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What Proportion of Time is a Particular Market Inefficient? … A Method for Analysing the Frequency of Market Efficiency when Equity Prices Follow Threshold Autoregressions

Author

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  • Ahmed Muhammad Farid

    (Faculty of Economics, Selwyn College, University of Cambridge, Sidgwick Avenue Cambridge, Cambridge, CB3 9DD, UK)

  • Satchell Stephen

    (University of Sydney, Camperdown, NSW 2006, Australia)

Abstract

We assume that equity returns follow multi-state threshold autoregressions and generalize existing results for threshold autoregressive models presented in Knight and Satchell 2011. “Some new results for threshold AR(1) models,” Journal of Time Series Econometrics 3(2011):1–42 and Knight, Satchell, and Srivastava (2014) for the existence of a stationary process and the conditions necessary for the existence of a mean and a variance; we also present formulae for these moments. Using a simulation study, we explore what these results entail with respect to the impact they can have on tests for detecting bubbles or market efficiency. We find that bubbles are easier to detect in processes where a stationary distribution does not exist. Furthermore, we explore how threshold autoregressive models with i.i.d trigger variables may enable us to identify how often asset markets are inefficient. We find, unsurprisingly, that the fraction of time spent in an efficient state depends upon the full specification of the model; the notion of how efficient a market is, in this context at least, a model-dependent concept. However, our methodology allows us to compare efficiency across different asset markets.

Suggested Citation

  • Ahmed Muhammad Farid & Satchell Stephen, 2018. "What Proportion of Time is a Particular Market Inefficient? … A Method for Analysing the Frequency of Market Efficiency when Equity Prices Follow Threshold Autoregressions," Journal of Time Series Econometrics, De Gruyter, vol. 10(2), pages 1-22, July.
    • Handle: RePEc:bpj:jtsmet:v:10:y:2018:i:2:p:22:n:1
    DOI: 10.1515/jtse-2016-0021
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
    2. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    3. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-930, September.
    4. Knight John & Satchell Stephen, 2011. "Some New Results for Threshold AR(1) Models," Journal of Time Series Econometrics, De Gruyter, vol. 3(2), pages 1-42, April.
    5. Marsh, Terry A & Merton, Robert C, 1986. "Dividend Variability and Variance Bounds Tests for the Rationality ofStock Market Prices," American Economic Review, American Economic Association, vol. 76(3), pages 483-498, June.
    6. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    7. Knight, John & Satchell, Stephen & Srivastava, Nandini, 2014. "Steady state distributions for models of locally explosive regimes: Existence and econometric implications," Economic Modelling, Elsevier, vol. 41(C), pages 281-288.
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    Cited by:

    1. Muhammad Farid Ahmed & Stephen Satchell, 2019. "Some Dynamic and Steady-State Properties of Threshold Auto-Regressions with Applications to Stationarity and Local Explosivity," JRFM, MDPI, vol. 12(3), pages 1-18, July.
    2. Galyna Grynkiv & Lars Stentoft, 2018. "Stationary Threshold Vector Autoregressive Models," JRFM, MDPI, vol. 11(3), pages 1-23, August.

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    More about this item

    Keywords

    market efficiency; bubbles; threshold auto-regressions;
    All these keywords.

    JEL classification:

    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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