"Locally Exact Discrete Time Representations of Non-Linear Continuous Time Models" (with T Simos and M Tsionas), September 2023 (pdf).

"GLS Detrending in Continuous Time," currently under revision.

"Time-Varying Parameters and Heteroskedasticity: Continuous Time Systems with Unequally-Spaced Data" (with H Zhang), currently under revision.

Articles in Refereed Journals and Books

1. "Frequency Domain Estimation of Cointegrating Vectors with Mixed Frequency and Mixed Sample Data," Journal of Econometrics 217, 2020, 140-160.
2. "Deterministic Parameter Change Models in Continuous and Discrete Time," Journal of Time Series Analysis 41, 2020, 134-145 (with AMR Taylor).
3. "Frequency Domain Estimation of Continuous Time Cointegrated Models with Mixed Frequency and Mixed Sample Data," Journal of Time Series Analysis 40, 2019, 887-913.
4. ``Editorial: Econometric Modelling with Mixed Frequency and Temporally Aggregated Data,'' Journal of Time Series Analysis 40, 2019, 869-871 (with PA Zadrozny).
5. "Continuous Time Modelling Based on an Exact Discrete Time Representation," ch.14 in: K van Montfort, J Oud and M Voelkle (Eds.), Continuous Time Modeling in the Behavioral and Related Sciences, Springer, 2018, 317-357 (with JR McCrorie and MA Thornton).
6. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics 6, 2018, Article 11 (with M Kyriacou).
7. "Continuous Time ARMA Processes: Discrete Time Representation and Likelihood Evaluation," Journal of Economic Dynamics and Control 79, 2017, 48-65 (with MA Thornton).
8. "The Estimation of Continuous Time Models with Mixed Frequency Data," Journal of Econometrics 193, 2016, 390-404.
9. "The Exact Discretisation of CARMA Models with Applications in Finance," Journal of Empirical Finance 38, 2016, 739-761 (with MA Thornton).
10. "Testing for a Unit Root in a Near-Integrated Model with Skip-Sampled Data," Journal of Time Series Analysis 36, 2015, 630-649.
11. "The Calculation of Some Limiting Distributions Arising in Near-Integrated Models with GLS Detrending," Journal of Time Series Analysis 36, 2015, 562-586.
12. "A Jackknife Correction to a Test for Cointegration Rank," Econometrics 3, 2015, 355-375.
13. "Monetary Policy, Exchange Rates and Stock Prices in the Middle East Region," International Review of Financial Analysis 37, 2015, 14-28 (with HE Abou Wafia).
14. "Testing for Seasonal Unit Roots by Frequency Domain Regression," Journal of Econometrics 178, 2014, 243-258 (with JS Ercolani and AMR Taylor).
15. "Continuous Time ARMA Processes in Discrete Time: Representation and Embeddability," Journal of Time Series Analysis 34, 2013, 552-561 (with MA Thornton).
16. "Jackknife Estimation with a Unit Root," Statistics and Probability Letters 83, 2013, 1677-1682 (with M Kyriacou).
17. "Jackknife Estimation of Stationary Autoregressive Models," Journal of Econometrics 172, 2013, 142-157.
18. "Temporal Aggregation in Macroeconomics," ch.13 in: N Hashimzade and MA Thornton (Eds), Handbook of Research Methods and Applications in Empirical Macroeconomics, Edward Elgar,Cheltenham, 2013, 289-309 (with MA Thornton).
19. "Discrete Time Representation of Continuous Time ARMA Processes," Econometric Theory 28, 2012, 219-238 (with M A Thornton).
20. "Cointegration and Sampling Frequency," The Econometrics Journal 14, 2011, 156-185.
21. "Discrete Time Representations of Cointegrated Continuous Time Models with Mixed Sample Data," Econometric Theory 25, 2009, 1030-1049.
22. "Econometric Theory Memorial to Albert Rex Bergstrom," Econometric Theory 25, 2009, 891-900 (with PCB Phillips and AMR Taylor).
23. "Corrigendum to 'Testing for Unit Roots with Flow Data and Varying Sampling Frequency' [Journal of Econometrics 119(1) (2004) 1-18]," Journal of Econometrics 144, 2008, 524-525.
24. "Frequency Domain Estimation of Temporally Aggregated Gaussian Cointegrated Systems," Journal of Econometrics 136, 2007, 1-29 (with JR McCrorie).
25. "Granger Causality and the Sampling of Economic Processes," Journal of Econometrics 132, 2006, 311-336 (with JR McCrorie).
26. "Identification and Estimation of Exchange Rate Models with Unobservable Fundamentals," International Economic Review 47, 2006, 573-582 (with JR McCrorie).
27. "Estimation of Differential-Difference Equation Systems with Unknown Lag Parameters," Econometric Theory 22, 2006, 483-498 (with JS Ercolani).
