Comparison of estimators for rolling samples using forest inventory and analysis data

The performance of three classes of weighted average estimators is studied for an annual inventory design similar to the Forest Inventory and Analysis program of the United States. The first class is based on an ARIMA(0,1,1) time series model. The equal weight, simple moving average is a member of this class. The second class is based on an ARIMA(0,2,2) time series model. The final class is based on a locally weighted least-squares regression prediction. The estimator properties were tested using a simulation population created from Forest Inventory and Analysis (FIA) data from northeastern Minnesota. Estimates of total volume per acre, on-growth volume per acre, mortality volume per acre, proportion of sawtimber acreage, proportion of poletimber acreage, and proportion of sapling acreage were calculated using several weighted average estimators in each year. These were compared to the simulation population, for which the true values are known, and an unbiased yearly estimator. When computing estimates, the ARIMA(0,1,1) based estimators produced the lowest root mean squared error of each of the three classes. However, in a few years the bias for some variables was high. The maximum percent increase between the estimator with the lowest root mean squared error and the simple moving average was 7.31%. Of all the estimators, the simple moving average performed well in terms of mean square error in virtually every situation. It tended to be best among the estimators tested if spatial variation was large and change was relatively small. It was not consistently best in terms of mean square error in the presence of moderate change and large spatial variation.