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Quantifying Inter-Annual Seasonal Drift in Tomato Prices Using Dynamic Time Warping: Evidence from Kolar Market

Manojkumar Patil, Lalith Achoth, K. B. Vedamurthy, K. B. Umesh, Siddayya, M. N. Thimme Gowda

Abstract

Tomato prices in Kolar market exhibit high volatility alongside recurring seasonal patterns, but the consistency of these patterns across years remains unclear. This study analysed weekly tomato prices and arrivals from 2010-2024 to quantify inter-annual variability using descriptive statistics, seasonal indices, and Dynamic Time Warping (DTW). Descriptive analysis confirmed extreme fluctuations (CV = 77% for prices, 102% for arrivals) with positive skewness and heavy tails, indicating frequent extreme events. Seasonal indices revealed recurring intra-year cycles, but year-to-year alignment varied substantially. DTW analysis for 2021-2024 quantified pattern similarity, showing that 2022-2023 had the highest alignment (DTW distance: 23,258) despite extreme price spikes, whereas 2021-2022 exhibited the weakest alignment (distance: 39,049), reflecting structural shifts in market dynamics. Path length metrics indicated minimal temporal warping in 2022-2023 (71 points) versus extensive alignment in 2021-2022 (83 points). These results demonstrate that while seasonal patterns recur, their temporal consistency is not fixed, highlighting the need for forecasting models that adapt to both magnitude volatility and temporal shifts. The study also illustrates the utility of DTW for agricultural price analysis and the limitations of relying solely on fixed seasonal patterns in volatile commodity markets.

Quantifying Inter-Annual Seasonal Drift in Tomato Prices Using Dynamic Time Warping: Evidence from Kolar Market

Abstract

Tomato prices in Kolar market exhibit high volatility alongside recurring seasonal patterns, but the consistency of these patterns across years remains unclear. This study analysed weekly tomato prices and arrivals from 2010-2024 to quantify inter-annual variability using descriptive statistics, seasonal indices, and Dynamic Time Warping (DTW). Descriptive analysis confirmed extreme fluctuations (CV = 77% for prices, 102% for arrivals) with positive skewness and heavy tails, indicating frequent extreme events. Seasonal indices revealed recurring intra-year cycles, but year-to-year alignment varied substantially. DTW analysis for 2021-2024 quantified pattern similarity, showing that 2022-2023 had the highest alignment (DTW distance: 23,258) despite extreme price spikes, whereas 2021-2022 exhibited the weakest alignment (distance: 39,049), reflecting structural shifts in market dynamics. Path length metrics indicated minimal temporal warping in 2022-2023 (71 points) versus extensive alignment in 2021-2022 (83 points). These results demonstrate that while seasonal patterns recur, their temporal consistency is not fixed, highlighting the need for forecasting models that adapt to both magnitude volatility and temporal shifts. The study also illustrates the utility of DTW for agricultural price analysis and the limitations of relying solely on fixed seasonal patterns in volatile commodity markets.

Paper Structure

This paper contains 21 sections, 8 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Study Area and Data
  4. Data Cleaning
  5. Descriptive Statistics
  6. Seasonal Indices
  7. Dynamic Time Warping (DTW)
  8. DTW Algorithm
  9. Step 1: Distance Matrix.
  10. Step 2: Cumulative Cost Matrix.
  11. Step 3: Optimal Warping Path.
  12. Step 4: DTW Distance.
  13. Implementation Details
  14. Software and Statistical Tools
  15. Results and Discussion
  16. ...and 6 more sections

Figures (4)

  • Figure 1: Weekly trends of tomato arrivals and modal prices in Kolar market (2010--2025).
  • Figure 2: Weekly seasonal indices of tomato arrivals and modal prices in Kolar market (2010--2025).
  • Figure 3: DTW analysis of modal price patterns (2021--2024). Left panels: DTW alignment paths; right panels: warped (time-aligned) price series. Lower DTW distances indicate higher inter-annual pattern similarity.
  • Figure 4: DTW analysis of arrivals patterns (2021--2024).