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%matplotlib inline
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import datetime
from dateutil.relativedelta import relativedelta
import seaborn as sns
import statsmodels.api as sm
from statsmodels.tsa.stattools import acf
from statsmodels.tsa.stattools import pacf
from statsmodels.tsa.seasonal import seasonal_decompose
Data Quarterly Time Series of the Number of Australian Residents https://vincentarelbundock.github.io/Rdatasets/csv/datasets/austres.csv
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df=pd.read_csv("https://vincentarelbundock.github.io/Rdatasets/csv/datasets/austres.csv ")
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df=df.drop('Unnamed: 0',1)
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df.head()
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df.tail()
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len(df)
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df.shape[0]
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start = datetime.datetime.strptime("1971-03-31", "%Y-%m-%d")
print(start)
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#!pip install arrow
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start = datetime.datetime.strptime("1971-03-31", "%Y-%m-%d")
print(start)
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date_list = [start + relativedelta(months=x) for x in range(0,3*df.shape[0])]
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date_list
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len(date_list)
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c2=[]
for i in range(0,3*len(df),3):
c2.append(date_list[i])
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c2
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len(c2)
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df['index'] =c2
df.set_index(['index'], inplace=True)
df.index.name=None
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df.head()
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df=df.drop('time',1)
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df.tail()
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df.austres.plot(figsize=(12,8), title= 'Number of Australian Residents', fontsize=14)
plt.savefig('austrailian_residents.png', bbox_inches='tight')
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decomposition = seasonal_decompose(df.austres, freq=4)
fig = plt.figure()
fig = decomposition.plot()
fig.set_size_inches(15, 8)
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# Define the p, d and q parameters to take any value between 0 and 2
p = d = q = range(0, 2)
print(p)
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import itertools
import warnings
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# Generate all different combinations of p, q and q triplets
pdq = list(itertools.product(p, d, q))
print(pdq)
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# Generate all different combinations of seasonal p, q and q triplets
seasonal_pdq = [(x[0], x[1], x[2], 12) for x in list(itertools.product(p, d, q))]
print('Examples of parameter combinations for Seasonal ARIMA...')
print('SARIMAX: {} x {}'.format(pdq[1], seasonal_pdq[1]))
print('SARIMAX: {} x {}'.format(pdq[1], seasonal_pdq[2]))
print('SARIMAX: {} x {}'.format(pdq[2], seasonal_pdq[3]))
print('SARIMAX: {} x {}'.format(pdq[2], seasonal_pdq[4]))
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y=df
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warnings.filterwarnings("ignore") # specify to ignore warning messages
c4=[]
for param in pdq:
for param_seasonal in seasonal_pdq:
try:
mod = sm.tsa.statespace.SARIMAX(y,
order=param,
seasonal_order=param_seasonal,
enforce_stationarity=False,
enforce_invertibility=False)
results = mod.fit()
print('ARIMA{}x{}12 - AIC:{}'.format(param, param_seasonal, results.aic))
c4.append('ARIMA{}x{}12 - AIC:{}'.format(param, param_seasonal, results.aic))
except:
continue
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warnings.filterwarnings("ignore") # specify to ignore warning messages
c3=[]
for param in pdq:
for param_seasonal in seasonal_pdq:
try:
mod = sm.tsa.statespace.SARIMAX(y,
order=param,
seasonal_order=param_seasonal,
enforce_stationarity=False,
enforce_invertibility=False)
results = mod.fit()
c3.append( results.aic)
except:
continue
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c3
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len(c3)
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import numpy as np
index_min = np.argmin(c3)
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index_min
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c4[index_min]
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type(c4[index_min])
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from statsmodels.tsa.x13 import x13_arima_select_order
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order1=c4[index_min][6:13]
order1
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type(order1)
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order1=[int(s) for s in order1.split(',')]
order1
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type(order1)
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seasonal_order1=c4[index_min][16:27]
seasonal_order1
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seasonal_order1=[int(s) for s in seasonal_order1.split(',')]
seasonal_order1
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mod = sm.tsa.statespace.SARIMAX(df.austres, trend='n', order=order1, seasonal_order=seasonal_order1)
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results = mod.fit()
print (results.summary())
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results.predict(start=78,end=99)
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results.predict(start=78,end=99).plot()
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