# Time Series analysis ARIMA

I am trying to predict "daily_cases" using time series analysis. The time series plot looks like -

The ACF plot of original series is given below-

The above ACF plot suggests that trend is present which needs to be removed using appropriate differencing.

The ACF and PACF plots of 1-differenced series are given below-

The above plots suggest an ARMA(1,1) process which was also validated by "arma_order_select_ic()" function in python on the basis of "aic" and "bic" scores.

But, after fitting the model I get weird fitted values ,which were way different from observed values(differing by 10000!).

• Hi: I know that the I in ARIMA stands for integrated. What I'm saying is that, when you make the call to the ARIMA function in python, it may be giving you the fitted model AFTER THE SERIES IS DIFFERENCED. If you want to predict the original data, you need to figure out what the predictions about the differenced series imply about the predictions of the not differenced series. Say it was ARIMA(1,1,0). Then the estimated modelis $Y_t - Y_{t-1} = \phi (Y_{t-1} - Y_{t-2})$ but this is the differenced series. So, fitted's will be differences. – mlofton Jul 27 at 21:07