How to pass time series data to SARIMA, ARIMA, SARIMAX, etc

Question

I am trying to predict stock price of a company, the data is non stationary.

Steps I followed -

1. Analyze the raw data
2. Determine whether the raw time series data is stationary or not using ADF and KPSS
3. Applied first differencing and seasonal differencing to make the data stationary
4. Determine the MA and AR lags using the stationary data by plotting ACF, PACF plots

My question is should I pass raw data (non-stationary, from Step 1) to time series model like SARIMA, ARIMA and SARIMAX and use the stationary data(Step 3) to determine MA and AR lag coefficients for the model

OR

I should pass the stationary data(Step 3) to the time series model like SARIMA, ARIMA, SARIMAX, etc. and use the MA and AR lag coefficients for the model. And then to determine the predicted original time series , I should undo all the transformations that I did in Step 3 to make the time series data stationary.

Thank you for your help

Answer 1

In general, you're going to use the data as is to fit the model, but use the data analysis to choose/validate/understand your parameters (p,d,q,P,D,Q, etc). For the most part, it's advisable to do a grid search on your parameters anyway to get the best fitting model, but having some intuitive understanding of where to set the grid search limits will always help.