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I am identifying autocorrelation in two time series (both are stationary at I(0) from the ADF test) and from what I have understood so far, from difference web resources, that for a series to have no auto-correlation, AC and PAC values should be closer to zero and the p-values should be larger than 0.05. I have also checked the Durbin-Watson statistic for these two series and it is 2.00 for both, which indicates: no auto-correlation. However, I am conflicted about the outcome of the correlogram analysis.

In the first time series, AC and PAC are closer to zero and the p-values are larger than 0.05, which meets my understanding and accordingly, I conclude that there is no auto-correlation in this series.

Sample: 7/01/2006 7/12/2016             
Included observations: 3665                             

 Autocorrelation    Partial Correlation     AC   PAC     Q-Stat  Prob
    |      |            |      |    1   -0.010  -0.010  0.3496  0.554
    |      |            |      |    2   0.017   0.017   1.3769  0.502
    |      |            |      |    3   -0.043  -0.042  8.0150  0.046
    |      |            |      |    4   -0.033  -0.034  11.961  0.018
    |      |            |      |    5   -0.024  -0.024  14.149  0.015
    |      |            |      |    6   -0.003  -0.005  14.192  0.028
    |      |            |      |    7   0.003   0.000   14.215  0.047
    |      |            |      |    8   -0.013  -0.017  14.881  0.062
    |      |            |      |    9   -0.015  -0.017  15.711  0.073
    |      |            |      |    10  -0.006  -0.007  15.844  0.104
    |      |            |      |    11  0.020   0.019   17.320  0.099
    |      |            |      |    12  -0.015  -0.017  18.191  0.110
    |      |            |      |    13  0.008   0.005   18.428  0.142
    |      |            |      |    14  0.024   0.025   20.538  0.114
    |      |            |      |    15  -0.013  -0.013  21.164  0.132
    |      |            |      |    16  -0.000  -0.001  21.165  0.172
    |      |            |      |    17  -0.006  -0.004  21.294  0.213
    |      |            |      |    18  -0.036  -0.036  26.043  0.099
    |      |            |      |    19  -0.006  -0.006  26.159  0.126
    |      |            |      |    20  0.006   0.006   26.280  0.157
    |      |            |      |    21  -0.017  -0.021  27.327  0.160
    |      |            |      |    22  0.008   0.005   27.571  0.190
    |      |            |      |    23  0.017   0.018   28.670  0.192
    |      |            |      |    24  -0.033  -0.035  32.647  0.112
    |      |            |      |    25  0.010   0.007   32.985  0.131
    |      |            |      |    26  -0.001  0.002   32.987  0.162
    |      |            |      |    27  0.010   0.006   33.377  0.185
    |      |            |      |    28  0.004   0.003   33.449  0.220
    |      |            |      |    29  0.016   0.016   34.355  0.227
    |      |            |      |    30  -0.027  -0.028  37.004  0.177
    |      |            |      |    31  -0.015  -0.014  37.796  0.187
    |      |            |      |    32  -0.003  0.002   37.834  0.220
    |      |            |      |    33  0.022   0.019   39.549  0.201
    |      |            |      |    34  -0.007  -0.010  39.746  0.229
    |      |            |      |    35  0.005   0.005   39.830  0.264
    |      |            |      |    36  -0.002  -0.004  39.840  0.303

In the second series, AC is larger than zero for upto 2 lags and PAC is larger than zero upto lag 1, whereas the p-values are less than 0.05.Does this mean that this series has auto-correlation?

Sample: 7/01/2006 7/12/2016             
Included observations: 3665             

Autocorrelation Partial Correlation     AC   PAC     Q-Stat  Prob
    |***   |            |***   |    1   0.403   0.403   596.44  0.000
    |*     |            |      |    2   0.121   -0.050  649.76  0.000
    |      |            |      |    3   0.070   0.047   667.64  0.000
    |      |            |      |    4   0.071   0.038   686.34  0.000
    |      |            |      |    5   0.043   -0.002  693.06  0.000
    |      |            |      |    6   0.006   -0.015  693.22  0.000
    |      |            |      |    7   0.008   0.010   693.43  0.000
    |      |            |      |    8   -0.005  -0.017  693.52  0.000
    |      |            |      |    9   -0.014  -0.009  694.20  0.000
    |      |            |      |    10  -0.005  0.006   694.29  0.000
    |      |            |      |    11  -0.001  -0.001  694.29  0.000
    |      |            |      |    12  -0.013  -0.014  694.96  0.000
    |      |            |      |    13  0.010   0.027   695.36  0.000
    |      |            |      |    14  0.012   -0.001  695.92  0.000
    |      |            |      |    15  -0.034  -0.048  700.21  0.000
    |      |            |      |    16  -0.035  -0.003  704.76  0.000
    |      |            |      |    17  -0.023  -0.008  706.74  0.000
    |      |            |      |    18  0.010   0.026   707.11  0.000
    |      |            |      |    19  0.028   0.023   710.03  0.000
    |      |            |      |    20  0.047   0.035   718.13  0.000
    |      |            |      |    21  0.024   -0.011  720.32  0.000
    |      |            |      |    22  0.011   0.003   720.78  0.000
    |      |            |      |    23  0.017   0.009   721.83  0.000
    |      |            |      |    24  0.008   -0.011  722.04  0.000
    |      |            |      |    25  -0.008  -0.012  722.27  0.000
    |      |            |      |    26  0.040   0.059   728.26  0.000
    |      |            |      |    27  0.055   0.019   739.51  0.000
    |      |            |      |    28  0.033   0.002   743.48  0.000
    |      |            |      |    29  0.004   -0.010  743.54  0.000
    |      |            |      |    30  0.004   0.002   743.61  0.000
    |      |            |      |    31  0.017   0.009   744.70  0.000
    |      |            |      |    32  0.022   0.011   746.45  0.000
    |      |            |      |    33  0.033   0.023   750.59  0.000
    |      |            |      |    34  0.062   0.048   764.82  0.000
    |      |            |      |    35  0.031   -0.010  768.36  0.000
    |      |            |      |    36  0.034   0.029   772.53  0.000

Can I please get some help in the interpretation of the two series?

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Your first series seems uncorrelated whole your second series looks like an Ar(1). The Q statistics you are computing are incorrectly suggesting structure. The reason is you have a ton (3665) of observations this the s.e. is 1/sqrt(n) or .016 which is very very small thus you are getting a false signal of importance/significance. You have to not overbelieve these approximate t tests.

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