts_log_diff = ts_log - ts_log.shift()
ts_log_diff.dropna(inplace=True)
'''
ts_log_diff2 = ts_log_diff - ts_log_diff.shift()
ts_log_diff2.dropna(inplace=True)
test_stationarity(ts_log_diff2)
'''
from statsmodels.tsa.seasonal import seasonal_decompose
decomposition = seasonal_decompose(ts_log)

trend = decomposition.trend
seasonal = decomposition.seasonal
residual = decomposition.resid
fore = trend
'''
plt.subplot(411)
plt.plot(ts_log, label='Original')


plt.plot(fore, label='fore')


plt.subplot(411)
plt.plot(ts_log, label='Original')
plt.legend(loc='best')
plt.subplot(412)
plt.plot(trend, label='Trend')
plt.legend(loc='best')
plt.subplot(413)
plt.plot(seasonal,label='Seasonality')
plt.legend(loc='best')
plt.subplot(414)
plt.plot(residual, label='Residuals')
plt.legend(loc='best')
plt.tight_layout()


ts_log_decompose = residual
ts_log_decompose.dropna(inplace=True)
test_stationarity(ts_log_decompose)'''

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()
'''


from statsmodels.tsa.arima_model import ARIMA
'''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))'''

'''
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))
'''
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))

predictions_ARIMA_diff = pd.Series(results_ARIMA.fittedvalues, copy=True)
predictions_ARIMA_diff_cumsum = predictions_ARIMA_diff.cumsum()
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 = 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)))