28. "The Purchasing Power Parity Puzzle, Temporal Aggregation, and Half-Life Estimation," Economics Letters 86, 2005, 193-198. A supplementary document containing proofs is available here.
29. "Testing for Unit Roots with Flow Data and Varying Sampling Frequency," Journal of Econometrics 119, 2004, 1-18.
30. "The Asymptotic Efficiency of Cointegration Estimators Under Temporal Aggregation," Econometric Theory 19, 2003, 49-77. A supplementary document containing proofs of theorems etc. can be found here.
31. "Modelling Cyclical Behaviour with Differential-Difference Equations in an Unobserved Components Framework," Econometric Theory 18, 2002, 387-419 (with JS McGarry) (full tables of results in PDF format).
32. "Temporal Aggregation and the Finite Sample Performance of Spectral Regression Estimators in Cointegrated Systems: A Simulation Study," Econometric Theory 17, 2001, 591-607.
33. "A Statistical Analysis of Wheat Price Fluctuations in England: 1685-1850," Journal of Agricultural Economics 50, 1999, 564-588 (with RE Bailey) (the data are available in the following file formats: Text (.crv), Gauss (.dat) and (.dht), Stata (.dta).
34. "A Note on Modelling Seasonal Processes in Continuous Time," Journal of Time Series Analysis 20, 1999, 139-143.
35. "Discrete Time Representation of Stationary and Non-Stationary Continuous Time Systems," Journal of Economic Dynamics and Control 23, 1999, 619-639.
36. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review 39, 1998, 1053-1072.
37. "The Impact of Real Wage and Mortality Fluctuations on Fertility and Nuptiality in Precensus England," Journal of Population Economics 11, 1998, 413-434 (with RE Bailey).
38. "The Estimation of Systems of Joint Differential-Difference Equations," Journal of Econometrics 85, 1998, 1-31.
39. "Forecasting with the Almost Ideal Demand System: Evidence from Some Alternative Dynamic Specifications," Applied Economics 29, 1997, 935-943 (with KB Nowman).
40. "A Theory of Commodity Price Fluctuations," Journal of Political Economy 104, 1996, 924-957 (with RE Bailey) (the unpublished technical appendix is available in PDF here).
41. "The Estimation of Continuous Parameter Long-Memory Time Series Models," Econometric Theory 12, 1996, 374-390.
42. "Fractional Integration, Trend Stationarity and Difference Stationarity: Evidence from Some U.K. Macroeconomic Time Series," Economics Letters 50, 1996, 19-24.
43. "Speed of Adjustment and Estimation of the Partial Adjustment Model," Applied Economics Letters 3, 1996, 21-23.
44. "On the Simulation of Random Vector Time Series with Given Spectrum," Mathematical and Computer Modelling 22, 1995, 1-6.
45. "Long Term Demographic Interactions in Pre-Census England," Journal of the Royal Statistical Society (Series A) 156, 1993, 339-362 (with RE Bailey).
46. "A Nonnested Approach to Testing Continuous Time Models Against Discrete Alternatives," Journal of Econometrics 57, 1993, 319-343.
47. "Consumers' Demand in the Long Run: Some Evidence from UK Data," Applied Economics 25, 1993, 727-733.
48. Computers and Mathematics with Applications 25, 1993, 93-99.
49. "Forecasting with Continuous Time and Discrete Time Series Models: An Empirical Comparison, ch.5 in: PCB Phillips (Ed.), Models, Methods and Applications of Econometrics: Essays in Honor of AR Bergstrom, Basil Blackwell, Oxford, 1993, 37-54.
50. "An Econometric Model of the Aggregate Motor Insurance Market in the United Kingdom," Journal of Risk and Insurance 59, 1992, 409-425.
51. "Estimation of a Continuous Time Dynamic Demand System," Journal of Applied Econometrics 7, 1992, 53-64.
52. "Discrete Models for Estimating General Linear Continuous Time Systems," Econometric Theory 7, 1991, 531-542.
53. "Forecasting Discrete Stock and Flow Data Generated by a Second Order Continuous Time System," Computers and Mathematics with Applications 22, 1991, 107-114.
54. "An Alternative Time Series Model of Consumption: Some Empirical Evidence," Applied Economics 23, 1991, 1361-1366.
55. "Gaussian Estimation of a Continuous Time Model of Demand for Consumer Durable Goods with Applications to Demand in the United Kingdom, 1973--1984," ch.12 in: AR Bergstrom, Continuous Time Econometric Modelling, Oxford University Press, Oxford, 1990, 279-319 (with AR Bergstrom).
56. "Forecasting with Demand Systems: A Comparative Study," Journal of Econometrics 44, 1990, 363-376.

