Spectral Data Analysis of Retail Consumer Attention Cycles

An advanced signal processing pipeline built from scratch to analyze and decompose digital consumer behavior matrices for Nike and Adidas within the Italian retail geography ($geo='IT'$).

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Project Abstract & Objective

Daily Search Volume Index (SVI) data is heavily distorted by stochastic behavioral noise. This project implements the Discrete Fourier Transform (DFT) via Fast Fourier Transform (FFT) algorithms to transition time-series consumer data into the frequency domain.

The objective is to statistically verify whether public interest is sustained by predictable lifestyle harmonics (regular weekly/monthly cycles) or driven by transient stochastic shocks (hype cycles, limited product drops, or sports events).

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Core Empirical Results & Visualizations

1. Adidas Spectral Analysis (The Lifestyle Rhythm)

Adidas exhibits a clean frequency spectrum heavily dominated by structured human behavior and standard retail calendars.

• Daily Resolution (90 Days): Shows a powerful, sharp resonance spike at exactly $P = 7.0$ days, proving a strict weekend-driven retail browsing loop.
• Weekly Resolution (3 Years): Strongly dominated by annual seasonality ($P = 52.0$ weeks) and semi-annual adjustments ($P = 26.0$ weeks).

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2. Nike Spectral Analysis (The Scarcity Impulse Train)

Nike's spectrum mathematically validates the "Impulse Train" hypothesis, showing a behaviorscape driven by dynamic shocks rather than steady routine.

• Daily Resolution (90 Days): Shares the universal $P = 7.0$ days weekly pulse but operates on a much noisier baseline variance floor.
• Weekly Resolution (3 Years): Displays a dense cluster of high-frequency components concentrated between $P = 2.5$ to $3.5$ weeks, capturing the transient bursts of limited sneaker drops and transient hype marketing.

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Computational Architecture & Pipeline Stages

Stage A & B: Data Ingestion & Linear Detrending

• Extraction: Automated pipeline using pytrends API fetching 90-day daily blocks and 3-year weekly blocks.
• Detrending: Application of SciPy's linear detrending operators to drop macro internet growth trends and minimize spectral leakage.

Stage C: Dual-Filtering Execution

1. Combinatorial Threshold Filter: Isolates high-amplitude seasonal frequencies while wiping out weak background noise.
2. Low-Pass Filter (Suggested by Prof. Strazzanti): Retains frequencies close to zero to isolate smooth macro-cycles and eliminate high-frequency turbulence.

Stage D: Time-Domain Inverse Transformation

• Reconstructs the cleaned frequency matrices back into real-valued continuous time-series models using the Inverse Fast Fourier Transform (IFFT).

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How to Run the Pipeline

1. Install dependencies:

   pip install -r requirements.txt

2. Run the master orchestrator to download data, apply Fourier equations, and output charts:

   python main.py