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weekly = pm.auto_arima(training.y, start_p=1, start_q=1,
               max_p=7, max_q=7, # maximum p and q
               m=7,              # frequency of series
               d=0,              # order of differencing
               seasonal=True,    # Yes Seasonality
               error_action='ignore', 
               suppress_warnings=True,
               )

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# 7,0,7 ARIMA Model
model = ARIMA(training.y, order=(7,0,7))
model_fit = model.fit(disp=0)

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# ACF plot of 1st differenced series
fig, axes = plt.subplots(1, 2, sharex=True)
axes[0].plot(df['y'].diff()); axes[0].set_title('1st Differencing')
axes[1].set(ylim=(0,2),xlim=(-1,50))
plot_acf((df['y'].diff()).dropna(), ax=axes[1])
 
plt.show()

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# PACF plot of differenced series
plt.rcParams.update({'figure.figsize':(9,3), 'figure.dpi':120})
 
fig, axes = plt.subplots(1, 2, sharex=True)
axes[0].plot(df['y'].diff()); axes[0].set_title('1st Differencing')
axes[1].set(ylim=(0,2),xlim=(-1,40))
plot_pacf((df['y'].diff()).dropna(), ax=axes[1])
plt.show()

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adf_stats = adfuller(df['y'])
'ADF Statistic: %f' % adf_stats[0]
'p-value: %f' % adf_stats[1]

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def dh_plotter(training,testing,forecast,title):
  
   # Add testing/training tables
   train_table =createTableFromData({'Date':training.ds,'Training':training.y,
'Testing':[0.0],'Forecast':[0.0]}, columns=None, convertUnknownToString=False)
   test_table = createTableFromData({'Date':testing.ds,'Training':[0.0],'Testing'
:testing.y,'Forecast':forecast}, columns=None, convertUnknownToString=False)
 
   # Merge together to create output table
   output_table = ttools.merge(train_table,test_table)\

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manning_table = createTableFromData({'Date':df.ds,'Search Frequency':df.y},\  
    columns=None, convertUnknownToString=False)\
   .update('Date=convertDateTime(Date+`T16:30 NY`)')
 
manning_plot = Plot.plot("Search Frequency", manning_table, 'Date','Search_Frequency')\
   .chartTitle("Peyton Manning Search Frequency")\
   .xLabel('Date')\
   .yLabel('Search Frequency')\
   .figure
 

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# specifying model conditions
step = pm.NUTS(target_accept=.99)
start = pm.find_MAP()

# execute sampling
modelTrace pm.sample(draws=500, tune=500, step=step, start=start, chains=5)

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# create variance prior
sigma = pm.HalfCauchy('sigma', beta=2)

# create likelihood with modelled counts and observed counts
obsDeath = pm.TruncatedNormal('obsDeath', mu=sirDeath, sigma=sigma, lower=0, upper=pop,
    observed=dataDeath)

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# create number of removed based on analytic solution and above parameters
sirRem = pm.Deterministic('sirRem',
    pop - ((s0 + i0)**(beta/(beta - gamma)))*
    (s0 + i0*tt.exp(time*(beta - gamma)))**(-gamma/(beta - gamma)))
# create number of deaths as a proportion of the number of removed
sirDeath = pm.Deterministic('sirDeath', rho*sirRem)