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After the Collective Forest Tenure Reform (CFTR) in China, the enthusiasm of farmers for forestry management is stimulated. However, the forest tenure security varies among farmers, making the research conclusions of its impact on forestry management efficiency inconsistent. Based on the survey data of 1,627 households from the collective forest regions in 6 provinces of China in 2017, this paper not only discusses the differences of farmers' forestry management efficiency after the reform, but also further explores the heterogeneous impact of forest tenure security on forestry management efficiency in combination with different forest management types.

This study employed the stochastic frontier production function model to measure the forestry management efficiency of farmers. Then, Tobit models were used to discuss the influencing factors of farmers' forestry management efficiency.

The results demonstrate that the improvement of farmers' forest tenure security can effectively improve forestry management efficiency, but the effect is affected by forest management types. For farmers who manage economic forests and non-timber forests, safe tenure promotes the forestry management efficiency; while for those who manage ecological public welfare forests, tenure security plays an opposite role.

Therefore, satisfying farmers' differentiated demands for forest tenure according to forest management types to improve forest tenure security and further refining supporting policies of collective forestry reform is of great significance to improve the efficiency of farmers' forestry management in collective forest regions.

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.