Again, I find myself drawn-in to a Linked-In question that forces me to clearly articulate my understanding:
Question: Could some one explain the ARIMA forecasting model in a simplified manner?
My Answer:
An autoregressive integrated moving average (ARIMA) models are best understood in the context of Box–Jenkins methodology, who’s steps are as follows:
- Model identification and model selection.
- Parameter estimation.
- Model checking.
Box–Jenkins methodology applies autoregressive moving average (ARMA) or ARIMA models to find the best fit of a time series to past values of a time series, in order to make forecasts and understand the underlying process/es. Briefly put, the model selected is the simplest one that accounts for the properties of the time series, then the parameters for the specific model are chosen for best fit to the data, and then the model and parameters are checked for the appropriate mathematical properties (namely, being stationary, meaning parameters such as the mean and variance do not change over time). Simply put, ideally the process leaves us with a model that captures the structure in the time series, with a residual that is simply noise.
So, why use ARIMA models instead of ARMA ? ARIMA models are used instead of ARMA models when the time series exhibits non-stationarity (i.e. parameters such as the mean and variance change over time), and are thus more general than ARMA. ARIMA encompasses random-walk and random-trend models, autoregressive models, and exponential smoothing models, etc.
How does it do this? Let’s start with a semi-formal definition of ARIMA(p,d,q) model, where:
- p is the number of autoregressive terms,
- d is the number of nonseasonal differences, and
- q is the number of lagged forecast errors in the prediction equation.
such that p, d, and q are integers greater than or equal to zero and refer to the order of the autoregressive, integrated, and moving average parts of the model, respectively. So p captures the order of an autoregressive model (a linear regression of the current value of the series against one or more prior values of the series); d is the order of the differencing used to make the time series stationary; and q is the order of the moving average model (a linear regression of the current value of the series against the white noise or random shocks of one or more prior values of the series). Permutations of integer values for all of these components define a large family of time series models to fit to data. It is with this family, and fairly simple addition of seasonal components, that many statistical packages allow us to model/fit time series with an ARIMA.
NOTE: To really understand and apply ARIMA correctly requires a mathematical understanding of everything stated above. See the links at bottom for a start on the mathematical definitions that substantiate the conceptual overview provided.
I hope that this is of some help.
Links:
These are my links for August 24th through August 27th:
- Andrew Wayne & Michal Arciszewski, Emergence in physics | PhilPapers – This paper begins by tracing interest in emergence in physics to the work of condensed matter physicist Philip Anderson. It provides a selective introduction to contemporary philosophical approaches to emergence. It surveys two exciting areas of current work that give good reason to re-evaluate our views about emergence in physics. One area focuses on physical systems wherein fundamental theories appear to break down. The other area is the quantum-to-classical transition, where some have claimed that a complete explanation of the behaviors and features of the objects of classical physics entirely in quantum terms is now within our grasp. We suggest that the most useful way to approach the emergent/non-emergent distinction is in epistemic terms, and more specifically that the failure of reductive explanation is constitutive of emergence in physics.
- SISA allows you to do statistical analysis directly on the Internet. – SISA allows you to do statistical analysis directly on the Internet. Click on one of the procedure names below, fill in the form, click the button, and the analysis will take place on the spot. Study the user friendly guides to statistical procedures to see what procedure is appropriate for your problem.
- Wrong Tomorrow – time vs. pundits – What does this site do?It keeps track of predictions of the future by public figures.
How does it work?
When someone makes a prediction, people post it to the site along with a brief description and a URL. We monitor it and change its status to true or false when appropriate.
What are the submission criteria?
1. The prediction needs to make an empirically testable claim about the world.
2. The prediction should be significant.
3. The prediction must be by a public figure.
4. The prediction should be testable within five years.
5. Negative predictions (about things that are never expected to happen) are allowed.
What is the purpose of this site?
Research has shown that experts make predictions at a rate worse than chance. This site exists in order to hold people and media outlets accountable for pretending to see into an unpredictable future.
- OpenSecrets.org: Money in Politics — See Who’s Giving & Who’s Getting – OpenSecrets.org is your nonpartisan guide to money’s influence on U.S. elections and public policy. Whether you’re a voter, journalist, activist, student or interested citizen, use our free site to shine light on your government. Count cash and make change.
These are my links for June 30th from 10:03 to 13:45:
- Statistical Resources on the Web/Environment –
- Data Mining Community’s Top Resource – Data Mining Community's Top Resource Since 1997 for Data Mining and Analytics Software, Jobs, Consulting, Courses, Education, News, and more.
- Time Series Analysis – In the following topics, we will first review techniques used to identify patterns in time series data (such as smoothing and curve fitting techniques and autocorrelations), then we will introduce a general class of models that can be used to represent time series data and generate predictions (autoregressive and moving average models). Finally, we will review some simple but commonly used modeling and forecasting techniques based on linear regression.
- Free Online Course Materials | MIT OpenCourseWare – Free lecture notes, exams, and videos from MIT.
No registration required.
- NIST/SEMATECH e-Handbook of Statistical Methods –
These are my links for June 28th through June 30th:
- Time Series Analysis for Business Forecasting – Realization of the fact that “Time is Money” in business activities, the dynamic decision technologies presented here, have been a necessary tool for applying to a wide range of managerial decisions successfully where time and money are directly related. In making strategic decisions under uncertainty, we all make forecasts. We may not think that we are forecasting, but our choices will be directed by our anticipation of results of our actions or inactions.Indecision and delays are the parents of failure. This site is intended to help managers and administrators do a better job of anticipating, and hence a better job of managing uncertainty, by using effective forecasting and other predictive techniques.
- predict.i2pi csv upload – predict.i2pi lets you upload a CSV file with observations and will try to come up with predictions for the data.
- NetMBA Business Knowledge Center – ICMBA’s mission is to provide quality business knowledge resources to a geographically dispersed audience via the Internet. Via this web site, ICMBA publishes articles covering a range of topics in the various subjects of business administration. Over time, the articles will cover both basic and advanced topics, and include frameworks and theories that are useful for solving the more challenging problems of business administration.The content of this site is designed to be beneficial to both students of business and practicing professionals. Students will find it useful for deepening their understanding of key course topics. We hope that business professionals will find it to be a good reference source, particularly when their library of business books is not easily accessible.
- Netflix Prize: Home – The Netflix Prize seeks to substantially improve the accuracy of predictions about how much someone is going to love a movie based on their movie preferences. Improve it enough and you win one (or more) Prizes. Winning the Netflix Prize improves our ability to connect people to the movies they love.
- Math Magic – Math Magic is a web site devoted
to original mathematical recreations.
If you have a math puzzle,
discovery, or observation, please
e-mail me about it.
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