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How Irrational Behavour Creates Order and How This Order Can Be Determined : The Theory and Practice of Fractal Market Analysis

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Academic year: 2021

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1

Introduction ... 1

2

Financial Market Theory ... 2

2.1 History ... 2

2.2 Recent Advancements in Behavioural Finance ... 3

2.2.1 Investor Sentiment and Market Overreactions ... 3

2.2.2 Positive Feedback and Herding ... 5

2.2.3 Generalizing and Simulating Irrational Behaviour ... 5

2.3 Fractal Theory and the Macro Level ... 7

2.3.1 The Macroeconomics of Human Behaviour ... 8

2.3.2 A Portfolio of Assets with Chaotic Prices ... 8

2.3.3 From Heterogenous Investment Horizons to Scalability and Fractals ... 9

3

Method ... 10

3.1 The “Boiling Water” Metaphor of the Market Fractal... 10

3.2 Related Empirical Research: A Note on Data Audification ... 11

3.3 Frequency Domain Representation ... 11

3.4 Harmonic Analysis of a Financial Time Series: Introducing the OFS Transform ... 12

3.4.1 A Definition of the Fourier Series ... 12

3.4.2 Periodic Functions and OLS Regression Analysis ... 12

3.4.3 Estimating “p” and “q” through Optimization: The OFS Defined ... 13

3.4.4 An OFS of Order “N”, and the “Break” Parameter ... 14

3.5 Defining the Research Hypotheses ... 15

4

Results and Discussion ... 16

4.1 Forecasting ... 18

5

Limitations and Conclusions ... 21

List of references ... 22

Appendix 1: Further Research Prospects ... 25

5.1 Applying OFS to Longer-Period Historical Data ... 25

5.1.1 Correcting for Market Capitalization ... 25

5.1.2 GARCH and Variable OFS Coefficients ... 26

Appendix 2: List of the Derived OFS Coefficients ... 28

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 SNf

 

xa0 2 

ancos nx

 

bnsin nx

 

n1 N

 Yi

1

2Xi

i  log Y

 

i 12Xii  Yie12Xiu i

(16)

 d sin x

 

dx 2 

1 

2 

2  d psin qx

 

dx 2  yp1sin q

1xh1

p2cos q

2xh2

C  yip1sin q

1xih1

p2cos q

2xih2

Ci  ytp1sin q

1th1

p2cos q

2th2

Ct  yt

p1sin q

1th1

p2cos q

2th2

C

2 t1 n

min  p1, q1, h1, p2, q2, h2  Ca0 2  q1,q2n  p1, p2b1,a1  h1,h20

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 h1, h2   2;  2      p1,q1, p2,q2 0   n 6 S 2 1 4

K3

2      ytp1sin q

1th1

p2cos q

2th2

Ct

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 S 1 n

yiy

3 i1 n

1 n

yiy

2 i1 n

      3 2 , K  1 n

yiy

4 i1 n

1 n

yiy

2 i1 n

      2

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