Technical Reports

57. "Consumers' Demand and Excise Duty Receipts Equations for Alcohol, Tobacco, Petrol and DERV," Technical Report for HM Customs and Excise, November 1998; published as Government Economic Service Working Paper No.138, November 1999.

Book Reviews

58. "Unobserved Components and Time Series Econometrics," by SJ Koopman and N Shephard (Eds.), Oxford University Press, Oxford, 2015, Journal of Time Series Analysis 37, 2016, 862-863.
59. "Challenging Time Series: Limits to Knowledge, Inertia and Caprice," by TD Stanley, Edward Elgar, Cheltenham, 2000, Economic Journal 111, 2001, F200--F202.
60. "Handbook of Applied Econometrics, Volume I," by MH Pesaran and MR Wickens (Eds.), Blackwells, Oxford, 1995, and "Handbook of Applied Econometrics, Volume II," by MH Pesaran and P Schmidt (Eds.), Blackwells, Oxford, 1997 (joint review), Economic Journal 110, 2000, F803-F805.
61. "Dynamic Disequilibrium Modeling," by WA Barnett, G Gandolfo and C Hillinger (Eds.), Cambridge University Press, Cambridge, 1996, Economic Journal 107, 1997, 1900-1902.
62. "Estimation and Inference in Econometrics," by R Davidson and JG MacKinnon, Oxford University Press, Oxford, 1993, Economic Journal 104, 1994, 703-705.
63. "Aggregation, Consumption and Trade: Essays in Honour of Hendrik S Houthakker," by L Phlips and LD Taylor (Eds.), Kluwer Academic Publishers, Dordrecht, 1992, Economic Journal 103, 1993, 1335-1337.

The Analysis of Non-stationary Time Series in Economics and Finance: Cointegration, Trend Breaks, and Mixed Frequency Data

Principal Investigator: A.M. Robert Taylor, Essex Business School, University of Essex
Co-Investigator: Marcus J. Chambers, Department of Economics, University of Essex

Summary

Macroeconomic and financial time series are typically non-stationary (or unstable), in that their means, variances and autocovariances evolve over time. As a result standard multivariate time series models can only be validly applied to the changes in these variables. Such models, however, contain no information about any long run relationships between the series, as are often predicted by economic or finance theory. A solution is provided by co-integration analysis which recognises that certain combinations of the variables are stationary (stable). A key example is term structure data, where it is often found that while individual interest rates appear to be unstable, the spreads between the rates appear stable.

