An autoregressive moving average (ARMA) process consists of both autoregressive and moving average terms. If the process has terms from both an AR(p) and MA(q) process, then the process is called ARMA(p, q) and can be expressed as
Topics
- Basic Concepts
- ARMA(1, 1) processes
- ARMA(p, q) processes
- Calculating model coefficients using maximum likelihood
- Calculating model coefficients using Solver
- Evaluating the model
- Forecasting
- Real Statistics data analysis tool
- Real Statistics ARMA tool options
For proofs of some of the properties, see ARMA Proofs.
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) 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
Hi Charles,
Thanks for your great website! I’m trying to work out which model to use to forecast price of a stock. I tried Real Statistics ACF function on daily returns and they seem autocorrelated. However, I need a month-long period forecasts. Monthly non-overlapping stock returns no longer appear autocorrelated, standard deviations of such monthly data are not stationary, and further differencing does not result in any stationary parameters. So non-overlapping monthly data then seem like pure white noise (random walk?). Does that mean that neither ARMA no ARIMA are suitable? What model can you suggest in this case?
Hello Alex,
I don’t understand the scenario well enough to be able to make a recommendation. Have you tested whether the data is indeed pure white noise?
Charles
Hi Charles,
No, I’ve not tested the data to see if it is pure white noise and I do not know such tests. Can you suggest some? I just assumed that if I cannot see autocorrelation and stationary variance for monthly stock returns, that implies the data is white noise.
Regards,
Alex