This is my first message on CrossValidated to get some insights on an issue I am facing while trying to model properly a time series. I am relatively new to this science so please brace with me.
My time series is related to energy consumption with a daily seasonality (96 values per day). Here a description:
For the model definition, I used an auto.arima as a start but the model returned (SARIMA (1,0,0)(0,1,0)) has residuals that are not white noise, this means that the stochastic part of my series is not entirely modeled. Below a summary of residuals checking:
Ljung-Box test data: Residuals from ARIMA(5,1,1)(0,1,1) Q* = 248.44, df = 185, p-value = 0.001282 Model df: 7. Total lags used: 192
I tried to create my own model using differentiation but still end up with residuals that are not white noise which is frustrating. I differentiated twice to remove seasonal and trend patterns, this is what I obtained :
After second differentiation:
I chose a SARIMA(0,1,4)(0,1,1) because:
we can see a very significant spike on lag 96 on acf with an exponential decay on pacf seasonal lags which suggests a seasonal MA1.
And we observe another significant spike on lag 4 on acf for which I chose a non-seasonal MA4.
At the end, I obtained these residuals:
Do you think it is reasonable to choose such models in regard to the significance of residuals correlations ? Do you have any advice on how should I carry on from here ?
Thank you in advance for your help ?