IDEAS home Printed from https://ideas.repec.org/a/wly/isacfm/v24y2017i4p111-124.html
   My bibliography  Save this article

An empirical investigation of analytical procedures using mixture distributions

Author

Listed:
  • J. Christopher Westland

Abstract

Analytical procedures are evaluations of account and transaction flow information made by a study of plausible relationships between both accounting and non‐accounting data. This study investigates the performance of Tweedie distributions (which have Gaussian distributions as members) in improving fit of zero‐inflated, non‐negative, kurtotic and multimodal analytical review data. The study found that account valuations are more informative than marginal data in analytical review, that mixture Poisson–Gamma distributions offer better fit than Gaussian distributions, even under assumptions of central limit theorem convergence, and that mixture Poisson–Gamma distributions provide better predictions of future account and transaction volumes and values. Model performance improvement with price versus returns data in this empirical study was substantial: from less than one‐quarter of variance, to almost two‐thirds. Tweedie generalized linear model risk assessments were found to be a magnitude smaller than traditional risk assessments, lending support to market inefficiency and increased risk from idiosyncratic factors. An example with several differing distributions shows that use of mixture distributions instead of point estimation can reduce sample size while retaining the power of the audit tests. The results of this study are increasingly important as accounting datasets are growing exponentially larger over time, requiring well‐defined roles for models, algorithms, data and narrative which can only be achieved with statistical protocols and algorithmic languages.

Suggested Citation

  • J. Christopher Westland, 2017. "An empirical investigation of analytical procedures using mixture distributions," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 24(4), pages 111-124, October.
  • Handle: RePEc:wly:isacfm:v:24:y:2017:i:4:p:111-124
    DOI: 10.1002/isaf.1405
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/isaf.1405
    Download Restriction: no

