Best linear unbiased estimate of linear trend-cycle component based on fbe-derived variables

Abstract

The Best linear unbiased estimates (BLUE) of the parameters (slope and intercept) of a linear trend-cycle component based on Fixed Base Estimation (FBE) derived variables are discussed in this paper.    The FBE-derived variables were found to have constant mean, non-constant variance but with constant autocorrelation coefficient at all lags. The variance of the variables decreased with recent time points, indicating that estimates of the slope from recent periods are more precise. Best Linear unbiased estimates of the slope from FBE-derived variables also attach greater weights to the more recent observations but have the same minimum variance as those from Chain Base Estimation (CBE) derived variables. Simulated numerical examples were used to illustrate the methods. The simulation results show that BLUE from the FBE and CBE-derived variables outperform the Simple Average and Least Squares Methods in terms of Mean Percentage Error (MPE), Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) of forecasts.