ARMA model: daily average discharge of Chattahoochee river (…

Questions

ARMA mоdel: dаily аverаge discharge оf Chattahоochee river (35 points) 2a. Leave the last 5 days of the data (July 28th to August 1st 2023) as test data and use the rest of the log-daily average discharge as training data. Fit an ARMA model using the training period of log-daily data. Find the order of the ARMA model using a max order 6 for p and q and max d of 1. Use AICc as the criterion for the order selection. What are the selected orders? Is your model causal?  2b. Plot the residual process for the model in 2a, its ACF and the QQ-plot. Comment on the goodness of fit.  2c. Fit a seasonal ARIMA(3,1,1) model, where the seasonal order is (1,0,1) with a period of 7 days( period = 7). Do not include the mean. Display the fitted coefficients and plot its residual ACF. Compare this model to the one fitted in 2a. Does the additional of seasonality improve the model fit? is there anything unusual in the model output? If yes, why? 2d. Use the fitted model in Question 2a and 2c and perform a 5-step ahead prediction of the log-daily average discharge for July 28th to August 1st 2023. You have to: Plot the predicted values from both models and overlaying the test values. Calculate the MAPE and the precision measure for both predictions. Comment on your results Which of the two error measures would you recommend use it to evaluate the forecasting performance of the two models? Why?

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