Maximum likelihood estimation using differences in an autoregressive-1 process

Abstract

In a first-order autoregressive (AR-1) process with unknown mean, conventional maximum likelihood analysis requires joint estimation of the mean and AR coefficient. Differencing the series removes the mean, and for short series it should be more efficient to estimate the AR coefficient from the likelihood function of the differences. The exact likelihood function of the differences is given. A computer simulation study compares the behavior of the estimator obtained by maximizing the likelihood of the differences with that of the conventional maximum likelihood estimator. A root-mean-squared-error criterion shows superiority of the estimator based on differences for series of 50 time points or less.

Keywords:

• maximum likelihood
• autoregressive-1 process
• first differences