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I have multiple time series on which I want to identify statistically significant (if any) trends. To that end, I started by conducting the Augmented Dickey Fuller (ADF) test to identify which series are not stationary (thus implying an underlying trend):

original/input

Augmented Dickey-Fuller Test (p-value):
#0: 0.7400121258386816 -> (not stationary)
#1: 0.003756531421338549 -> (stationary)
#2: 0.8356431503570756 -> (not stationary)
#3: 1.2618571533446908e-07 -> (stationary)

In order to identify relevant monotonic trends, I want to conduct the Mann-Kendall test, but I need to ensure that samples are independent and not serially correlated. ACF/PACF analysis on the time series suggest/are influenced by trends, and therefore require de-trending transformations to achieve stationarity:

original ACF original PACF

However, I'm struggling on 1) how to detrend non-stationarity series - using gradient vs difference; It should be noted I'm not trying to model the trend at this stage (as I'm not yet sure a trend exists) and can't perform correlation analysis on the residuals without making assumptions on an underlying model.

detrended series

Additionally, I'm unsure about 2) which analysis tool to use: ACF, PACF or the Ljung-Box test? I am getting very different results with each:

detrended ACF detrended PACF

Ljung-Box Test (p-value):
          org_#0   grad_#0   diff_#0    org_#1   grad_#1   diff_#1        org_#2   grad_#2   diff_#2    org_#3   grad_#3   diff_#3
1   5.832414e-06  0.652845  0.130720  0.023136  0.649813  0.000918  6.256156e-05  0.692498  0.036099  0.574666  0.882558  0.001247
2   2.251164e-08  0.005893  0.030928  0.004227  0.027847  0.003637  1.582695e-06  0.003751  0.056359  0.825435  0.090845  0.004315
3   1.014388e-10  0.012420  0.038536  0.001468  0.035400  0.010453  8.091142e-08  0.008257  0.123269  0.895700  0.187108  0.012288
4   2.102519e-12  0.011219  0.049601  0.001637  0.072348  0.022559  6.321557e-09  0.018818  0.215027  0.789189  0.262034  0.021165
5   2.409707e-13  0.005992  0.051696  0.002315  0.109543  0.032003  6.076601e-10  0.026010  0.273688  0.854404  0.367491  0.028546
6   5.651045e-14  0.004371  0.040586  0.002245  0.151084  0.044142  4.085782e-11  0.015675  0.061854  0.918215  0.313839  0.044380
7   2.305528e-14  0.002721  0.022965  0.003423  0.167607  0.073019  4.044796e-11  0.020773  0.040071  0.914727  0.420027  0.026616
8   2.235907e-14  0.003622  0.036035  0.006228  0.218115  0.109756  4.466094e-11  0.028620  0.063734  0.439324  0.164661  0.003724
9   5.095045e-14  0.004166  0.034175  0.010811  0.238909  0.159675  7.262066e-11  0.039198  0.076998  0.540013  0.226233  0.002383
10  1.516367e-13  0.004739  0.051209  0.011125  0.248227  0.155707  2.031204e-10  0.040187  0.106888  0.452840  0.289605  0.003102

Ljung-Box Test (statistical significance, pvalue < 0.05):
    org_#0  grad_#0  diff_#0  org_#1  grad_#1  diff_#1  org_#2  grad_#2  diff_#2  org_#3  grad_#3  diff_#3
1     True    False    False    True    False     True    True    False     True   False    False     True
2     True     True     True    True     True     True    True     True    False   False    False     True
3     True     True     True    True     True     True    True     True    False   False    False     True
4     True     True     True    True    False     True    True     True    False   False    False     True
5     True     True    False    True    False     True    True     True    False   False    False     True
6     True     True     True    True    False     True    True     True    False   False    False     True
7     True     True     True    True    False    False    True     True     True   False    False     True
8     True     True     True    True    False    False    True     True    False   False    False     True
9     True     True     True    True    False    False    True     True    False   False    False     True
10    True     True    False    True    False    False    True     True    False   False    False     True

For context, each sample in original time series is a metric computed from a segment of a longer series of repetitive/periodic electrical measurements, therefore I don't expect any correlation to occur as each value should be independent (no overlap between consecutive segments). Nevertheless, I'm seeing some unexpected serial correlation among the samples even after de-trending, thefore I'm not sure if I can use the MK test here. What would be the best approach?

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