# The time series shows random walk behavior from PACF and ACF plot but adf test shows its stationary

I am new to time series and wanted to practice it by forecasting an hourly time series. The adf and kpss test results show that the series is stationary.

Test Statistic                -1.023836e+01
p-value                        4.822092e-18
#Lags Used                     2.500000e+01
Number of Observations Used    8.734000e+03
Critical Value (1%)           -3.431099e+00
Critical Value (5%)           -2.861871e+00
Critical Value (10%)          -2.566946e+00


KPSS test results

Test Statistic            0.109422
p-value                   0.100000
#Lags Used               54.000000
Critical Value (10%)      0.347000
Critical Value (5%)       0.463000
Critical Value (2.5%)     0.574000
Critical Value (1%)       0.739000


However, the pacf and acf plots show that the series is a random walk.

Is the series a random walk and is it possible to forecast it?

• Hi: can you show a plot of the series itself ? That might help to get some answers. Commented Dec 25, 2023 at 8:36
• I have added the plot for the series. Commented Dec 25, 2023 at 16:07
• Hi: I agree that the acf makes it look possibly not stationary but how do you conclude random walk. I forget all the rules for interpreting the acf and pacf so your conclusion could be correct. I'm just asking why ? I mainly ask because a random walk would tend not to hover around a constant mean like that series does. Also, a large + AR(1) coefficient ( near 1 ) can give an ACF sort of like yours, I totally forget the PACF rules. Commented Dec 26, 2023 at 17:54
• I referred this : stats.stackexchange.com/questions/87000/… and came to the conclusion that its a random walk. The ACF and PACF plots in the post are similar to mine. Commented Dec 27, 2023 at 1:17
• that's fine. these things are part art and part science. but do notice that the acf in that picture is pretty different from the acf in your picture. I would compare the predictions of a random walk versus an AR(1) because, for high $\phi$, those two series are known to be quite difficult to differentiate from. Commented Dec 27, 2023 at 21:46