An ARFIMA multi-level model of dual-component expectations in repeated cross-sectional survey data

Abstract

Expectations for price in financial markets continue to be extensively investigated in multi-component models. An empirical assessment of the components of these models is challenged by the form of measured expectations in single components and sampling in repeated cross-sectional designs. We report an operationalization of a multi-component model of expectations in cross-sectional and time series data that are estimated in an ARFIMA multi-level model. Our results indicate the significance of measures of components we define at both agent and aggregate levels in predicting a widely cited measure of consumer expectations.

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Notes

  1. 1.

    Gallup, Graham-Harvey, American Association of Individual Investors, Index of Consumer Sentiment and Shiller Indices.

  2. 2.

    Here, as elsewhere, “neighbors” are assumed to be those that share distinct correspondences in key socio-demographics with an agent. In competitive markets for assets such as equities, note that there can be practical as well as emotion-based reasons for being influenced by neighbors. It may be that non-professional agents assume that the consensus of others generally provides better information on the metrics of an asset price than they have as individuals.

  3. 3.

    If exogenous variables vary within each time period (e.g., month), means should be calculated and appropriate noise models generated for each \(\bar{X}_{t}\).

  4. 4.

    While time series of the aggregate level ICS have historically been available, the Survey Research Center has recently been funded to make the cross-sectional data available. We remove the less than 5% of the cases with multiple missing values from the data.

  5. 5.

    The respective Q statistics for 40 lags were: residual ICS (37.789), total return (25.848), price–dividend ratio (24.037), ten-year bond (52.246). All p (not white noise) > 0.10.

  6. 6.

    Definitions of the forecasting alternatives are provided in Online Appendix Table A. 2.

References

  1. Andersson M, Hedesström M, Gärling T (2014) A social-psychological perspective on herding in stock markets. J Behav Finance 15(3):226–234

    Google Scholar 

  2. Arlot S, Celisse A (2010) A survey of cross-validation procedures for model selection. Stat Surv 4:40–79

    Google Scholar 

  3. Arrow KJ (1986) Rationality of self and others in an economic system. J Bus 59:S385–S399

    Google Scholar 

  4. Arthur WB ([1987] 2018) Self-reinforcing mechanisms in economics. In Anderson PW (ed) The economy as an evolving complex system. CRC Press, Boca Raton, pp 9–31

  5. Bafumi J (2010) Animal spirits: the effect of economic expectations on economic output. Appl Econ 43(25):3573–3589

    Google Scholar 

  6. Bartels LM (2009) Economic inequality and political representation. In: Jacobs L, King D (eds) The unsustainable American State. Oxford University Press, New York, pp 167–196

    Google Scholar 

  7. Bates D, Maechler M, Bolker B, Walker S (2014) lme4: linear mixed-effects models using Eigen and S4. R Package Version 1(7):1–23

    Google Scholar 

  8. Bentler PM, Wu EJ (2005) EQS 6.1 for windows. Multivariate Software INC, Encino

    Google Scholar 

  9. Beran J (2017) Statistics for long-memory processes. Routledge, New York

    Google Scholar 

  10. Bergmeir C, Benítez JM (2012) On the use of cross-validation for time series predictor evaluation. Inf Sci 191:192–213

