I am doing regression with ARIMA errors. The residuals are as shown in the figure below. Clearly, the scatter plot shows that this time series has some sort of periodicity or seasonality, but its very hard to identify the seasonality.
I also plotted the ACF and PACF of the residuals clearly it shows that model is non-stationary as the ACF is very slowly decaying. To estimate periodicity I plotted the periodogram of the time series.
As it can be seen in the periodogram that its very hard to estimate its seasonality, clearly there are more than one significant frequencies. How do I go about from here?
I also estimated the ACF and PACF after first differencing, looks like its being over differenced? How do I go about solving this problem?