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Abstract The mean-reverting nature of freight rates is one of the important subjects in maritime economics. The classic understanding of maritime economics (and that of the shipping industry) suggests that freight rate processes are mean-reverting and approach the level decided by the demand/supply ratio. However, statistical tests on freight rate processes often reveal these processes to be non-stationary, which means the processes would not have a mean-reverting nature. In this study, we investigated the mean-reverting nature of Panamax freight rates (Baltic Panamax 4 T/C Average) for two “means”: the actual freight rate process itself, and the deviation process of actual freight rates from estimated ones based on the demand/supply ratio. The AR (1) model can be applied to both processes, and their autoregressive coefficient φ was between 0 and 1. In the actual freight process, φ was close to 1, and a unit root test failed to reject that the process is non-stationary. By contrast, in the deviation process, φ was sufficiently smaller than 1, and a unit root test rejected that the process is non-stationary. The result can resolve the contradiction between two views on mean-reverting nature; if we focus on the actual freight rate process itself and do not consider demand/supply, the process is non-stationary and does not have a mean-reverting nature. If we focus on the deviation process of the actual freight rates from the level decided by the demand/supply ratio, the process is stationary and tends to approach zero.

Seasonal fluctuations play an important role in the pricing of a timber sale. A good understanding of timber price mechanisms and predictability in the timber market would be very practical for forest owners, managers, and investors, and is crucial for the correct functioning of the timber sector. This research aimed to analyze the effect of sale season on timber (sawlog and lumber) prices of high-value species groups (e.g., oriental beech, chestnut-leaved oak, common alder, velvet maple, and common hornbeam) in the Hyrcanian temperate forests (Northern Iran). The data were collected from official sale documents of the Azarroud Forestry Plan from 1992 to 2015. The relevant data of 592 sale lots at forest roadside were extracted into a data set. Then, the average timber prices (sawlog and lumber) per season/year in quarterly frequency were calculated. In doing so, two-time series of seasonal prices for the sawlog and lumber was obtained. The stationarity of the time series was statistically verified using the augmented Dickey–Fuller test. The effect of sale seasons on timber price was first analyzed using multiple linear regression analysis dummy variables. The results showed that autumn and summer have a significant positive effect on timber prices of 6.5% and 6.1%, respectively. Additionally, the decomposition of time series results showed that the highest prices of the sawlog and lumber were in quarter 3 and quarter 2, respectively, due to an increase in construction activities that picked up in the autumn season. Information about potential price fluctuations will be plausible and allow suppliers and users of sawlogs to adjust their supply and demand. This valuable information can be used in marketing and strategic forest management planning for Hyrcanian temperate forests and other temperate countries with similar conditions.

The objective of the study was to verify the applicability and usefulness of time series decomposition in analyzing the variability of timber prices and supply in Poland. The employed multiplicative model was the product of four components: cyclical, seasonal, and irregular fluctuations and the long-term trend. The elements of the time series were determined by means of the Census X11 method, while cyclicality was separated from the trend employing the Hodrick−Prescott filter. Data included quarterly information about the supply (volume) and prices (value) of the timber sold by the State Forests in the years 2005−2018. Analyses were performed for tree species with the greatest economic significance, that is, pine, oak, spruce, beech, birch, and alder, and for their most popular assortments: general purpose large-diameter timber (W0) and medium-diameter timber (S2A). Time series decomposition of quarterly timber production volume and prices revealed irregular, seasonal, and cyclic fluctuations. Within an annual time horizon, irregular fluctuations accounted on average for 6.7% and 28% of overall variability in timber prices and supply, respectively; they exhibited low amplitudes (+5%, −25%, respectively). Cyclical fluctuations were primarily found for prices and were characterized by substantial variations in cycle length (2−4 years) and change amplitude (3−27 Euros). Cyclical fluctuations in timber prices and supply were usually negatively correlated with each other: the upper turning points of price cycles fell near the lower turning points of supply cycles (with a shift of 1 to 3 quarters). The seasonality of prices was also inversely correlated with supply: quarters with low supply exhibited higher prices and vice versa. Seasonal fluctuations were more pronounced for timber supply (36%) as compared to timber prices (20.3%). Different seasonality patterns were found for hardwood and softwood. The lowest supply of softwood was found in the first quarter and the highest in the third quarter (spruce) or fourth quarter (pine). The supply of hardwood was the highest in the first quarter and the lowest in the third quarter.