Fractal Analysis of Timber Prices: Evidence from the Polish Regional Timber Market

Timber price dynamics are most often analysed using trends, seasonality, and classical measures of volatility, which describe the magnitude of fluctuations but only to a limited extent capture the temporal structure of the price-generating process. The aim of this study is to identify the structural complexity and long-term memory of quarterly prices of WC0 pine timber in the regional timber market in Poland. The analysis is based on nominal net prices (PLN/m3) from 16 forest districts of the Regional Directorate of State Forests in Kraków over the period 2005–2024, with reference to nationally averaged timber prices. Long-term dependence is assessed using the Hurst exponent estimated by detrended fluctuation analysis (DFA) applied to log returns, while the geometric complexity of price trajectories is characterised by the fractal dimension and additionally validated using the Higuchi estimator. Cross-sectional results reveal substantial spatial heterogeneity in scaling properties, indicating the coexistence of persistent (trend-following) and corrective (anti-persistent) dynamics across forest districts. Rolling-window analysis (40 quarters) demonstrates temporal variability in price dynamics, with particularly pronounced shifts observed in 2019–2021. Cluster analysis based on time-varying Hurst exponent values identifies two groups of forest districts with distinct persistence trajectories, corresponding to more trend-dominated and corrective price dynamics. In contrast, national-level prices generally exhibit higher persistence than local prices, reflecting the effects of price aggregation. Overall, the results show that fractal analysis uncovers persistent spatial and temporal differences in timber price structures that remain invisible when relying solely on variance-based measures, with direct implications for the choice of planning horizons and timber sale strategies in regional markets.