In this assignment you will work on your project ARIMA section. Complete each of the following sections.
a) Examine your Y data (excluding the hold out period) to determine if it needs to be differenced to make it stationary. Show a time series plot of the raw Y data and autocorrelation functions (ACFs).
b) From your time series data plot and AFCs determine if you have seasonality. If you do, use seasonal differences to remove it and run the ACFs and PACFs on the non seasonal Y data series.
c) Fill out the ARIMA seasonal menu (P,D,Q) appropriately. If you have no trend as shown by the seasonally differenced ACFs run the ARIMA model and note the significance of each coefficient. Make model adjustments accordingly to improve results.
Note: You maynotuse an ARIMA model with non significant coefficients to forecast. If the coeffcients are not signficant derive another model that has signficant coefficents and the lowest residual MS value.
d) If it requires differencing for trendto make it stationary do so and run another time series plot and ACFs on the differenced data. If this requires differencing again do so but run time series plots and ACFs each time you do.
e) Run and show the PACFs on your stationary data series and identify the appropriate ARIMA model and show the initial ARIMA non seasonal menu section(p,d,q) filled out appropriately and any seasonal (P,D,Q) components in the seasonal menu filled out.
f) Run the ARIMA model and note the significance of each coefficient. Make model adjustments accordingly to improve results shown by the residual MS or MSE.
g) Calculate the two error measures that you used in other model analysis and comment on the acceptability of the size of the measure.
h) Note the LBQ associated P values for the selected lags. They should each be significant (above .05) to declare the residuals random. If they are not random select an alternative ARIMA model form that has random residuals.
i) Run an ARIMA forecast for your hold out period and show a time series plot of the residuals (Y actual and Y forecast) for the hold out period.
j) Calculate the hold out period MSE, RMSE and MAPE (Refer back to earlier chapters for the error measure formulas) and compare them to the Fit period ARIMA error measures (from g above).

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