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I have generated the ARIMAX(1,1,1) model to predict the future Barramundi catch. In this model, there are two exogenous variables (price and streamflow) that affect Barramundi catch. I have used 1st differenced data to run this model as the data was not stationary at level. Could you please help me out to identify the equation for it and how can I use this equation for the future prediction of catch especially for the undifferenced data? Here,[ARIMA(1,1,1) output]1 I have attached an excel file of my data. ARIMA data

Sabiha Sultana Marine
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  • The original data doesn't have to be anything ..other than equally spaced. There is no need for any differencing on any of your series at any level. Please follow https://stats.stackexchange.com/questions/221072/why-is-prewhitening-important/305634#305634 and https://autobox.com/pdfs/A.pdf . Note that your ma(1) -.947503 coefficient essentially cancels the unwarranted differencing operator. – IrishStat May 17 '19 at 19:53
  • Your data (should be coded) was over-differenced as suggested by your ma coefficient (-.9457) nearly -1.0 . Model the original data with two positive level shifts ( periods 123 and periods 309 ) and 1 downwards level shift at period 305. Note well that non -stationarity is a symptom with possible different causes. – IrishStat May 19 '19 at 20:41
  • ignore the level shift down reflection. – IrishStat May 19 '19 at 20:47
  • @IrishStat Thank you very much for your suggestions! I had to difference the series as the ACF of undifferenced series has a higher number of significant lags at lag 10, lag11, and lag 13 and the residual of the ARIMAX (1,0,1) model is autocorrelated. That's why I had to go for the differencing scheme. The residuals of ARIMA (1,1,1) has no serial correlation up to lag 9. Please click the following link, here I have attached the result of my ARIMAX modelling in details. https://1drv.ms/w/s!AgVYhKx6P-C2lXlz4OfthbcFYHuw – Sabiha Sultana Marine May 21 '19 at 01:40
  • Your logic to difference is flawed as it is based upon the outlier-impacted acf of the original series while assumptions are placed on the residuals from a useful model. Unfortunately you ignored the concept of adjusting for level shifts as that is another way of remedying non-stationarity. If you plot your residuals ( as you should always do unless you want to commit an error of omission) I think that you will not be happy with your over-differenced model. You might want to include that plot of the error residuals here for completeness sake. – IrishStat May 21 '19 at 09:12
  • the high acf at longer lags that you interpreted as being remedied by differencing was the result of the omitted but significant (seasonal) causal series when conducting a univariate analysis of Y . Your real question was not how to interpret/undifference but rather how good is my (potentially complicated) model ? – IrishStat May 21 '19 at 09:44
  • Thanks @IrishStat I will work on it. I thought that my model was okay and thats why I was asking for the equation for this model. However, I have some more data from another site for ARIMAX modelling, if that model suggests ARIMAX (1,1,1), then how can I apply the equation in my undifferenced (original data not 1st differenced data) series in excel? Please let me know. Thank you. – Sabiha Sultana Marine May 21 '19 at 10:28
  • I am unable to post to this question because it is closed. If you contact me directly I will be more than happy to help you. – IrishStat May 21 '19 at 11:12
  • @IrishStat Thank you very much for your reply. In your profile, I didnot get any personal message option. However, I'm available at my email address (marine.ftqc@sau.ac.bd). I would be happy to get your suggestions through email. Thanks. – Sabiha Sultana Marine May 21 '19 at 11:21

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