generate standard errors serie after autoarima

[rafrods]

Hello.
I'm doing payroll forecasting exercises and I have a monthly historical series with data between January 2016 and July 2023 (folha1), and I intend to make the forecast for the months of August until December 2023.

After doing the autoarima (the result indicated was for a model (0,1)(1,1) as shown in the images autoarimaestimation setup 1 and autoarimaestimation output1), my first question is: can I generate the series with the standard errors +-2 S.E., for the autoarima series generated? (just like it is generated in the forecast from an equation)?

One of the ways I managed to generate it was by making a manual prediction from quick -> estimate equation -> I inserted the equation generated by autoarima (as shown in the image autoarimaquickestimation setup and autoarimaestimations quick x autoarima outputs) -> from the output I went to proc -> forecast -> and I made a forecast for the same period (according to the image forecastfolha1 setup)

The forecast generated was the same as autoarima (according to the image autoarima and forecast estimation results (same results)), and I could have selected the option to generate the series corresponding to the standard error, and generate the two series of standard errors from of commands:

series name of the series generated in the forecast_high1 = name of the series generated in the forecast + 2*name of the series of standard errors generated in the forecast

series name of the series generated in the forecast_low1 = name of the series generated in the forecast - 2*name of the series of standard errors generated in the forecast

PS: (Autoarima doesn't have the option for generate the standard errors series, like forecast setup have the "S.E. (optional):")

However, I have a second issue that compromised the generation of standard error series from the above procedure because, from the moment I had access to the August and September data, I updated my database, consisting of a monthly historical series with data between January 2016 and September 2023 (folha2), and I made the forecast for the months of October to December 2023.

After doing the autoarima (the result indicated was also for a model (0,1)(1,1) , as shown in the images autoarimaestimation setup 2 and autoarimaestimation output2)), and as I don't know how to generate the series with standard errors from the series generated by autoarima, I proceeded along the same path mentioned previously: manual prediction from quick -> estimate equation (as per the image autoarimaquickestimation setup 2 and autoarimaestimations quick x autoarima outputs 2) -> I inserted the equation generated by autoarima -> from the output I went to proc -> forecast -> and made a forecast for the same period (as per the image forecastfolha2 setup)

However, the series generated by the forecast was different from the series generated by Autoarima (as shown in the image autoarima and forecast estimation sheet2 results (different results)), preventing me from generating the two series of standard errors using the commands mentioned previously.

I found it strange because for the series between January 2016 and July 2023, the forecast based on an estimation with the parameters pointed out by autoarima coincided with the forecast generated by autoarima, and for the series between January 2016 and September 2023, the prediction based on an estimation with the parameters indicated by autoarima, was different from the prediction generated by autoarima.

That would be the second question, is this difference in predictions possible?

Attached is my workfile and some prints.

[rafrods]

Attachments in

https://drive.google.com/drive/folders/ ... sp=sharing

[EViews Gareth]

Can you provide instructions on how to replicate this?

[rafrods]

Can you provide instructions on how to replicate this?

I sent the Eviews workfile with the printscreens on the google drive link above.

By the way, i sent the Eviews workfile again and the instructions.

1) Open "folha1" file -> proc -> automatic arima forecast (select auto (none/log), estimation sample 2016m01 2023m07, forecast lenght 5 - until 2023m12), max diff 2, max AR 4, max MA 4, Max SAR 2, Max SMA 2, periodicity 12, Regressors = C, Model Selection - Schwarz), output forecast name = autoarimafolha 1
2) I saw the especification (0,1)(1,1), and reproduce the arima forecast from the equation appointed by automatic arima forecast: d(folha1) c ar(12) ma(1) sma(12).
3) From the equation output result (the same as from automatic arima forecast), i click on forecast buttom (forecast from equation), select folha1 as serie to forecast, dynamic forecast, give a name for the forecast (forecastfolha1) and for the S.E. (optional), and put the forecast sample as 2023m08 to 2023m12.
4) comparing the serie results from automatic arima forecast and from forecast from equation, the results is the same (autoarimafolha1 and forecastfolha1)
5) I create another serie inserting the data of 2023m08 and 2023m09 (named folha2) and did the same procedure as appointed in "1" (changing the forecast lenght to 3, and named the output forecast as autoarimafolha2), "2" (d(folha2) c ar(12) ma(1) sma(12)), "3" (changing the forecast sample as 2023m09 to 2023m12, and the name of the forecast - forecastfolha2).
6) the comparision of the serie results from automatic arima forecast and from forecast from equation is different for the new serie (autoarimafolha2 and forecastfolha2).

[EViews Gareth]

In the equation you created, change the optimization method to OPG

[rafrods]

In the equation you created, change the optimization method to OPG

Thank you. It seems ok.