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Empirical Data and Modeling of Financial and Economic Processes

Delve into the empirical data and modeling realms of financial and economic processes, exploring theories versus changing realities. Highlighting past, present, and future trends in understanding market dynamics.

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Empirical Data and Modeling of Financial and Economic Processes

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  1. D E P A R T M E N T O F M A T H E M A T I C S U P P S A L A U N I V E R S I T Y EMPIRICAL DATA AND MODELING OF FINANCIAL AND ECONOMIC PROCESSES by Maciej Klimek

  2. Bad news from Goldman Sachs

  3. Financial theories vs. changing reality • OLD, BUT PERSISTENT: • The moving target problems: • insufficient sequences of statistical data • “uncertainty principle” = beliefs/practice changing the market • Convenience more important than realism (eg CAPM, prevalence of • Gaussian distribution, ignoring areas of applicability etc) • “Natural science” approach to social phenomena (major weakness of • Econophysics) • NEW, LARGELY UNEXPLORED: • Theoretical background pre-dates the IT-revolution • (eg Efficient Market Hypothesis) • Globalization of markets vs. theories based on several developed • countries (eg new research: Virginie Konlack and Ivivi Mwaniki – • comparing stock markets in Kenya and Canada) • Complexity of financial instruments obscuring risks • (eg subprime mortgages vs. CDO’s and the like)

  4. Example: ABN-test Okabe, Matsuura, Klimek 2002

  5. Notation Block frame approach – Klimek, Matsuura, Okabe 2007

  6. Block frames

  7. Basic theorem

  8. Fundamental properties

  9. The blueprint algorithm

  10. Probability and Hilbert Spaces

  11. Hilbert lattices

  12. Basic objects associated with time series:

  13. dissipation coefficients

  14. MAIN IDEA

  15. Instead of analysing a d-dimensional time series Xn We use the d(m+1) dimensional time series This is computationally intensive, hence the need for efficient algorithms!

  16. Example: Tests of stationarity A weak stationarity test: Given time series data X(n) calculate the sample covariance Use the blueprint algorithm to calculate the alleged fluctuations ν+(n) Normalize: W(n)-1ν+(n), where W (n) 2=V (n),W (n) -1 is the Moore-Penrose pseudoinverse of W (n) and Apply a white noise test to the resulting data Original version: Okabe & Nakano 1991

  17. The ABN – test • If a stochastic process is strictly stationary and P • is a Borel function of k variables, then the process • is also strictly stationary • Strict stationarity implies weak statinarity • Given a time series test for breakdown of weak stationarity • a large selection of series constructed through polynomial • compositions. These new series are part of the information • structure of the original one!

  18. Applications: • Forecasting • “Extended” stationarity analysis • Causality tests • General adaptive modeling of time series • improving on ARCH, GARCH and similar • models. • Volatility modelling.

  19. Contact: Maciej.Klimek@math.uu.se

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