    Google Scholar 

  11. Bikhchandani S, Sharma S (2000) Herd behavior in financial markets. IMF Staff Pap 47(3):279–310

    Google Scholar 

  12. Bosse DA, Phillips RA (2016) Agency theory and bounded self-interest. Acad Manag Rev 41(2):276–297

    Google Scholar 

  13. Box GE, Jenkins GM, Reinsel GC, Ljung GM (2015) Time series analysis: forecasting and control. Wiley, Hoboken

    Google Scholar 

  14. Buonaccorsi JP (2010) Measurement error: models, methods, and applications. Chapman and Hall, New York

    Google Scholar 

  15. Bürkner PC (2017) brms: an R package for Bayesian multilevel models using Stan. J Stat Softw 80(1):1–28

    Google Scholar 

  16. Carro A, Toral R, San Miguel M (2015) Markets, herding and response to external information. PLoS ONE 10(7):e0133287

    Google Scholar 

  17. Chen SS (2011) Lack of consumer confidence and stock returns. J Empir Finance 18(2):225–236

    Google Scholar 

  18. Cont R, Bouchaud JP (2000) Herd behavior and aggregate fluctuations in financial markets. Macroecon Dyn 4(2):170–196

    Google Scholar 

  19. Crato N, Ray BK (1996) Some problems in the overspecification of ARMA and processes using ARFIMA models. In: Proceedings of the 3rd Congress of the Portuguese Statistical Society, pp 527–539

  20. Curtin RT (1982) Indicators of consumer behavior: the University of Michigan surveys of consumers. Public Opin Q 46:340–352

    Google Scholar 

  21. Eckrot A, Jurczyk J, Morgenstern I (2016) Ising model of financial markets with many assets. Phys A Stat Mech Appl 462:250–254

    Google Scholar 

  22. Enders W (2008) Applied econometric time series. Wiley, Hoboken

    Google Scholar 

  23. Fisher KL, Statman M (2003) Consumer confidence and stock returns. J Portf Manag 30(1):115–127

    Google Scholar 

  24. Fox JP, Glas CA (2003) Bayesian modeling of measurement error in predictor variables using item response theory. Psychometrika 68(2):169–191

    Google Scholar 

  25. Gelman A, Hill J (2006) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, Cambridge

    Google Scholar 

  26. Gelper S, Fried R, Croux C (2010) Robust forecasting with exponential and Holt–Winters smoothing. J Forecast 29(3):285–300

    Google Scholar 

  27. Graves T, Franzke CL, Watkins NW, Gramacy RB, Tindale E (2017) Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models. Phys A Stat Mech Appl 473:60–71

    Google Scholar 

  28. Greenwood R, Shleifer A (2014) Expectations of returns and expected returns. Rev Financ Stud 27(3):714–746

    Google Scholar 

  29. Griliches Z, Ringstad V (1970) Error-in-the-variables bias in nonlinear contexts. Econom J Econom Soc 38:368–370

    Google Scholar 

  30. Harras G, Sornette D (2011) How to grow a bubble: a model of myopic adapting agents. J Econ Behav Organ 80:137–152

    Google Scholar 

  31. Hommes C, Sonnemans J, Tuinstra J, Van de Velden H (2008) Expectations and bubbles in asset pricing experiments. J Econ Behav Organ 67(1):116–133

    Google Scholar 

  32. Hopkins DJ (2012) Whose economy? Perceptions of national economic performance during unequal growth. Public Opin Q 76(1):50–71

    Google Scholar 

  33. Hsiao C (2014) Analysis of panel data. Cambridge University Press, Cambridge

    Google Scholar 

  34. Hüsler A, Sornette D, Hommes CH (2013) Super-exponential bubbles in lab experiments: evidence for anchoring over-optimistic expectations on price. J Econ Behav Organ 92:304–316

    Google Scholar 

  35. Hyndman RJ, Athanasopoulos G (2018) Forecasting: principles and practice. OTexts, Melbourne

    Google Scholar 

  36. Kahneman D (2003) Maps of bounded rationality: psychology for behavioral economics. Am Econ Rev 93(5):1449–1475

    Google Scholar 

  37. Kellstedt PM, Linn S, Hannah AL (2015) The usefulness of consumer sentiment: assessing construct and measurement. Public Opin Q 79(1):181–203

    Google Scholar 

  38. Klinger S, Weber E (2016) Detecting unemployment hysteresis: a simultaneous unobserved components model with Markov switching. Econ Lett 144:115–118

    Google Scholar 

  39. Kraft P, Weber C, Lebo M (2015) The ArfimaMLM package for R. https://cran.r-project.org/web/packages/ArfimaMLM/ArfimaMLM.pdf

  40. Lebo MJ, Weber C (2015) An effective approach to the repeated cross-sectional design. Am J Polit Sci 59:242–258

    Google Scholar 

  41. Lucas R, Mortensen D, Shiller R, Wallace N (2013) Rational expectations: retrospect and prospect. Macroecon Dyn 17:1169–1192

