Skip to main content
SpringerLink
Log in

Comparison of hypothesis testing techniques for markov processes estimated from micro versus macro data

  • Part II Inference For Stochastic Models
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

We estimate the parameters of a Markov chain model using two types of simulated data: micro, or actual interstate transition counts, and macro aggregate frequency. We compare, by means of Monte Carlo experiments, the validity and power for micro likelihood ratio tests with their macro counterparts, previously developed by the authors to complement standard least-squares point estimates. We consider five specific null hypotheses, including parameter stationarity, entity homogeneity, a zero-order process, a specified probability value, and equal diagonal probabilities. The results from these micro-macro comparisons should help to indicate whether micro panel data collection is justified over the use of simpler state frequency counts.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I.G. Adelman, A stochastic analysis of the size distribution of firms, J. Amer. Statist. Assoc. 53(1958)893.

    Google Scholar 

  2. T.W. Anderson and L.A. Goodman, Statistical inference about Markov chains, Ann. Math. Statist. 28(1957)89.

    Google Scholar 

  3. I.V. Basawa and B.L.S. Prakasa Rao,Statistical Inference for Stochastic Processes (Academic Press, London, 1980).

    Google Scholar 

  4. F.K. Bedall, Test statistics for simple Markov chains. A Monte Carlo study, Biometrical Journal 20(1978)41.

    Google Scholar 

  5. P. Billingsley,Statistical Inference for Markov Processes (The University of Chicago Press, Illinois, 1961).

    Google Scholar 

  6. P. Billingsley, Statistical methods in Markov chains, Ann. of Math. Statist. 32(1961)12.

    Google Scholar 

  7. G.E.P. Box, W.G. Hunter and J.S. Hunter,Statistics for Experimenters (Wiley, New York, 1978).

    Google Scholar 

  8. G.C. Chow, Tests of equality between sets of coefficients in two linear regressions, Econometrica 28(1960)591.

    Google Scholar 

  9. L. Collins,Industrial Migration in Ontario: Forecasting Aspects of Industrial Activity through Markov Chain Analysis (Statistics Canada, Ottawa, 1972).

    Google Scholar 

  10. N.R. Collins and L.E. Preston, The size structure of industrial firms, American Economic Review 51(1961)986.

    Google Scholar 

  11. F.M. Fisher, Tests of equality between sets of coefficients in two linear regressions. An expository note, Econometrica 38(1970)361.

    Google Scholar 

  12. J.D. Kalbfleisch and J.F. Lawless, Least-squares estimation of transition probabilities from aggregate data, Can. J. Statist. 12(1984)169.

    Google Scholar 

  13. J.D. Kalbfleisch, J.F. Lawless and W.M. Vollmer, Estimation in Markov models from aggregate data, Biometrics 39(1983)907.

    Google Scholar 

  14. C.M.L. Kelton, Estimation of time-independent Markov processes with aggregate data: A comparison of techniques, Econometrica 49(1981)517.

    Google Scholar 

  15. C.M.L. Kelton, Nonstationary Markov modeling: An application to wage-influenced industrial relocation, Int. Regional Science Review 9(1984)75.

    Google Scholar 

  16. C.M.L. Kelton and W.D. Kelton, Advertising and intra-industry brand shift in the U.S. brewing industry, J. of Industrial Economics 30(1982)293.

    Google Scholar 

  17. C.M.L. Kelton and W.D. Kelton, Development of specific hypothesis tests for estimated Markov chains, J. of Statistical Computation and Simulation (1984), to appear.

  18. C.M.L. Kelton and W.D. Kelton, Markov process models: A general framework for estimation and inference in the absence of state transition data, in:Mathematical Modelling in Science and Technology, Proc. 4th Int. Conf. on Mathematical Modelling, ed. X.J. Avula et al. (Pergamon Press, Zurich, 1984) p. 299.

    Google Scholar 

  19. W.D. Kelton and C.M.L. Kelton, Hypothesis tests for Markov process models estimated from aggregate frequency data, J. Amer. Statist. Assoc. 79(1984)922.

    Google Scholar 

  20. S. Kullback, M. Kupperman and H.H. Ku, Tests for contingency tables and Markov chains, Technometrics 4(1962)573.

    Google Scholar 

  21. J.F. Lawless and D.L. McLeish, The information in aggregate data from Markov chains, Biometrika 71(1984)419.

    Google Scholar 

  22. T.C. Lee, G.G. Judge and A. Zellner,Estimating the Parameters of the Markov Probability Model from Aggregate Time Series Data, 2nd ed. (North-Holland, Amsterdam, 1977).

    Google Scholar 

  23. W.F. Lever, The intra-urban movement of manufacturing: A Markov approach, Transactions, Institute of British Geographers 56(1972)21.

    Google Scholar 

  24. P.A.W. Lewis, A.S. Goodman and J.M. Miller, A pseudo-random number generator for the system/360, IBM Systems Journal 8(1969)136.

    Google Scholar 

  25. E.C. MacRae, Estimation of time-varying Markov processes with aggregate data, Econometrica 45(1977)183.

    Google Scholar 

  26. A. Madansky, Least squares estimation in finite Markov processes, Psychometrika 24 (1959) 137.

    Google Scholar 

  27. J. Meredith, Selecting optimal training programs in a hospital for the mentally retarded, Oper. Res. 24(1976)899.

    Google Scholar 

  28. G.A. Miller, Finite Markov processes in psychology, Psychometrika 17(1952)149.

    Google Scholar 

  29. B.K. Shah, Data analysis problems in the area of pharmacokinetics research, Biometrics 32(1976)145.

    Google Scholar 

  30. S. Spilerman, The analysis of mobility processes by the introduction of independent variables into a Markov chain, American Sociological Review 37(1972)277.

    Google Scholar 

  31. M.A. Stephens, EDF statistics for goodness of fit and some comparisons, J. Amer. Statist. Assoc. 69(1974)730.

    Google Scholar 

  32. L.G. Telser, Advertising and cigarettes, The Journal of Political Economy 70(1962)471.

    Google Scholar 

  33. L.G. Telser, The demand for branded goods as estimated from consumer panal data, The Review of Economics and Statistics 44(1962)300.

    Google Scholar 

  34. H. Theil,Principles of Econometrics (Wiley, New York, 1971).

    Google Scholar 

  35. F.H. Trinkl, A stochastic analysis of programs for the mentally retarded, Oper. Res. 22(1974)1175.

    Google Scholar 

  36. A.P. Van der Plas, On the estimation of the parameters of Markov probability models using macro data, Ann. of Statist. 11(1983)78.

    Google Scholar 

  37. S.J. Yakowitz, A stochastic model for daily river flows in an arid region, Water Resources Research 9(1973)1271.

    Google Scholar 

  38. S.J. Yakowitz, Small-sample hypothesis tests of Markov order, with application to simulated and hydrologic chains, J. Amer. Statist. Assoc. 71(1976)132.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Wayne State University, Detroit, Michigan, USA

    C. M. L. Kelton

  2. Department of Management Sciences, University of Minnesota, 55455, Minneapolis, Minnesota, USA

    W. D. Kelton

Authors
  1. C. M. L. Kelton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. D. Kelton
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kelton, C.M.L., Kelton, W.D. Comparison of hypothesis testing techniques for markov processes estimated from micro versus macro data. Ann Oper Res 8, 175–194 (1987). https://doi.org/10.1007/BF02187090

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02187090

Keywords and phrases

Search

Navigation