An autoregressive integrated moving average (ARIMA) process (aka a Box-Jenkins process) adds differencing to an ARMA process. An ARMA(p,q) process with d-order differencing is called an ARIMA(p,d,q) process. Thus, for example, an ARIMA(2,1,0) process is an AR(2) process with first-order differencing.
Topics
References
Greene, W. H. (2002) Econometric analysis. 5th Ed. Prentice-Hall
https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/reference/referencespapers.aspx?referenceid=1243286
Gujarati, D. & Porter, D. (2009)Â Basic econometrics. 5th Ed. McGraw Hill
http://www.uop.edu.pk/ocontents/gujarati_book.pdf
Hamilton, J. D. (1994) Time series analysis. Princeton University Press
https://press.princeton.edu/books/hardcover/9780691042893/time-series-analysis
Wooldridge, J. M. (2009) Introductory econometrics, a modern approach. 5th Ed. South-Western, Cegage Learning
https://cbpbu.ac.in/userfiles/file/2020/STUDY_MAT/ECO/2.pdf
Hello Mr. Charles, my name is Andi. I would like to ask for your assistance. I have some historical data sets that I want to forecast for the next year. I would like to know which time series method is most suitable for analyzing this data. Is it possible for me to send the data to you? Thank you.
Hello Andi,
Thanks for sending me your data.
There are many techniques for “analyzing” your time series data. First, it is important to understand what you mean by “analyzing”. I assume that you are primarily interested in “forecasting.” Techniques such as regression, ARIMA, Holt-Trend, Holt-Winters, etc. can be used.
Which approach to user depends on whether your historical data has a trend, has seasonality, etc.
The data you have sent me only has a few periods of historical data, which limits the accuracy of the forecasts. You can apply a few different techniques and see which one(s) have the smallest residuals for the historical data.
Charles
Thank you for the response, Mr. Charles. Actually, I mentioned “analyzing” because I wanted to know, based on the data I provided, which forecasting method would be best. I apologize; I am a beginner in statistics, especially time series analysis. Regarding the residuals, how can I determine the smallest residual among those methods? Is it through using MAE, MSE, or MAPE? Lastly, when I tried simulating ARIMA with one of the attached datasets (for example,
Year Utilization Number
2019 2
2020 3
2021 6
2022 4
2023 6 ),
I received an error message saying “Input Range must have exactly one column of data.” However, when I ran it the same way with the Holt Linear method, the simulation worked fine. Please provide guidance on this matter. Thank you.
Charles, appreciate the work you’ve done to build this package. I’ve done a simple ARIMA(1,0,0) and as I use the results equation to compute and plot a backcast, it appears I am one period off. It is as though the results are not predicting this period’s price but last period’s price when I expected it to give me this period based on last period. I can see this when I plot the result and see that they match up against the recorded data much better if I shift them by one period. What am I misinterpreting about the equation or result coefficient and constant cells?
Hello Catherine,
Are you observing this from one of the examples on the Real Statistics website? If not, can you email me an Excel spreadsheet with your data and results so that I can see first hand what you are saying?
Charles
This is a sheet we developed. What address should I use to send it to you?
Hello Catherine,
See Contact Us.
Charles
Hi Charles,
Can you please tell, how to calculate Alpha and Gamma in ARIMA process ? I have interval wise data.
Regards,
Veeru
The Real Statistics ARIMA data analysis tool will calculate the regression coefficients for you. I don’t call them alpha and gamma, but these are probably the phi and omega coefficients that you are referring to, although if you are using Holt-Winter then theya re called alpha, beta and gamma. In any case, see
https://www.real-statistics.com/time-series-analysis/arima-processes/arima-model-coefficients/
Charles
Hello Mr Charles, I want to know if there is a mistake in this statement of yours above where you said:
“Thus, for example, an ARIMA(2,0,1) process is an AR(2) process with first-order differencing”
Did you mean ARIMA(2,1,0)?
Or you want to say ARMA(2,1) with 0 differencing process
Hello Fountain,
I used a designation of ARIMA(p,q,d). Based on this designation, what I wrote was correct. However, it is more common to use the designation ARIMA(p,d,q). I have now changed the webpage to use this designation.
Thank you for catching this issue. I appreciate your help in improving the website.
Charles
Thanks for the reply, your webpage is the best webpage i have ever seen as regard excel and statistics, pls i hope you can share us more links to learn some theories that are not covered in this webpage like sampling technique and operations research
Fountain,
Thank you for your kind words. I am continuously adding new topics to the website and software. Sampling techniques and operations research are broad topics. Are these some subtopics that are especially interesting to you?
Charles
Yes, I am trying to specialize myself in the field of operations research and I sampling techniques is fun to work with as well.
Hi Charles,
I’m using your Seasonal ARIMA via the Excel Add-In, and was wondering if it is possible to produce prediction/confidence intervals for the model? Or if you alternatively have any guidance on how to manually compute this?
Thank you
Hello Peter,
I have not yet included this in Real Statistics. Perhaps the following link will be useful>
https://pdfs.semanticscholar.org/ed89/b95c7c6978b52e6276aa6106019cea8f76a7.pdf
Charles
Can we use ARIMA model to forecast wind energy and for how much long duration we can use it. I have data for 2 years and for every 15 minutes.
Ram,
Yes, you can use ARIMA for this purpose, but I can’t say whether this is the best approach or not. This depends on the details.
Charles