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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

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. Bad news from Goldman Sachs. Financial theories vs. changing reality.

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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

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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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