I am a beginner in time series analysis and machine learning. I have a dataset where I want to analyse and predict a time series data. I have a pollutant variable and four meteorological parameters like humidity and temperature for about a month, hourly data. The websites I found in the internet were numerous with so many approaches that I couldn't get a clue how to begin. To be honest, I want to use time series analysis for my thesis, and there aren't any people here that can help regarding this. That is why I am asking here. I am trying to predict the pollutant variable which is more like a parameter.
A history of what I have achieved so far: I first learnt about the ARIMA model which I was unsuccessful with. I performed an ADF test to check for stationarity which came significant, so that was a relief. The pollutant variable has a trend and a seasonal variation of 4 hours and 24 hours, i.e. daily variation which I understood from the ACF plot, by finding the lags in the ACF plot. The ARIMA model was unsuccessful in detecting any trend or seasonality and gave a straight line, so I moved on. I learned about SARIMA and used the parameters SARIMA(4,1,4)(1,1,1,24) and the prediction fitted well with the test part with an RMSE of 0.03
I actually want to show that my meteorological parameters especially humidity influences the pollutant variable, so I incorporated an exogenous SARIMAX with the exogenous variables as humidity, temperature and pressure and I again got a good prediction with an RMSE OF 0.002 with a lag of one hour which I don't understand. But anyways it made me happy.
The problem is, the scatterplots between the pollutant variable and the weather parameters especially humidity are not good at all for linear regression as R square value is too low. But I don't think they are linearly related.
I also tried the Granger Casuality Test, but the results were unexpected. The humidity values seem to be affected by the pollutant variables at lags 4 and 24 but not the pollutant vs humidity values which only show a significant lag at 4.
Is there any way to show these dependencies? I am trying to compile my results into a thesis form so that I don't understand what things I should include in the write up to support my thesis. Like what tests should I perform, or what things I need to show to make it look complete a little.