GoT_grangercausality_stationary1

# Are Tyrion and Cersei stationary processes?

# ADF and KPSS tests:

def ADF_test(x):
     adf_result = adfuller(x.values)
     t_stat, p_value, _, _, critical_values, _  = adf_result

     print(f'ADF statistic: {t_stat:.2f}')
     #for key, value in critical_values.items():
     #     print('critical values:')
     #     print(f'   {key}, {value:.2f}')

     print(f'AFD: p-value: {p_value:.2f}')
     # ADF null hypothesis: There is a unit root and the series is non-stationary.
     print("ADF: non-stationary - unit root" if p_value >= ALPHA else "ADF: stationary or only difference-stationary")
     boo_ADF = (p_value < ALPHA)   # True: (difference-)stationary
     return boo_ADF


def KPSS_test(x):
     kpss_result = kpss(x.values)
     t_stat, p_value, _, critical_values  = kpss_result

     print(f'KPSS statistic: {t_stat:.2f}')
     # for key, value in critical_values.items():
     #     print('critical Values:')
     #     print(f'   {key}, {value:.2f}')

     print(f'KPSS: p-value: {p_value:.2f}')
     # KPSS null hypothesis: The series is at least trend-stationary. 
     print("KPSS: non-stationary - unit root") if p_value < ALPHA else print("KPSS: stationary or only trend-stationary")
     boo_KPSS = (p_value >= ALPHA)  # True: (trend-)stationary)
     return boo_KPSS


# combine the ADF and KPSS results and derive the recommendation
def is_Stationary(x):
     boo_ADF = ADF_test(x)
     boo_KPSS = KPSS_test(x)
     n_diffscore = boo_KPSS *10 + boo_ADF*1     # combine the KPSS and ADF result in a single score with 4 possible values: 0,1,10,11
     diff_eval = EvalDiff(n_diffscore)          # get the recommendation statement
     print(diff_eval)
     return diff_eval


# translate the test score into a recommendation statement
def EvalDiff(diffscore):
    # 4 possible combinations of KPSS and ADF test results
     ADF1_KPSS1 = "Stationary: ADF and KPSS in agreement."
     ADF0_KPSS1 = """ADF finds a unit root; but KPSS finds that the series is stationary
         around a deterministic trend. Thus, the series is only trend-stationary. Difference it (or de-trend it by other methods)."""
     ADF1_KPSS0 = """ADF does not find a unit root; but KPSS finds that it is non-stationary.
          Thus, the series is only difference-stationary. Difference it."""
     ADF0_KPSS0 = "Not stationary. KPSS and ADF in agreement. Difference it."
    
     switcher={
        11:ADF1_KPSS1,
        10:ADF0_KPSS1,
        1:ADF1_KPSS0,
        0:ADF0_KPSS0
        }
     return switcher.get(diffscore, "invalid")



# the following pmdarima method returns the recommended order of differencing, based on the larger result of ADF or KPSS
def nDiff(x):
     n_adf = ndiffs(x, max_d=4, test="adf")
     n_kpss = ndiffs(x, max_d=4, test="kpss")
     n_diff = max(n_adf, n_kpss)
     return n_diff