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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
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#Note: aim is not to teach stock price forecasting. It's a very complex domain and I have almost no clue about it. Here I will demonstrate the various techniques which can be used for time-series forecasting
data = pd.read_csv('AirPassengers.csv')
print data.head()
print '\n Data Types:'
print data.dtypes
Reading as datetime format:
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dateparse = lambda dates: pd.datetime.strptime(dates, '%Y-%m')
# dateparse('1962-01')
data = pd.read_csv('AirPassengers.csv', parse_dates='Month', index_col='Month',date_parser=dateparse)
print data.head()
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#check datatype of index
data.index
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#convert to time series:
ts = data['#Passengers']
ts.head(10)
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#1. Specific the index as a string constant:
ts['1949-01-01']
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#2. Import the datetime library and use 'datetime' function:
from datetime import datetime
ts[datetime(1949,1,1)]
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#1. Specify the entire range:
ts['1949-01-01':'1949-05-01']
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#2. Use ':' if one of the indices is at ends:
ts[:'1949-05-01']
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Note: ends included here
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#All rows of 1962:
ts['1949']
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plt.plot(ts)
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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
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test_stationarity(ts)
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ts_log = np.log(ts)
plt.plot(ts_log)
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moving_avg = pd.rolling_mean(ts_log,12)
plt.plot(ts_log)
plt.plot(moving_avg, color='red')
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ts_log_moving_avg_diff = ts_log - moving_avg
ts_log_moving_avg_diff.head(12)
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ts_log_moving_avg_diff.dropna(inplace=True)
ts_log_moving_avg_diff.head()
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test_stationarity(ts_log_moving_avg_diff)
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expwighted_avg = pd.ewma(ts_log, halflife=12)
plt.plot(ts_log)
plt.plot(expwighted_avg, color='red')
# expwighted_avg.plot(style='k--')
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ts_log_ewma_diff = ts_log - expwighted_avg
test_stationarity(ts_log_ewma_diff)
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#Take first difference:
ts_log_diff = ts_log - ts_log.shift()
plt.plot(ts_log_diff)
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ts_log_diff.dropna(inplace=True)
test_stationarity(ts_log_diff)
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from statsmodels.tsa.seasonal import seasonal_decompose
decomposition = seasonal_decompose(ts_log)
trend = decomposition.trend
seasonal = decomposition.seasonal
residual = decomposition.resid
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()
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ts_log_decompose = residual
ts_log_decompose.dropna(inplace=True)
test_stationarity(ts_log_decompose)
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from statsmodels.tsa.arima_model import ARIMA
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#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()
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#MA model:
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))
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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))
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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))
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predictions_ARIMA_diff = pd.Series(results_ARIMA.fittedvalues, copy=True)
print predictions_ARIMA_diff.head()
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predictions_ARIMA_diff_cumsum = predictions_ARIMA_diff.cumsum()
print predictions_ARIMA_diff_cumsum.head()
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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()
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plt.plot(ts_log)
plt.plot(predictions_ARIMA_log)
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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)))
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