    Google Scholar 

  42. Mahdi E, Ian McLeod A (2012) Improved multivariate portmanteau test. J Time Ser Anal 33(2):211–222

    Google Scholar 

  43. McCoy BM, Wu TT (2014[1973]) The two-dimensional Ising model. Harvard University Press, Cambridge

  44. Mosquera-Donate G, Boguná M (2015) Follow the leader: herding behavior in heterogeneous populations. Phys Rev E 91(5):052804

    Google Scholar 

  45. Peña D, Rodríguez J (2002) A powerful portmanteau test of lack of fit for time series. J Am Stat Assoc 97(458):601–610

    Google Scholar 

  46. Prechter RR Jr (2001) Unconscious herding behavior as the psychological basis of financial market trends and patterns. J Psychol Financ Mark 2(3):120–125

    Google Scholar 

  47. Roehner BM, Sornette D (2000) “Thermometers” of speculative frenzy. Eur Phys J B Condens Matter Complex Syst 16:729–739

    Google Scholar 

  48. Sadaei HJ, Enayatifar R, Guimarães FG, Mahmud M, Alzamil ZA (2016) Combining ARFIMA models and fuzzy time series for the forecast of long memory time series. Neurocomputing 175:782–796

    Google Scholar 

  49. Sargent TJ (2013) Rational expectations and inflation. Princeton University Press, Princeton

    Google Scholar 

  50. Schmeling M, Schrimpf A (2011) Expected inflation, expected stock returns, and money illusion: what can we learn from survey expectations? Eur Econ Rev 55(5):702–719

    Google Scholar 

  51. Simon H (1972) Theories of bounded rationality. In: McGuire CB, Radner R (eds) Decision and organization. North-Holland, Amsterdam, pp 161–176

    Google Scholar 

  52. So BS, Shin DW (1999) Recursive mean adjustment in time-series inferences. Stat Probab Lett 43(1):65–73

    Google Scholar 

  53. Song W, Ryu D, Webb RI (2018) Volatility dynamics under an endogenous Markov-switching framework: a cross-market approach. Quant Finance 18:1–13

    Google Scholar 

  54. Sornette D (2014) Physics and financial economics (1776–2014): puzzles, Ising and agent-based models. Rep Prog Phys 77(6):062001

    Google Scholar 

  55. Sum V (2014) Effects of business and consumer confidence on stock market returns: cross-sectional evidence. Econ Manag Financ Mark 9(1):21

    Google Scholar 

  56. Tashman LJ (2000) Out-of-sample tests of forecasting accuracy: an analysis and review. Int J Forecast 16(4):437–450

    Google Scholar 

  57. Van Raaij WF (1989) Economic news, expectations and macro-economic behaviour. J Econ Psychol 10(4):473–493

    Google Scholar 

  58. Yaffee RA, McGee M (2000) An introduction to time series analysis and forecasting: with applications of SAS. Academic Press, New York

    Google Scholar 

  59. Zhou WX, Sornette D (2007) Self-organizing Ising model of financial markets. Eur Phys J B 55:175–181

    Google Scholar 

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Acknowledgements

The authors gratefully acknowledge editor and reviewer comments that contributed to the final manuscript. Preparations of the manuscript were completed when the first author was a Lucas Fellow. He thanks the Donald and Sally Lucas Foundation for their support. We have benefited from patient replies to our inquiries on ARFIMA-MLM coding and estimation by Chris Weber. Chahatpreet S. Grewal provided competent research assistance.

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Correspondence to Steven D. Silver.

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Silver, S.D., Raseta, M. An ARFIMA multi-level model of dual-component expectations in repeated cross-sectional survey data. Empir Econ 60, 683–699 (2021). https://doi.org/10.1007/s00181-019-01757-7

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Keywords

  • Expectations
  • Multi-component models
  • Estimation in RCSs
  • Behavioral finance

JEL Classification

  • B41
  • C29
  • G40