I'm currently working on my first machine learning problem in a workplace and have some time series data going back for two years from January. This data is call counts per day at a call center I work at and I am looking to forcast what this year would have been like had COVID not impacted our center (for various institutional and obvious factors). Currently, the graph of terms looks like this:

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My ADF results are:

Test Statistic -4.472941 p-value 0.000220 #Lags Used 20.000000 Number of Observations Used 710.000000 Critical Value (1%) -3.439594 Critical Value (5%) -2.865619 Critical Value (10%) -2.568942 dtype: float64

and KPSS:

Test Statistic 0.467180 p-value 0.049059 Lags Used 20.000000 Critical Value (10%) 0.347000 Critical Value (5%) 0.463000 Critical Value (2.5%) 0.574000 Critical Value (1%) 0.739000 dtype: float64


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I can see the ADF test looks to be saying this series is stationary. The Lags in the ACF appearing roughly every 7 lags looks to me like there is a correlation between weekdays (each data point being a day). However there is also the 2nd lag and it seems to repeat a couple times as well. It also doens't look like the ACF is trending cleanly towards zero. Anecdotally I believe there is seasonal variety but how can I statistically prove this. Should I difference by 7 days and run the ARIMA on that? How can I proceed picking hyper parameters and interpret these results.

  • $\begingroup$ Looks pretty stationary to me. If you believe there is seasonality, you can take a seasonal difference. So you will end up with a SARIMA then $\endgroup$ – Stochastic May 19 at 19:06

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