Working Paper
Work in progress
- Time-Varying Parameters and Heteroskedasticity: Continuous Time Systems with Unequally-Spaced Data (with Marcus Chambers) This paper presents an exact discrete time representation of a system of stochastic differential equations, which are observed at unequally-spaced intervals. Exact discrete time representations for unequally spaced data are provided when observations are strictly stocks, strictly flows, or a mixture of both. By allowing observation intervals to vary, the exact discrete time representations, in all cases, exhibit time-varying parameters and heteroskedasticity. Given that the underlying continuous time system is time invariant, the time-varying characteristic of the parameters and variances is thoroughly generatedby the unequal spaced intervals. This suggests that, in some circumstances, evidence of such time variation in estimated discrete time models may merely be a manifestation of the unequally spaced data rather than any inherent time variation in the model itself. Following the theory, some simulation experiments are conduced for assessing the extent that correctly measuring unequal observation intervals can have on the estimated parameters if continuous time models, in addition to an application to political popularity in the UK.
Work in progress
- Estimation of Continuous Time Models with Unequally Spaced Data with Applications to Macroeconomic Data