Effects of estimation length on parameter estimates of geometric Brownian motion for log price dynamics

Abstract

We investigated an effect of the estimation length of the time-series data on the parameter estimates of geometric Brownian motion for log prices. This is to examine how much the estimates vary depending upon the estimation length of the data for the simulation purpose of stochastic modeling. Using the monthly time-series data for akamatsu, sugi, and hinoki from January 1975 to December 2000, our analysis shows that the longer the estimation length, the more stable the estimated value of the drift coefficient and the volatility coefficient of geometric Brownian motion become, implying less variability in the estimates needed for the simulation analysis. On the other hand, the shorter estimation length would tend to reflect such a sudden change in the data as the “oil shock” or the short-term decreasing or increasing tendency, which results in the large degree of variability in parameter estimates. This stems from the fact that the long estimation length regards a short-term price changes as an intrinsic part of price volatility. These results imply that when conducting a scenario analysis under stochastic environments, for the shorter estimation length, the wider range of parameter settings should be incorporated into the analysis.

Key words:

• Forest management
• Forest economics
• Stochastic analysis
• Sensitivity analysis
• Maximum likelihood estimate