Practical co-integration analysis is complicated by the fact that economies periodically undergo episodes of structural change, such as stock market crashes or changes in government regime/policy. Empirical evidence suggests that these episodes often manifest themselves in the form of multiple changes in the underlying deterministic trend component of the variables and/or changes in the volatility of the unanticipated random shocks. Extant co-integration tests can result in misleading inference regarding the presence or otherwise of long run relationships between the variables when these forms of structural change are present. This will typically result in misspecified econometric models with poor forecasting ability. It is therefore important to develop new co-integration tests which can deliver reliable inference in such environments. Doing so constitutes the first part of this project and will involve the development of a new simulation-based (bootstrap) procedure.

In light of the recent financial crisis, attention has increasingly focused on understanding the interactions between the macroeconomy and the financial sector. To do so effectively, econometric methods are needed that are capable of handling the mismatch between the frequencies at which data on the financial sector (eg exchange rates, stock prices) and the macroeconomy (eg GDP) become available, and this constitutes the second part of the project. While financial data can be observed at very high frequencies, macroeconomic data are typically available only monthly at best. The vast majority of methods for modelling multivariate time series assume a common sampling frequency; this typically entails discarding information in the high frequency data by converting it to the lowest frequency. However, high frequency financial data contains information that can affect the future time path of the low frequency data, and its utilisation can enable policymakers to act promptly prior to the macroeconomic data becoming available. For example, a financial crisis can be observed long before its effects on GDP are observed, but the ability to predict what those effects might be, using an econometric model capable of dealing with mixed frequency data, can be an important aid to policy making. Methods to allow for structural changes when dealing with mixed frequency data will also be considered.

The theoretical development, to be conducted using large sample econometric theory, will exploit the expertise and experience of the applicants. Taylor has already examined the behaviour of non-constant volatility on co-integration tests which do not allow for structural change in the trend. Chambers has recently developed methods of combining mixed frequency data that preserve the underlying relationships between the series and has also analysed co-integrated systems under temporal aggregation. This project will build on these foundations.

The practical relevance of the theoretical results will be explored using simulation experiments. We will also provide clear guidance to empirical researchers, through worked examples on key international datasets, and make freely available computer programs, to facilitate the implementation of the new techniques.

Outputs

A full list of outputs produced by Rob and me can be found on his pages here.

The first of two one-day workshops took place at Essex on Monday 11 July, 2016 on the theme of "Co-integration, Multivariate Time Series Modelling and Structural Change"; the workshop programme is available here.

The second one-day workshop took place at Essex on Wednesday 5 July, 2017 on the theme of "Econometric Modelling with Mixed Frequency and Aggregated Data"; the workshop programme is available here.

Contact Details

For contact details please see the main page of this website.

Jackknife Methods of Estimation and Inference in Dynamic Econometric Models

Marcus J. Chambers, University of Essex (Award Number RES-000-22-3082)

Summary

Time series data in economics, finance and many other disciplines, are typically characterised by high degrees of correlation over time, and dynamic models that relate variables to their past values are in widespread use in the modelling and forecasting of such data. In samples of fixed size, however, estimators of the unknown parameters in such models are typically biased and can lead to misleading interpretations of the observed data and to inaccurate (and potentially costly) forecasts. The jackknife method of bias reduction was developed for use with random (uncorrelated) samples but, with suitable modifications, it can also be used with time series data; this research project will analyse and develop jackknife methods in dynamic models of the types used in both theoretical and empirical research in econometrics. In particular the research will analyse the performance of jackknife bias reduction methods in stationary and nonstationary time series models and evaluate their effects on related statistical hypothesis tests. The effectiveness of the jackknife with different estimation methods and on the accuracy of post-sample forecasts will also be explored. A combination of analytical statistical and econometric techniques will be used combined with appropriately designed computer simulations and applications to relevant data.

Papers

"Jackknife Estimation of Stationary Autoregressive Models," January 2010 (pdf); also available as University of Essex Department of Economics Discussion Paper 684 (pdf).

"Jackknife Bias Reduction in the Presence of a Unit Root," January 2010 (with Maria Kyriacou) (pdf); also available as University of Essex Department of Economics Discussion Paper 685 (pdf).

Gauss Code

Some Gauss code to calculate the jackknife estimator in a linear regression model and a univariate AR(1) is contained in the following file: (.src)

Contact Details

For contact details please see the main page of this website.