Multifractal wavelet dynamic mode decomposition modeling for marketing time series

Paper: arXiv 2403.13361

Authors: Mohamed Elshazli A. Zidan, Anouar Ben Mabrouk, Nidhal Ben Abdallah, Tawfeeq M. Alanazi

Abstract

Marketing is the way we ensure our sales are the best in the market, our prices the most accessible, and our clients satisfied, thus ensuring our brand has the widest distribution. This requires sophisticated and advanced understanding of the whole related network. Indeed, marketing data may exist in different forms such as qualitative and quantitative data. However, in the literature, it is easily noted that large bibliographies may be collected about qualitative studies, while only a few studies adopt a quantitative point of view. This is a major drawback that results in marketing science still focusing on design, although the market is strongly dependent on quantities such as money and time. Indeed, marketing data may form time series such as brand sales in specified periods, brand-related prices over specified periods, market shares, etc. The purpose of the present work is to investigate some marketing models based on time series for various brands. This paper aims to combine the dynamic mode decomposition and wavelet decomposition to study marketing series due to both prices, and volume sales in order to explore the effect of the time scale on the persistence of brand sales in the market and on the forecasting of such persistence, according to the characteristics of the brand and the related market competition or competitors. Our study is based on a sample of Saudi brands during the period 22 November 2017 to 30 December 2021.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 5.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a mathematically sophisticated framework combining Dynamic Mode Decomposition (DMD), wavelets, and multifractal analysis for time-series forecasting. While mathematically rich and applied to real-world Saudi brand data, the empirical validation lacks extensive out-of-sample stress testing and open-source code for full reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Marketing Time Series & Persistence] --> B[Data Input: Saudi Brands Time Series 2017–2021]
    B --> C[Methodology: Combine DMD & Wavelet Decomposition]
    C --> D[Computational Process: Multi-scale Dynamic Mode Decomposition]
    D --> E[Analysis: Time-Scale Effect on Sales & Price Dynamics]
    E --> F[Outcomes: Improved Persistence Analysis & Market Forecasting]