THREE-STAGE ITERATIVE PROCEDURE FOR SPACE-TIME MODELING

• NCJ Number: 60692
• Journal: Technometrics Volume: 22 Issue: 1 Dated: (FEBRUARY 1980) Pages: 35-47
• Author(s): P E PFEIFER; S J DEUTSCH
• Date Published: 1980
• Length: 13 pages
• Grant Number(s): 75NI-99-0091; 78NI-AX-004
• Sponsoring Agency: US Dept of Justice; US Dept of Justice NIJ Pub
• Sale Source: National Institute of Justice/
• Publication Type: Statistics
• Language: English
• Country: United States of America
• Note: REPRINT

Annotation

THIS PAPER DESCRIBES THE EXTENSION OF A THREE-STAGE ITERATIVE MODEL BUILDING PROCEDURE TO ACCOMMODATE THE SPACE-TIME AUTOREGRESSIVE MOVING AVERAGE (STARMA) MODELS USING RAW ARREST DATA FROM BOSTON.

Abstract

THE EMPIRICAL MODEL OF THE MULTIPLICATIVE AUTOREGRESSIVE MOVING AVERAGE MODEL FAMILY, TOGETHER WITH THE MODEL BUILDING PROCEDURE KNOWN AS THE BOX-JENKINS METHOD, HAVE PROVEN USEFUL IN VARIED STATISTICAL ANALYSES. HOWEVER, THESE MODELS ARE UNIVARIATE AND CAN ONLY DEAL WITH HISTORY AT ONE PARTICULAR POINT OR REGION IN SPACE. MULTIVARIATE TIME SERIES MODELING IS AN ALTERNATIVE. FURTHER REFINEMENT CAN OCCUR IF THE SYSTEM TO BE MODELED EXHIBITS SYSTEMATIC DEPENDENCE BETWEEN OBSERVATION AT EACH REGION AND OBSERVATIONS AT NEIGHBORING REGIONS. THIS IS CALLED SPATIAL CORRELATION. THE PAPER PROPOSES A COMPREHENSIVE CLASS OF STARMA MODELS; DEVELOPS GENERAL PROCEDURES FOR THE IDENTIFICATION STAGE IN WHICH A TENTATIVE STARMA MODEL IS SELECTED; DESCRIBES THE SECOND STAGE OF THE MODELING PROCEDURE, ESTIMATION (OR THE FITTING) OF THE TENTATIVE MODEL; AND EXAMINES THE LAST STAGE, DIAGNOSTIC CHECKING. FINALLY, RAW ARREST DATA (TOTAL ASSAULTS WERE CHOSEN AS THE MODEL) FROM 822 REPORTING AREAS IN BOSTON WERE COMBINED TO GIVE MONTHLY FIGURES FOR 14 NORTHEAST BOSTON AREAS. THIS ANALYSIS PROVIDES SUBSTANTIAL APPLICATION OF THE SPACE-TIME MODEL CLASS AND ITS ASSOCIATED MODELING PROCEDURES. MATHEMATICAL EQUATIONS, CHARTS, FIGURES, AND REFERENCES ARE INCLUDED. (AUTHOR ABSTRACT MODIFIED)