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Testing of Nonstationarities in the Unit Circle, Long Memory Processes, and Day of the Week Effects in Financial Data

In: Advances In Quantitative Analysis Of Finance And Accounting

Author

Listed:
  • Guglielmo Maria Caporale

    (Centre for Empirical Finance, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK)

  • Luis A. Gil-Alana

    (Universidad de Navarra, Faculty of Economics, Edificio Biblioteca, Entrada Este, E-31080, Pamplona, Spain)

  • Mike Nazarski

    (Universidad de Navarra, Faculty of Economics, Edificio Biblioteca, Entrada Este, E-31080, Pamplona, Spain)

Abstract

This paper examines a version of the tests of Robinson (1994) that enables one to test models of the form (1 – Lk)dxt = ut, where k is an integer value, d may be any real number, and ut is I(0). The most common cases are those with k = 1 (unit or fractional roots) and k = 4 and 12 (seasonal unit or fractional models). However, we extend the analysis to cover situations such as (1–L5)d xt = ut, which might be relevant, for example, in the context of financial time series data. We apply these techniques to the daily Eurodollar rate and Dow Jones index, and find that for the former series the most adequate specifications are either a pure random walk or a model of the form xt = xt−5 + εt, implying in both cases that the returns are completely unpredictable. In the case of Dow Jones index, a model of the form (1 – L5)d xt = ut is selected, with d constrained between 0.50 and 1, implying nonstationarity and mean-reverting behavior.

Suggested Citation

  • Guglielmo Maria Caporale & Luis A. Gil-Alana & Mike Nazarski, 2007. "Testing of Nonstationarities in the Unit Circle, Long Memory Processes, and Day of the Week Effects in Financial Data," World Scientific Book Chapters, in: Cheng-Few Lee (ed.), Advances In Quantitative Analysis Of Finance And Accounting, chapter 2, pages 23-50, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812772213_0002
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    Keywords

    Monte Carlo Simulations; REIT; IPO; Fractional Integration; Seasonality; Long Memory; Macroeconomic Shocks; VAR; Interest Rates;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • M41 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Accounting

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