High peaks at same fixed lag in both acf and pacf of residuals of model from auto.arima and tbats output. Really stuck with this one

Question

I have data for every 15 mins for 4 years. ADF test shows that my data is stationary. I tried fitting model using auto.arima and seasonal=F,and I get the output as ARIMA(3,1,2) but the residual acf and pacf both have significant peaks at lag=96.

I tried differencing my time series at lag=96 and fitted auto.arima again to get an output of ARIMA(3,0,6) but now the peaks became much more significant.

I have become clueless how to get rid of these peaks

P.S. auto.arima with seasonal=TRUE parameter hangs my R session.

Any help would be highly appreciated.

Thanks in advance

Answer 1

How would you fit ARIMA model with lots of autocorrelations? discusses the need for anthropogenic variables (deterministic input series) rather than using memory or sines & cosines ( see Is Prophet from Facebook any different from a linear regression? for a discussion along these lines) in building models.

I have seen very successful applications where 96 hourly models are used in conjunction with daily patterns based upon calendar effects while incorporating user specified supporting predictors both at the interval level and at the daily level.

Take a look at Forecasting hourly time series with daily, weekly & annual periodicity where I built a model for 1 of the 24 hours ... you would have 96 models one for each of the 15 minute intervals.