Paper: arXiv 2504.07021

Abstract

In this study, we employ k-means clustering algorithm of polyspectral means to analyze 49 stocks in the Indian stock market. We have used spectral and bispectral information obtained from the data, by using spectral and bispectral means with different weight functions that will give us varying insights into the temporal patterns of the stocks. In particular, the higher order polyspectral means can provide significantly more information than what we can gather from power spectra, and can also unveil nonlinear trends in a time series. Through rigorous analysis, we identify five distinctive clusters, uncovering nuanced market structures. Notably, one cluster emerges as that of a conglomerate powerhouse, featuring ADANI, BIRLA, TATA, and unexpectedly, government-owned bank SBI. Another cluster spotlights the IT sector with WIPRO and TCS, while a third combines private banks, government entities, and RELIANCE. The final cluster comprises publicly traded companies with dispersed ownership. Such clustering of stocks sheds light on intricate financial relationships within the stock market, providing valuable insights for investors and analysts navigating the dynamic landscape of the Indian stock market.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.2: no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced higher-order spectral analysis (polyspectra, bispectral means) and derived mathematical formulas, indicating high math complexity. It uses real financial data from the NIFTY 50, performs clustering with a defined methodology (k-means, gap statistic), and presents concrete results (specific stock clusters), demonstrating strong empirical implementation.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Clustering 49 Indian Stocks using Higher-Order Spectra"] --> B["Data Input<br>Indian Stock Market Time Series"]
  B --> C["Methodology<br>Polyspectral Means with Weight Functions"]
  C --> D["Computational Process<br>K-means Clustering of Bispectral Means"]
  D --> E["Key Findings<br>Identification of 5 Distinctive Clusters"]
  E --> F["Outcomes<br>Market Structure Analysis & Investment Insights"]

Cited References (67)

  1. The Linguistic Significance of Current B ritish Slang (1995)
  2. Blowup for Nonlinear Hyperbolic Equations (1995)
  3. Nonlinear Operators and Nonlinear Equations of Evolution in B anach Spaces (1976)
  4. Insensitive Functionals, Inconsistent Gradients, Spurious Minima, and Regularized Functionals in Flow Optimization Problems (2002)
  5. An Algorithm Using Quadratic Interpolation (1996)
  6. Positive Bases in Numerical Optimization (2003)
  7. Hilbert modular forms and the G alois representations associated to H ilbert- B lumenthal abelian varieties (1998)
  8. Practical Methods of Optimization (1980)
and 59 more
  1. AMPL : A Modeling Language for Mathematical Programming (2003)
  2. English title of a chapter in the translation of a book in a foreign language (1988)
  3. Practical Optimization (1981)
  4. Multi-start and strategic oscillation methods – principles to exploit adaptive memory (2000)
  5. APPSPACK ( A synchronous Parallel Pattern Search Package)
  6. Conjectured Statistics for the $q,t$ - C atalan Numbers (preprint (2003)) — link
  7. Hilbert Schemes, Polygraphs, and the M acdonald Positivity Conjecture (2001) — link
  8. A Stationary Point Convergence Theory of Evolutionary Algorithms (1997)
  9. Multiple Bumping of Components of Deformation Spaces of Hyperbolic 3-Manifolds (2003) — link
  10. Homogenization and Porous Media (1996)
  11. Automatic Differentiation and its Role in Simulation-Based Optimization (2003)
  12. The resurgent J apanese economy and a J apan– U nited S tates free trade agreement (1997)
  13. On an Elliptic Curve over $Q(t)$ of Rank $\geq$14 (2001)
  14. Multi S implex 2.0
  15. Parallel GRASP with Path-Relinking for Job Shop Scheduling (1983)
  16. Title of a Book (1988)
  17. On the L agrange Functions of Quadratic Models that are Defined by Interpolation (2000)
  18. Matrix Algorithms. Volume 1: Basic Decompositions (1998)
  19. Finite Subgroups of Formal Groups (1997)
  20. On the meromorphic continuation of degree two L-functions (preprint (2003)) — link
  21. Basic Number Theory (1995)
  22. Indian stock market-review of literature (2013)
  23. Stock Market Volatility-A Study of Indian Stock Market (2017)
  24. Sectoral co-movements in the Indian stock market: a mesoscopic network analysis (2017)
  25. An empirical research and comprehensive analysis of stock market prediction using machine learning and deep learning techniques (2021)
  26. Portfolio investment diversification at global stock market: a cointegration analysis of emerging brics (P) group (2020)
  27. Clustering Indian stock market data for portfolio management (2010)
  28. Clustering of stock prices (1965)
  29. Financial investment opportunities and the macroeconomy (1991)
  30. The cross-section of expected stock returns (1992)
  31. Using clustering method to understand Indian stock market volatility (2016) — link
  32. Dynamic portfolio strategy using clustering approach (2017)
  33. Twitter mood predicts the stock market (2011)
  34. An introduction to polyspectra (2011)
  35. Direct estimation of equity market impact (2005)
  36. Finding groups in data: an introduction to cluster analysis (2009)
  37. Measurement of clustering tendency (1982)
  38. The application of cluster analysis in strategic management research: an analysis and critique (1996)
  39. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis (1987)
  40. Estimating the number of clusters in a data set via the gap statistic (2001)
  41. A cluster separation measure (1979)
  42. A dendrite method for cluster analysis (1974)
  43. Partitioning around medoids (program pam) (1990)
  44. Contribution to Data Science: Time Series, Uncertainty Quantification and Applications (2022)
  45. Quadratic Prediction of Time Series via Auto-Cumulants (2023)
  46. Polyspectral Mean Estimation of General Nonlinear Processes (2024) — link
  47. Nonlinearity in stock networks (2018)
  48. Nonlinearity in forecasting of high-frequency stock returns (2012)
  49. Developing a Nonlinear Model to Predict Stock Prices in India: An Artificial Neural Networks Approach. (2015)
  50. Update on the Merger of Bharti Infratel and Indus Towers (2020) — link
  51. Multifractal detrended cross-correlations between the Chinese exchange market and stock market (2012)
  52. Dynamics of market correlations: Taxonomy and portfolio analysis (2003)
  53. Stock market movement forecast: A systematic review (2020)
  54. Higher-order spectral analysis: A nonlinear signal processing framework, new jersey: Ptr prentice-hall (1993)
  55. Empirical properties of asset returns: stylized facts and statistical issues (2001)
  56. Testing for Gaussianity and linearity of a stationary time series (1982)
  57. Demystifying Market Movements: A Comparative Analysis of LR, RF and DT Techniques for Stock Price Prediction (2024)
  58. A Long Short-Term Memory Technique for NIFTY50 Stocks Price Prediction (2024)
  59. Sentiment analysis based stock price prediction using machine learning (2024)

0 of 67 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.