I have hourly and +4 years length of air pollution data (PM10). It has 24 (daily), 168 (weekly) and 8766 (yearly) seasonality. Also distribution is right skewed and has very long tail. I want to make anomaly detection on residuals of current data by fitting TBATS model but residuals still have seasonality (in terms of variance) at 24th hour (By the help of ACF and PACF plots). I know TBATS is very slow on long time series but my main goal is to be able to identify seasonally adjusted anomalies. For instance, 22C temperature can be an anomaly in winter but it is unlikely in summer but 50C is another anomaly in summer, too.
- Is this a good approach to determine seasonally adjusted anomalies? If not, why?
- If not, can you advice another method for a multiple seasonal and non-gaussian data?
- If yes, I expect a completely random residuals but variance of my residuals change by time i.e. high variance in winter time and low variance in summer time. Is it good interpretation to say that model can not handle seasonality well in my time series? or having seasonality in residuals is a common situation?
Thanks in advance