Monash University

Forecasting Accuracy and the Importance of Finding the Global Maxima of the Likelihood Function

Email address: Mahbuba.Yeasmin@buseco.monash.edu.au

Keywords: General linear model; Local maxima; MA errors; Marginal likelihood; Concentrated likelihood; Forecasting performance

JEL Classifications: C5; C53

Abstract:
The method of maximum likelihood estimation is widely used in econometrics because it can be applied to a wide range of different parametric models and the resultant estimators have good asymptotic properties (for example, see Cramer (1986)). Modern statistical computer packages allow one to carry out maximum likelihood estimation on reasonably complicated models with some degree of ease. An unfortunate drawback of the method, particularly when numerical methods are used to maximise the likelihood function is that we can sometimes end up with a local maxima rather than the global maxima. This is a well-known problem in econometrics, although a survey of recent textbooks suggests that the consequences of accepting a local maxima instead of the global maxima are not well articulated. While the consequences for the estimation of parameters of interest might seem obvious, less obvious is what effect using parameter estimates from a local maximum could have on the small sample forecasting performance of a model. This paper considers this problem in the context of the linear regression model with first-order moving average (MA) errors; a model that can have local and global maxima with one at or where is the MA parameter. We compare the accuracy of forecasts using three different estimation strategies. The first involves accepting the maximum that comes from maximising the likelihood from one fixed starting point, the second involves taking the best result from three fixed starting points and the third involves taking even greater care to find the global maxima by using 21 starting values. We find that for this particular case the extra care taken to find the global maximum can, in some circumstances, have dramatic effect on forecasting accuracy.

PDF file of paper: yeasmin.pdf

Session: Econometric Methods II

Time: Saturday, 7 July, 2:15pm - 3:45pm

Room: B