Michael A. Thornton

DISCRETE TIME REPRESENTATION OF CONTINUOUS TIME ARMA PROCESSES

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Handbook of Research Methods and Applications in Empirical Macroeconomics

Contents: 1. Introduction Nigar Hashimzade and Michael A. Thornton 2. A Review of Econometric Concepts and Methods for Empirical Macroeconomics Kerry Patterson and Michael A. Thornton PART I: PROPERTIES OF MACROECONOMIC DATA 3. Trends, Cycles and Structural Breaks Terence C. Mills 4. Unit Roots, Non-linearities and Structural Breaks Niels Haldrup, Robinson Kruse, Timo Terasvirta and Rasmus T. Varneskov 5. Filtering Macroeconomic Data D.S.G. Pollock PART II: MODELS FOR MACROECONOMIC DATA ANALYSIS 6. Vector Autoregressive Models Helmut Lutkepohl 7. Cointegration and Error Correction James Davidson 8. Estimation and Inference in Threshold Type Regime Switching Models Jesus Gonzalo and Jean-Yves Pitarakis 9. Testing Structural Stability in Macroeconometric Models Otilia Boldea and Alastair R. Hall 10. Dynamic Panel Data Models Badi H. Baltagi 11. Factor Models Jorg Breitung and In Choi 12. Conditional Heteroskedasticity in Macroeconomic Data: UK Inflation, Output Growth and their Uncertainties Menelaos Karanasos and Ning Zeng 13. Temporal Aggregation in Macroeconomics Michael A. Thornton and Marcus J. Chambers PART III: ESTIMATION AND EVALUATION FRAMEWORKS IN MACROECONOMICS 14. Generalized Method of Moments Alastair R. Hall 15. Maximum Likelihood Estimation of Time Series Models: The Kalman Filter and Beyond Tommaso Proietti and Alessandra Luati 16. Bayesian Methods Luc Bauwens and Dimitris Korobilis 17. Forecasting in Macroeconomics Raffaella Giacomini and Barbara Rossi PART IV: APPLICATIONS I: DYNAMIC STOCHASTIC GENERAL EQUILIBRIUM MODELS 18. The Science and Art of DSGE Modelling: I - Construction and Bayesian Estimation Cristiano Cantore, Vasco J. Gabriel, Paul Levine, Joseph Pearlman and Bo Yang 19. The Science and Art of DSGE Modelling: II - Model Comparisons, Model Validation, Policy Analysis and General Discussion Cristiano Cantore, Vasco J. Gabriel, Paul Levine, Joseph Pearlman and Bo Yang 20. Generalized Method of Moments Estimation of DSGE Models Francisco J. Ruge-Murcia 21. Bayesian Estimation of DSGE Models Pablo A. Guerron-Quintana and James M. Nason PART V: APPLICATIONS II: VECTOR AUTOREGRESSIVE MODELS 22. Structural Vector Autoregressions Lutz Kilian 23. Vector Autoregressive Models for Macroeconomic Policy Analysis Soyoung Kim PART VI: APPLICATIONS III: CALIBRATION AND SIMULATIONS 24. Calibration and Simulation of DSGE Models Paul Gomme and Damba Lkhagvasuren 25. Simulation and Estimation of Macroeconomic Models in Dynare Joao Madeira IndexFinancial support from the ESRC is gratefully acknowledged. Address for Correspondence: Jean-Yves Pitarakis, University of Southampton, School of Social Sciences, Economics Division, Southampton, SO17 1BJ, United-Kingdom. Email: j.pitarakis@soton.ac.uk

Continuous‐Time Autoregressive Moving Average Processes in Discrete Time: Representation and Embeddability

This article explores techniques to derive the exact discrete‐time representation for data generated by a continuous‐time autoregressive moving average (ARMA) process, augmenting existing methods with a stochastic integration‐by‐parts formula. The continuous‐time ARMA(2, 1) system is considered in detail, and a mapping from the parameters of a univariate discrete‐time ARMA(2, 1) process to a univariate continuous‐time ARMA(2, 1) process observed at discrete intervals is derived. This is used to derive conditions for the embeddability of such processes.

Removing seasonality under a changing regime: Filtering new car sales

The use of filters for the seasonal adjustment of data generated by the UK new car market is considered. UK new car registrations display very strong seasonality brought about by the system of identifiers in the UK registration plate, which has mutated in response to an increase in the frequency with which the identifier changes, while it also displays low frequency volatility that reflects UK macroeconomic conditions. Given the periodogram of the data, it is argued that an effective seasonal adjustment can be performed using a Butterworth lowpass filter. The results of this are compared with those based on adjustment using X-12 ARIMA and model-based methods.

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.