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Chapter 14 Simplifying to Improve Reliability of Geometric Brownian Motion Stock Index Forecasts

  • Amit Sinha
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Select Topics of Econophysics
This chapter is in the book Select Topics of Econophysics

Abstract

The geometric Brownian motion forecasts have been found to provide reliable forecast of S&P 500 index values. This manuscript explores and provides an approach that increases the accuracy of the forecasts obtained. Using average returns and standard deviation obtained from previous twenty years of return data as proxies for drift and diffusion terms in the geometric Brownian motion, reliable expected index values can be estimated from a pool of just one thousand simulated values.

Abstract

The geometric Brownian motion forecasts have been found to provide reliable forecast of S&P 500 index values. This manuscript explores and provides an approach that increases the accuracy of the forecasts obtained. Using average returns and standard deviation obtained from previous twenty years of return data as proxies for drift and diffusion terms in the geometric Brownian motion, reliable expected index values can be estimated from a pool of just one thousand simulated values.

Chapters in this book

  1. Frontmatter I
  2. Contents VII
  3. Foreword XI
  4. Chapter 1 Econophysics: An Introduction 1
  5. Chapter 2 Logistic Modelling of Economic Dynamics 13
  6. Chapter 3 Outlook About the Mathematical Foundation of Creativity in Economy: Monadic Approach and Holistic Role of the Zeta Riemann Function 25
  7. Chapter 4 The Visualization of the U.S. Economy Under the Application of the EGAP-Helix 57
  8. Chapter 5 Wealth Distribution Patterns in Different Socio-economic Environments: Data Mining, Estimation and Modelling 61
  9. Chapter 6 Kinetic Exchange Models of Income and Wealth Distribution: Self Organization and Poverty Level 79
  10. Chapter 7 Kinetic Monte Carlo Simulations of an Agent-Based Model of Market Dynamics 95
  11. Chapter 8 Quantifying Economic Dynamics: Unveiling the Formula for Monetary Energy (Em) 109
  12. Chapter 9 Sociophysics Model of Bubbles with Neural-Stochastic Differential Equations: A Stochastic Inflation Model 125
  13. Chapter 10 Criticality of the Bitcoin Market 145
  14. Chapter 11 Decoding Cryptocurrency Vulnerability: Assessing Risk and Factors 171
  15. Chapter 12 A Quasi-optimal Technique for Rebalancing a Cryptocurrency Wallet 181
  16. Chapter 13 Price Modelling under Generalized Fractional Brownian Motion 197
  17. Chapter 14 Simplifying to Improve Reliability of Geometric Brownian Motion Stock Index Forecasts 215
  18. Chapter 15 Do Economic and Financial Factors Affect Expected S&P 500? 229
  19. Chapter 16 Predictability of Technical Analysis 239
  20. Chapter 17 Fractal Regressions: An Econophysics Innovation to Apply in Economics and Finance 261
  21. Chapter 18 The Menace and Caress of Wave: The Econophysics of Informational Diffusion 277
  22. Chapter 19 Improving Chaos Control: Implications for Economic Policies 295
  23. Chapter 20 Of Time and the River: Comovement, Heterogeneity, and Multifractality in a World Lit by Lightning 311
  24. Chapter 21 Transfer Entropies between Market Stocks 329
  25. Chapter 22 Multifractal Analysis of Regimes in Financial Markets 341
  26. Chapter 23 Evidence of Chaos in the Moroccan Stock Market before and during the Covid-19 Pandemic 363
  27. Chapter 24 Complexity Measure, Kernel Density Estimation, Bandwidth Selection, and the Efficient Market Hypothesis 393
  28. Chapter 25 Exploring the Intersection of Chemistry and Economic: The Emergence of Econochemistry 411
  29. Chapter 26 Developing a 3D Printed Prototype for Visualizing Large Development Indicator Performance in Any Country: The Domestic Development Domestic Integrated Structures (DDGIS) 421
  30. Acknowledgements 435
  31. List of Contributors 437
  32. List of Figures 445
  33. List of Tables 453
  34. About the Editor 455
  35. Index 457
https://doi.org/10.1515/9783110987584-014

Chapters in this book

  1. Frontmatter I
  2. Contents VII
  3. Foreword XI
  4. Chapter 1 Econophysics: An Introduction 1
  5. Chapter 2 Logistic Modelling of Economic Dynamics 13
  6. Chapter 3 Outlook About the Mathematical Foundation of Creativity in Economy: Monadic Approach and Holistic Role of the Zeta Riemann Function 25
  7. Chapter 4 The Visualization of the U.S. Economy Under the Application of the EGAP-Helix 57
  8. Chapter 5 Wealth Distribution Patterns in Different Socio-economic Environments: Data Mining, Estimation and Modelling 61
  9. Chapter 6 Kinetic Exchange Models of Income and Wealth Distribution: Self Organization and Poverty Level 79
  10. Chapter 7 Kinetic Monte Carlo Simulations of an Agent-Based Model of Market Dynamics 95
  11. Chapter 8 Quantifying Economic Dynamics: Unveiling the Formula for Monetary Energy (Em) 109
  12. Chapter 9 Sociophysics Model of Bubbles with Neural-Stochastic Differential Equations: A Stochastic Inflation Model 125
  13. Chapter 10 Criticality of the Bitcoin Market 145
  14. Chapter 11 Decoding Cryptocurrency Vulnerability: Assessing Risk and Factors 171
  15. Chapter 12 A Quasi-optimal Technique for Rebalancing a Cryptocurrency Wallet 181
  16. Chapter 13 Price Modelling under Generalized Fractional Brownian Motion 197
  17. Chapter 14 Simplifying to Improve Reliability of Geometric Brownian Motion Stock Index Forecasts 215
  18. Chapter 15 Do Economic and Financial Factors Affect Expected S&P 500? 229
  19. Chapter 16 Predictability of Technical Analysis 239
  20. Chapter 17 Fractal Regressions: An Econophysics Innovation to Apply in Economics and Finance 261
  21. Chapter 18 The Menace and Caress of Wave: The Econophysics of Informational Diffusion 277
  22. Chapter 19 Improving Chaos Control: Implications for Economic Policies 295
  23. Chapter 20 Of Time and the River: Comovement, Heterogeneity, and Multifractality in a World Lit by Lightning 311
  24. Chapter 21 Transfer Entropies between Market Stocks 329
  25. Chapter 22 Multifractal Analysis of Regimes in Financial Markets 341
  26. Chapter 23 Evidence of Chaos in the Moroccan Stock Market before and during the Covid-19 Pandemic 363
  27. Chapter 24 Complexity Measure, Kernel Density Estimation, Bandwidth Selection, and the Efficient Market Hypothesis 393
  28. Chapter 25 Exploring the Intersection of Chemistry and Economic: The Emergence of Econochemistry 411
  29. Chapter 26 Developing a 3D Printed Prototype for Visualizing Large Development Indicator Performance in Any Country: The Domestic Development Domestic Integrated Structures (DDGIS) 421
  30. Acknowledgements 435
  31. List of Contributors 437
  32. List of Figures 445
  33. List of Tables 453
  34. About the Editor 455
  35. Index 457
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