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# check if the VAR residuals are white noise or still contain a signal
# a Durbin-Watson test statistic of 2.0 (as opposed to 0 or 4) would indicate no detectable autocorrelation

dw = durbin_watson(res.resid)

print(f'Durbin-Watson statistic (Tyrion): {dw[0]:.2f}')
print(f'Durbin-Watson statistic (Cersei): {dw[1]:.2f}')

if (1.9 <= dw[0] <= 2.1) and (1.9 <= dw[1] <= 2.1):
    print("test passed: no discernible signal in the residuals")

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# run the VAR model again, for the differenced time series, and add the order of differencing 
#   to the lags that had minimized the AIC in the preceding VAR1 model  (Dave Giles 2011, step #8)
VARmodel2 = VAR(df_iTC)    # df_iTC contains the integrated / differenced time series we prepared in our testing of stationarity
resVAR2 = VARmodel2.fit(maxlags=lag_min_aic + n_diff_Tyrion, ic='aic')

lag_order = resVAR2.k_ar
print("VAR2 lag-order: " + str(lag_order))

resVAR2.summary()

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# test for cointegration using Engle-Granger
# null hypothesis: Tyrion and Cersei are NOT cointegrated
score, pvalue, _ = coint(df["Tyrion"], df["Cersei"], maxlag=lag_min_aic)
pvalue
print(f'cointegration: score: {score:.2f}')
print(f'cointegration: p-value: {pvalue:.10f}')
print("cointegrated - there MUST be Granger causality" if pvalue < ALPHA else "NOT cointegrated (uncertain about Granger causality)")

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# run the granger causality test for Cersei as causal agent
print("lags (min AIC): " + str(lag_min_aic))
gct_Cersei_caus = grangercausalitytests(x=ar_iTC, verbose=True, maxlag=lag_min_aic)  

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# swap Tyrion's and Cersei's columns
ar_iCT = ar_iTC.copy()
ar_iCT[:, [1,0]] = ar_iCT[:, [0,1]]

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# run the granger causality test for Tyrion as causal agent
print("lags (min AIC): " + str(lag_min_aic))
gct_Tyrion_caus = grangercausalitytests(x=ar_iCT, verbose=True, maxlag=lag_min_aic)

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# going off the rails:
# how does causality develop over a far more expansive range of lags than the VAR model justifies?
# causality tests up to a lag of 20 weeks

MAXLAG = 20
TEST = "ssr_ftest"    # choose the F-test as criterion

lags_max = range(0,MAXLAG)

# test Tyrion and get his p-values:

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# convert "Week" object/string to date and set datetime index

df.rename(columns={"Week": "Date"}, inplace=True)
df.Date = df["Date"]
df.Date = pd.to_datetime(df.Date)
df.set_index(df.Date)

df[["Tyrion", "Cersei"]] = df[["Tyrion", "Cersei"]].apply(pd.to_numeric, errors="ignore")
df.info()

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df = pd.read_csv("got_Cersei_Tyrion.csv")
df

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# Stationarity and SARIMA model

import pandas as pd
import datetime as dt
import numpy as np
import matplotlib.pyplot as plt

import pmdarima as pmd

import statsmodels.api as sm