Recursive Algorithms of Time Series Observations Recognition

Abstract. The paper presents new method for sequential classification of the time series observations. Methods and algorithms of sequential recognition are obtained on the basis of the recursive equations for sufficient statistics. These recursive equation

INFORMATICA,2000,Vol.11,No.3,311–324311©2000InstituteofMathematicsandInformatics,Vilnius

RecursiveAlgorithmsofTimeSeriesObservationsRecognition

EdwardSHPILEWSKI

InstituteofMathematicsandInformatics

Go tauto12,2600Vilnius,Lithuania

e-mail:edwszp@ktl.mii.lt

Received:May2000

Abstract.Thepaperpresentsnewmethodforsequentialclassi cationofthetimeseriesobserva-tions.Methodsandalgorithmsofsequentialrecognitionareobtainedonthebasisoftherecursiveequationsforsuf cientstatistics.Theserecursiveequationsallowtoconstructalgorithmsofcur-rentclassi cationofobservablesequencesintherateofenteringitsvaluesintotheon-lineopera-tion.Classi cationalgorithmsarerealizedintheformofcomputerprograms,includingpersonalcomputers.Theyallowtobuildmulti-channelconveyercomputationalstructuresforthesequentialrecognizersoftimeseriesobservations.

Keywords:timeseries,processesclasses,samples,sequentialclassi cation.

1.Introduction

RecognitionofrandomprocessesbasedonadescriptionofclassesbydynamicmodelintheformofdifferentialanddifferencestochasticequationswasconsideredinapaperbyShpilewski(1971)andbyPetrowandShpilewski(1974).Further,theMarkovmod-elsgainedawidedisseminationinpractice(Shpilewski,1980).Theproposedapproachtotherecognitionofstationaryrandomprocessesappearedtobeextremelyfruitful.Itallowedtoobtainconstructivemethodsofrecognitionofrandomprocesseswithcontin-uousanddiscretetime,toworkoutdynamicclassi cationalgorithmsintherecognitionofsequencesincurrenttime.

SequentialrecognitionofMclassestimeseriesobservationareconsideredinthegivenpaper.Apracticallyimportantclassofstochasticmodelsfordescribingadiscreterandomprocessesare(Box,Jenkins,1970):

–autoregressiveprocessesoforderp,AR(p)

y[n]= p

am[i]y[n i]+v[n],(1)

i=1

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