Box-Jenkins

Box-Jenkins

In econometrics, the Box-Jenkins methodology, named after the statisticians George Box and Gwilym Jenkins, applies autoregressive moving average ARMA or ARIMA models to find the best fit of a time series to past values of this time series, in order to make forecasts.

Modeling approach

The original model uses an iterative three-stage modeling approach:

#"Model identification and model selection": making sure that the variables are stationary, identifying seasonality in the dependent series (seasonally differencing it if necessary), and using plots of the autocorrelation and partial autocorrelation functions of the dependent time series to decide which (if any) autoregressive or moving average component should be used in the model.
#"Parameter estimation" using econometric computation algorithms to arrive at coefficients which best fit the selected ARIMA model. The most common methods use maximum likelihood estimation or non-linear least-squares estimation.
#"Model checking" by testing whether the estimated model conforms to the specifications of a stationary univariate process. In particular, the residuals should be independent from each other and constant in mean and variance over time. (Plotting the mean and variance of residuals over time and performing a Ljung-Box test or plotting autocorrelation and partial autocorrelation of the residuals are helpful to identify misspecification.) If the estimation is inadequate, we have to return to step one and attempt to build a better model.The data they used was from a gas furnace. This data is well-known as the Box and Jenkins gas furnace data for benchmarking predictive models.

References

* Box, George and Jenkins, Gwilym (1970) "Time series analysis: Forecasting and control", San Francisco: Holden-Day.
* Pankratz, Alan (1983) "Forecasting with univariate Box–Jenkins models: concepts and cases", New York: John Wiley & Sons.

External links

* [http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc445.htm Box-Jenkins models] in the Engineering Statistics Handbook of NIST


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Box-Jenkins-Methode — Die Box Jenkins Methode oder das Box Jenkins Programm geht auf G. E. P. Box und G. M. Jenkins und ihr Buch aus dem Jahre 1970 Time Series Analysis Forecasting and Control zurück. Es markierte eine neue Epoche in der… …   Deutsch Wikipedia

  • Box-Jenkins Model — A mathematical model designed to forecast data within a time series. The Box Jenkin model alters the time series to make it stationary by using the differences between data points. This allows the model to pick out trends, typically using… …   Investment dictionary

  • Box-Jenkins-Verfahren — von G.E.P. Box und G.M. Jenkins entwickeltes parametrisches Verfahren zur statistischen ⇡ Zeitreihenanalyse und prognose. Man unterscheidet zwischen ⇡ AR(p) Prozessen, ⇡ MA(q) Prozessen, ⇡ ARMA(p,q) Prozessen und ⇡ ARIMA(p,d,q) Prozessen, wobei… …   Lexikon der Economics

  • Jenkins-Traub algorithm — The Jenkins Traub algorithm for polynomial zeros is a fast globally convergent iterative method. It has been described as practically a standard in black box polynomial root finders .Given a polynomial P ,:P(z)=sum {i=0}^na iz^{n i}, quad a… …   Wikipedia

  • Jenkins High School — Infobox School name = Jenkins High School native name = Herschel Vespasian Jenkins High School latin name = imagesize = caption = location = streetaddress = 1800 East Derenne Avenue region = city = Savannah state = Georgia county = Chatham… …   Wikipedia

  • Jenkins County — Verwaltung US Bundesstaat: Georgia Verwaltungssitz: Millen Adresse des Verwaltungssitzes: Jenkins County Administration P.O. Box 797 Millen, Georgia, 30442 0797 Gründung: 17. August 1905 …   Deutsch Wikipedia

  • Box Top Robbery — Infobox Rocky and Bullwinkle story arc name = Box Top Robbery caption = l to r: Rocky Bullwinkle, Boris Natasha (disguised as Hemlock Soames Watkins), Fiduciary J. Blurt season = 1 story arc =2 segments = 12 date start = April 1960 date conc =… …   Wikipedia

  • Gwilym Jenkins — Gwilym Meirion Jenkins (1933 – July 10, 1982) was a British statistician and systems engineer . His most notable contribution was pioneering work with George Box on autoregressive moving average models, also called Box Jenkins models, in time… …   Wikipedia

  • George E. P. Box — Infobox Scientist image width = 150px name = George E. P. Box box width = birth date = 18 October 1919 birth place = Gravesend, Kent, England death date = death place = residence = United Kingdom, United States citizenship = nationality =… …   Wikipedia

  • George Box — George Edward Pelham Box Naissance 18 octobre 1919 Gravesend (Angleterre) (Angleterre) Domicile Angleterre,Etats Unis Nationalité …   Wikipédia en Français

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”