Comparative Analysis of Stochastic Models for Financial Uncertainty in Forest Management

摘要

We propose 13 continuous time stochastic models based on the state-dependent volatility process for stochastic log price dynamics, and then conduct a comparative analysis for their performance. Comparison is carried out on the basis of AIC (Akaike's Information Criterion), the mean squared error of the model, and the likelihood ratio test. Parameter estimation is performed by using the local linearization method. Our experiments with 13 tree species sold on the Japanese timber market show that the general form of the state-dependent stochastic model yields the highest performance in terms of AIC for most logs. In addition, we find that price dynamics with a tendency to increase over time can be captured by such a stochastic model, with the drift term as a linear function of the state. It is also shown that a functional form of the diffusion part or volatility of the model plays an important role in model performance with regard to the AIC, while a functional form of the drift part of the model does so in the mean squared error for forecasting one period ahead.