Time-Series Analysis

Introduction to Fast Fourier Transform inFinance ArXiv ID: ssrn-559416 “View on arXiv” Authors: Unknown Abstract The Fourier transform is an important tool in Financial Economics. It delivers real time pricing while allowing for a realistic structure of asset returns, taki Keywords: Fourier transform, asset pricing, financial economics, time series analysis, real-time pricing, Financial Derivatives Complexity vs Empirical Score Math Complexity: 8.0/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper involves advanced mathematical concepts like Fourier transforms, complex numbers, and convolution, but it is a conceptual pedagogical piece focusing on methodology rather than providing empirical data, backtests, or implementation details for real-world trading. flowchart TD A["Research Goal: Use Fourier Transform<br>for Real-Time Financial Pricing"] --> B["Key Methodology: Fast Fourier Transform<br>FFT Algorithm"] B --> C["Data Inputs: Asset Return Time Series<br>& Market Data"] C --> D["Computational Process: FFT of<br>Return Distributions to Price Derivatives"] D --> E["Key Findings: Efficient Real-Time Pricing<br>Model for Financial Derivatives"]

A Multifractal Model of Asset Returns ArXiv ID: ssrn-78588 “View on arXiv” Authors: Unknown Abstract This paper presents the “multifractal model of asset returns” (“MMAR”), based upon the pioneering research into multifractal measures by Man Keywords: Multifractal Models, Asset Returns, Stochastic Processes, Time Series Analysis, Volatility Modeling, Equity Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 6.0/10 Quadrant: Holy Grail Why: The paper employs advanced mathematical concepts like multifractal measures, long-dependence, and scaling laws, indicating high mathematical complexity. It also discusses empirical implications, comparisons with GARCH/FIGARCH, and references companion empirical work, showing substantial empirical rigor. flowchart TD Goal["Research Goal:<br>Create model for asset return volatility<br>(MMAR)"] --> Inputs["Data/Input:<br>Equity index returns<br>High-frequency time series"] Inputs --> Method["Key Method:<br>Multifractal measures &<br>stochastic cascade process"] Method --> Comp["Computational Process:<br>Model calibration &<br>time-scale analysis"] Comp --> Findings["Key Findings/Outcomes:<br>1. Captures heavy tails<br>2. Explains volatility clustering<br>3. Superior to GARCH models"] Findings --> Final["Conclusion:<br>MMAR accurately describes<br>multifractal nature of markets"]