An alternative time series model of consumption: some empirical evidence

This paper presents some empirical evidence for a time series model of aggregate consumer' expenditure which is formulated in continuous time. It is argued that such models, expressed in terms of stochastic differential equations, are more realistic in representing the dynamic evolution of many economic time series, particularly at the aggregate level. However, such models impose complicated restrictions on the discretely observed data, which must be taken account of in estimation. The appropriate methodology is applied to a version of the consumption function for UK data, and is found to provide a good description of the data. The estimated continuous time model is compared with more popular discrete models, and is found to provide superior dynamic post-sample predictions over 16 quarters. The formulation of econometric models in continuous time may provide an alternative and potentially successful approach to the modelling of time series in many aspects of economics.