ESTIMATING DIFFERENTIAL EQUATION MODELS ON TIME SERIES SOME SIMULATION EVIDENCE

• NCJ Number: 63805
• Journal: Sociological Methods and Research Volume: 8 Issue: 1 Dated: (AUGUST 1979) Pages: 3-33
• Author(s): P DOREIAN; N HUMMON
• Date Published: 1979
• Length: 31 pages
• Corporate Author: Sage Publications, Inc
• Publication Format: Article
• Publication Type: Vocabulary/Thesaurus
• Language: English
• Country: United States of America
• Note: REVISED VERSION OF A PAPER PRESENTED TO THE FIFTH INTERNATIONAL SYMPOSIUM ON MUTTIVARIATE ANALYSIS, UNIVERSITY OF PITTSBURGH, JUNE 19-24, 1978

Annotation

THIS SOCIOLOGICAL RESEARCH PAPER EXPLORES THE STATISTICAL PROPERTIES OF ESTIMATES PROPOSED FOR SYSTEMS OF SIMULTANEOUS DIFFERENTIAL EQUATION SYSTEMS.

Abstract

DIFFERENTIAL EQUATIONS WERE USED IN A PREVIOUS STUDY TO MODEL LABOR TURNOVER AND GOVERNMENTAL POPULARITY. IN ORDER TO ESTIMATE DIFFERENTIAL EQUATION MODELS, CERTAIN DATA REQUIREMENTS NEED TO BE MET. THIS PAPER ASSUMES THE FOLLOWING REQUIREMENTS: (1) THERE IS A SUBSTANTIVE PROBLEM AREA WHERE A DIFFERENTIAL EQUATION MODEL IS FEASIBLE AND (2) THERE IS A BODY OF TIME SERIES DATA THAT CAN BE USED TO ESTIMATE THE DIFFERENTIAL EQUATION MODEL. THE MODEL IS THEN APPLIED TO BRITISH GOVERNMENT POPULARITY TIME SERIES DATA. THE ESTIMATION PROCEDURE WAS THE ITERATIVE SEARCH ALREADY DESCRIBED. SINCE THE PROCEDURES WERE ITERATIVE AND COMPUTATIONALLY BURDENSOME, ALTERNATIVE SIMPLER METHODS WERE ALSO EXPLORED VIA MONTE CARLO SIMULATIONS. THE SIMPLER METHODS PROVIDED REASONABLY GOOD DIAGNOSTICS AS TO WHETHER OR NOT THE MORE COMPLICATED PROCEDURES WERE WORTHWHILE. PROBLEMS OF AUTOCORRELATION, INTEREQUATION LINKAGE, AND ERROR VARIANCE WERE SYSTEMATICALLY VARIED, AND THE EFFECTS OF THESE VARIATIONS ON THE PARAMETER ESTIMATES WERE DETAILED. TABLES, NOTES, AND REFERENCES ACCOMPANY THE REPORT. (AUTHOR ABSTRACT MODIFIED-MJW)