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Temporal Aggregation of Random Walk Processes and Implications for Asset Prices

Author

Listed:
  • Yamin Ahmad

    (Department of Economics, University of Wisconsin - Whitewater)

  • Ivan Paya

    (Department of Economics, Lancaster University Management School)

Abstract

This paper examines the impact of time averaging and interval sampling data assuming that the data generating process for a given series follows a random walk with uncorrelated increments. We provide expressions for the corresponding variances, and covariances, for both the levels and differences of the aggregated series, demonstrating how the degree of temporal aggregation impacts these particular properties. Moreover, we analytically derive any differences that arise between the aggregated series and its disaggregated counterpart, and show that they can be decomposed into a distortionary and small sample effect. We also provide exact expressions for the variance and sharpe ratios, and correlation coefficients for any level of aggregation. We discuss our results in the context of asset prices, which have utilized these extensively.

Suggested Citation

  • Yamin Ahmad & Ivan Paya, 2014. "Temporal Aggregation of Random Walk Processes and Implications for Asset Prices," Working Papers 14-01, UW-Whitewater, Department of Economics.
    • Handle: RePEc:uww:wpaper:14-01
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    File URL: http://www.uww.edu/documents/colleges/cobe/economics/wpapers/14-01_Ahmad_Paya.pdf
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    References listed on IDEAS

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    Cited by:

    1. Ahmad, Yamin & Craighead, William D., 2011. "Temporal aggregation and purchasing power parity persistence," Journal of International Money and Finance, Elsevier, vol. 30(5), pages 817-830, September.
    2. Jesús Otero & Theodore Panagiotidis & Georgios Papapanagiotou, 2021. "Testing for exuberance in house prices using data sampled at different frequencies," Working Paper series 21-13, Rimini Centre for Economic Analysis.

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    More about this item

    Keywords

    Temporal Aggregation; Random Walk; Variance Ratio; Sharpe Ratio;
    All these keywords.

    JEL classification:

    • F47 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Forecasting and Simulation: Models and Applications
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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