Box jenkins method of forecasting

Box jenkins method of forecasting, stationary non stationary data sets

1. OPERATIONS MANAGEMENT
By-:
Er. Vaibhav Agarwal
Asst. Prof.
SOM, BBDU
Lucknow
BOX-JENKINS METHOD OF
FORECASTING

2. BOX-JENKINS METHOD OF FORECASTING
•In time series analysis, the Box–Jenkins method, named after the statisticians George Box and Gwilym
Jenkins.
•Box-Jenkins Model is a mathematical model designed to forecast data within a time series.
•Time-Series is of two types:
TIME-
SERIES
STATIONARY
SEASONAL
NON-
SEASONAL
NON-
STATIONARY
SEASONAL
NON-
SEASONAL

3. If the ACF(autocorrelation factor) of the time series values either cuts off or dies down
fairly quickly, then the time series values should be considered STATIONARY.

4. If the ACF (auto correlation factor) of the time series values either cuts off or dies down
extremely slowly, then it should be considered NON-STATIONARY .

6. •Astationaryprocessisonewhosestatisticalpropertiesdonotchangeovertime.
•Anon-stationaryprocess/time-serieshavepropertieswhichchangeovertime.
•TheBox-Jenkinsmodelaltersthenon-stationarytimeseriestomakeitstationarybyusingthe
differencesbetweendatapoints.
•AllstationarytimeseriescanbemodeledasAutoRegressive(AR)orMovingAverage(MA)or
ARMAmodels.
•TheBOX-JENKINSmethodappliesAutoregressiveMovingAverageARMAorARIMAmodels
tofindthebestfitofatime-seriesmodeltopastvaluesofatimeseries.
•Thisallowsthemodeltopickouttrends,typicallyusingautoregresssion,movingaveragesand
seasonaldifferencinginthecalculations.

7. DEFINITIONof'AutoregressiveIntegratedMovingAverage-ARIMA.
•Astatisticalanalysismodelthatusestimeseriesdatatopredictfuturetrends.
•Box-Jenkins(ARIMA)isanimportantforecastingmethodthatcanyieldhighlyaccurate
forecastsforcertaintypesofdata.
•Itisaformofregressionanalysisthatseekstopredictfuturemovements.
•Itconsiderstherandomvariations.
•Itexaminingthedifferencesbetweenvaluesintheseriesinsteadofusingtheactualdata
values.
•Lagsofthedifferencedseriesarereferredtoas“autoregressive"andlagswithinforecasted
dataarereferredtoas“movingaverage”.

8. •ThismodeltypeisgenerallyreferredtoasARIMA(p,d,q),model.
•prepresentsautoregressive,
•drepresentsintegrated,and
•qrepresentsthemovingaveragepartsofthedataset.
•ARIMAmodelingcantakeintoaccounttrends,seasonality,cycles,errorsandnon-
stationaryaspectsofadatasetwhenmakingforecasts.
•AseasonalBox-JenkinsmodelissymbolizedasARIMA(p,d,q)*(P,D,Q),wherethep,d,q
indicatesthemodelordersfortheshort-termcomponentsofthemodelandP,D,Q
indicatethemodelordersfortheseasonalcomponentsofthemodel.

9. •Box-Jenkinsisanimportantforecastingmethodthatcangeneratemoreaccurateforecaststhan
othertimeseriesmethodsforcertaintypesofdata.
•Asoriginallyformulated,modelidentificationrelieduponadifficult,timeconsumingandhighly
subjectiveprocedure.
•Today,softwarepackagessuchasForecastProuseautomaticalgorithmstobothdecidewhentouse
Box-Jenkinsmodelsandtoautomaticallyidentifytheproperformofthemodel.
•Box-Jenkinsmodelsaresimilartoexponentialsmoothingmodels.
•Box-Jenkinsmodelsareadaptive,canmodeltrendsandseasonalpatterns,andcanbeautomated.
•Box-Jenkinsmodelsarebasedonautocorrelations(patternsintime)ratherthanastructuralviewof
level,trendandseasonality.
•Box-Jenkinstendstosucceedbetterthanexponentialsmoothingforlonger,morestabledatasets
andnotaswellfornoisier,morevolatiledata.

10. The Box-Jenkins methodology
has four steps:
•Model Identification,
•Estimation,
•Diagnostics checking,
•Forecasting.

11. THANK YOU
REFERENCES:
1.‘The Box-Jenkins Methodology for Time Series Models’, Theresa Hoang Diem Ngo,
Warner Bros. Entertainment Group, Burbank, CA, SAS Global Forum 2013, Paper 454-
2013.
2.https://en.wikipedia.org/wiki/Box%E2%80%93Jenkins
3.http://www.forecastpro.com/Trends/forecasting101June2012.html
4.‘Stationary and non-stationary time series’, G. P. Nason, Chapter 11.
5.A Study of Sales Data using Box-Jenkins ARIMA Techniques, MichaelmasTerm, Sample
Report, 2011.