    File URL: https://libkey.io/10.1002/isaf.1405?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Anderson, John C. & Jennings, Marianne M. & Kaplan, Steven E. & Reckers, Philip M. J., 1995. "The effect of using diagnostic decision aids for analytical procedures on judges' liability judgments," Journal of Accounting and Public Policy, Elsevier, vol. 14(1), pages 33-62.
    2. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    3. Arrington, Ce & Hillison, W & Jensen, Re, 1984. "An Application Of Analytical Hierarchy Process To Model Expert Judgments On Analytical Review Procedures," Journal of Accounting Research, Wiley Blackwell, vol. 22(1), pages 298-312.
    4. Taleb, Nassim Nicholas, 2007. "Black Swans and the Domains of Statistics," The American Statistician, American Statistical Association, vol. 61, pages 198-200, August.
    5. Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
    6. Eugene F. Fama & Kenneth R. French, 2008. "Dissecting Anomalies," Journal of Finance, American Finance Association, vol. 63(4), pages 1653-1678, August.
    7. Edwin J. Elton & Martin J. Gruber, 1997. "Modern Portfolio Theory, 1950 to Date," New York University, Leonard N. Stern School Finance Department Working Paper Seires 97-3, New York University, Leonard N. Stern School of Business-.
    8. Roll, Richard, 1977. "A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory," Journal of Financial Economics, Elsevier, vol. 4(2), pages 129-176, March.
    9. Roll, Richard & Ross, Stephen A, 1980. "An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
    10. Fama, Eugene F. & French, Kenneth R., 2005. "Financing decisions: who issues stock?," Journal of Financial Economics, Elsevier, vol. 76(3), pages 549-582, June.
    11. Duke, Gl & Neter, J & Leitch, Ra, 1982. "Power Characteristics Of Test Statistics In The Auditing Environment - An Empirical-Study," Journal of Accounting Research, Wiley Blackwell, vol. 20(1), pages 42-67.
    12. Libby, R, 1985. "Availability And The Generation Of Hypotheses In Analytical Review," Journal of Accounting Research, Wiley Blackwell, vol. 23(2), pages 648-667.
    13. Elton, Edwin J. & Gruber, Martin J., 1997. "Modern portfolio theory, 1950 to date," Journal of Banking & Finance, Elsevier, vol. 21(11-12), pages 1743-1759, December.
    14. Fama, Eugene F. & French, Kenneth R., 2012. "Size, value, and momentum in international stock returns," Journal of Financial Economics, Elsevier, vol. 105(3), pages 457-472.
    15. Knechel, W. Robert, 2007. "The business risk audit: Origins, obstacles and opportunities," Accounting, Organizations and Society, Elsevier, vol. 32(4-5), pages 383-408.
    16. Ajinkya, Bipin B. & Jain, Prem C., 1989. "The behavior of daily stock market trading volume," Journal of Accounting and Economics, Elsevier, vol. 11(4), pages 331-359, November.
    17. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    18. William H. Greene, 1994. "Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models," Working Papers 94-10, New York University, Leonard N. Stern School of Business, Department of Economics.
    19. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
    20. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1851-1872, September.
    21. Asare, S. K. & Wright, A., 1997. "Hypothesis revision strategies in conducting analytical procedures," Accounting, Organizations and Society, Elsevier, vol. 22(8), pages 737-755, November.
    22. Stringer, Kw, 1975. "Statistical Technique For Analytical Review," Journal of Accounting Research, Wiley Blackwell, vol. 13, pages 1-9.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sebastien Valeyre, 2020. "Refined model of the covariance/correlation matrix between securities," Papers 2001.08911, arXiv.org.
    2. Avanidhar Subrahmanyam, 2010. "The Cross†Section of Expected Stock Returns: What Have We Learnt from the Past Twenty†Five Years of Research?," European Financial Management, European Financial Management Association, vol. 16(1), pages 27-42, January.
    3. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, December.
    4. John G. Cragg & Burton G. Malkiel, 1982. "References, Index," NBER Chapters, in: Expectations and the Structure of Share Prices, pages 167-176, National Bureau of Economic Research, Inc.
    5. Moon K. Kim & Chunchi Wu, 1987. "Macro-Economic Factors And Stock Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(2), pages 87-98, June.
    6. Jon Poynter & James Winder & Tzu Tai, 2015. "An analysis of co-movements in industrial sector indices over the last 30 years," Review of Quantitative Finance and Accounting, Springer, vol. 44(1), pages 69-88, January.
    7. Trabelsi, Mohamed Ali, 2010. "Choix de portefeuille: comparaison des différentes stratégies [Portfolio selection: comparison of different strategies]," MPRA Paper 82946, University Library of Munich, Germany, revised 01 Dec 2010.
    8. Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June.
    9. Sebastien Valeyre & Sofiane Aboura & Denis Grebenkov, 2019. "The Reactive Beta Model," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 42(1), pages 71-113, March.
    10. Merton, Robert, 1990. "Capital market theory and the pricing of financial securities," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 1, chapter 11, pages 497-581, Elsevier.
    11. Haim Levy, 2010. "The CAPM is Alive and Well: A Review and Synthesis," European Financial Management, European Financial Management Association, vol. 16(1), pages 43-71, January.
    12. ALAM Nafis & TAN Ee Chain, 2012. "Impact Of Financial Crisis On Stock Returns: Evidence From Singapore," Studies in Business and Economics, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 7(2), pages 5-19, August.
    13. Dimson, Elroy & Mussavian, Massoud, 1999. "Three centuries of asset pricing," Journal of Banking & Finance, Elsevier, vol. 23(12), pages 1745-1769, December.
    14. Erdinc Altay, 2003. "The Effect of Macroeconomic Factors on Asset Returns: A Comparative Analysis of the German and the Turkish Stock Markets in an APT Framework," Finance 0307006, University Library of Munich, Germany.
    15. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "Estimation of large dimensional conditional factor models in finance," Working Papers unige:125031, University of Geneva, Geneva School of Economics and Management.
    16. Jank, Stephan, 2015. "Specialized human capital, unemployment risk, and the value premium," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113214, Verein für Socialpolitik / German Economic Association.
    17. Javier Rojo‐Suárez & Ana Belén Alonso‐Conde & Ricardo Ferrero‐Pozo, 2022. "Liquidity, time‐varying betas and anomalies: Is the high trading activity enhancing the validity of the CAPM in the UK equity market?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 45-60, January.
    18. Söhnke M. Bartram & Harald Lohre & Peter F. Pope & Ananthalakshmi Ranganathan, 2021. "Navigating the factor zoo around the world: an institutional investor perspective," Journal of Business Economics, Springer, vol. 91(5), pages 655-703, July.
    19. Martin Gold, 2010. "Fiduciary Finance," Books, Edward Elgar Publishing, number 13813.
    20. Maio, Paulo & Philip, Dennis, 2018. "Economic activity and momentum profits: Further evidence," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 466-482.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:isacfm:v:24:y:2017:i:4:p:111-124. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/1099-1174/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.