Continuous Time Modelling Based on an Exact Discrete Time Representation

This chapter provides a survey of methods of continuous time modelling based on an exact discrete time representation. It begins by highlighting the techniques involved with the derivation of an exact discrete time representation of an underlying continuous time model,providing specificc details for a second-order linear system of stochastic differential equations. Issues of parameter identification, Granger causality, nonstationarity, and mixed frequency data are addressed, all being important considerations in applications in economics and other disciplines. Although the focus is on Gaussian estimation of the exact discrete time model, alternative time domain (state space) and frequency domain approaches are also discussed. Computational issues are explored and two new empirical applications are included along with a discussion of applications in the field of macroeconometric modelling

Granger Causality and the Sampling of Economic Processes

This paper provides a discussion of the developments in econometric modelling that are designed to deal with the problem of spurious Granger causality relationships that can arise from temporal aggregation.We outline the distortional e ects of using discrete time models that explicitly depend on the unit of time and outline a remedy of constructing timeinvariant discrete time models via a structural continuous time model.In an application to testing for money-income causality, we demonstrate the importance of incorporating exact temporal aggregation restrictions on the discrete time data.We do this by conducting causality tests in discrete time models that: (a) impose the temporal aggregation restrictions exactly; (b) impose the temporal aggregation restrictions approximately; and (c) do not impose these restrictions at all

Identification and Estimation of Exchange Rate Models with Unobservable Fundamentals

This paper is concerned with issues of model specification, identification, and estimation in exchange rate models with unobservable fundamentals.We show that the model estimated by Gardeazabal, Reg�lez and V�zquez(International Economic Review, 1997) is not identified and demonstrate how to specify an identified model in-keeping with their intended approach.Estimates of the identified model are reported for five currencies over two time spans, and a restriction suggested by the asset market view of exchange rate determination is not rejected for any currency or time span.The forecasting performance of the model is also examined and is found to compare favourably with forecasts generated by a random walk with drift

Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems

This paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time.The model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows.We derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form, which acts as the basis for frequency domain Gaussian estimation of the unknown parameters using discrete time data.We formally establish the order of consistency and the asymptotic sampling properties of such an estimator.The function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution, while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution

The Physical Activity Messaging Framework (PAMF) and Checklist (PAMC): International consensus statement and user guide

\ua9 2021, The Author(s). Effective physical activity messaging plays an important role in the pathway towards changing physical activity behaviour at a population level. The Physical Activity Messaging Framework (PAMF) and Checklist (PAMC) are outputs from a recent modified Delphi study. This sought consensus from an international expert panel on how to aid the creation and evaluation of physical activity messages. In this paper, we (1) present an overview of the various concepts within the PAMF and PAMC, (2) discuss in detail how the PAMF and PAMC can be used to create physical activity messages, plan evaluation of messages, and aid understanding and categorisation of existing messages, and (3) highlight areas for future development and research. If adopted, we propose that the PAMF and PAMC could improve physical activity messaging practice by encouraging evidence-based and target population-focused messages with clearly stated aims and consideration of potential working pathways. They could also enhance the physical activity messaging research base by harmonising key messaging terminologies, improving quality of reporting, and aiding collation and synthesis of the evidence