(i) Econometric Model Determination
This research seeks to provide a general asymptotic theory for model determination techniques that are suited to with time series data that may be stochastically nonstationary. The primary result is the isolation of an asymptotically valid form of the conditional data density, or marginal likelihood, that can be used for model determination, inference and forecast evaluation. This has been shown to be an interesting exponential density that is easily used in practical work. The level of generality in the asymptotic theory allows for integrated and cointegrated processes, so that a wide range of potential applications come within the compass of the asymptotics. The asymptotic form of the conditional data density is equivalent to the prequential form of the likelihood, relating this approach to earlier work by Dawid (in JRSS, 1984), and this provides an alternative conceptual justification for the model selection methods. A special advantage of the methods in nonstationary data models is that they avoid the awkwardness of the nonstandard, model-specific (and sometimes nuisance-parameter dependent) asymptotic theory of conventional estimators and tests. The methods can also be used to select cointegrating rank in a general cointegrated VAR, or even jointly select cointegrating rank and lag order in a VAR. In this context, the methods give consistent order estimates, and this has been shown in joint work with John Chao in Journal of Econometrics, 1999, "Bayesian Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure". Part of the theory involved the use of embedding techniques that permit the embedding of a discrete time density in a continuous time density process in a manner that is analogous to the Skorohod embedding of a discrete scalar martingale in a Brownian motion. The theory then justifies the use of the conditional Bayes densities as proper probability densities and gives the form of the model to which these densities correspond. So the procedures have an asymptotic Bayesian justification. The main ideas and asymptotic analysis is contained in "Econometric Model Determination'' in Econometrica, 1996. and an earlier paper in Econometrica, 1996 with Werner Ploberger on asymptotic theory for time series. Research also involved the implementation of these methods to produce multivariate forecasting models in the Bayesian VAR (BVAR) class. This allows for reduced rank regressions(RRR's) and error correction models (ECM's), as well as conventional Bayesian VAR's with unit root priors. A by-product of the model selection work is an optimized version of the BVAR in which the hyperparameters are data-determined. This means that in practice these models can be used in a nearly automated way for forecasting purposes, and leads naturally to practical applications.
     (Supported by NSF Grant No. SBR 94-22922)
(ii) Practical Ex Ante Forecasting Work
The goal of this research is the practical implementation of automated econometric forecasting and policy analysis techniques based on ideas in my paper "Econometric Model Determination'' in Econometrica, 1996. The methods are data-driven and almost completely automatic, requiring only minimal input from the investigator in the selection of model classes and maximal lags. I have been applying these methods to provide quarterly forecasts of macroeconomic activity for a group of Asia- Pacific countries (including the USA, Japan, Korea, Australia and New Zealand) for the last three years Ongoing results of this research are published as a regular feature in the Asia Pacific Economic Review. Forecasts from the automated time series models are compared with the quarterly forecasts obtained from the Fair structural econometric model. So far, the results indicate that data-based ECM models have an ex ante forecasting performance that is almost as good as that of the Fair model for inflation and real GDP. It is also apparent from the results so far that, for the USA at least, ECM methods generally provide better forecasts 1-8 periods ahead than Bayesian VAR methods.
     (Supported by NSF Grant No. SBR 94-22922)
(iii) Economic News and Economic Activity
This research is joint with Deborah Blood and studies empirical links between mass media communication, consumer sentiment and economic activity. Cointegration tests, causality tests and some recursive analyses were run in VAR's with economic headline news, consumer sentiment, presidential popularity and leading economic indicators. The empirical results show strong evidence of the agenda setting effects of the media, especially on consumer sentiment, allowing for actual economic conditions. The evidence also indicates a disruption in the normal pattern of the relationship between the news, economic activity and presidential popularity during the period 1990--1991, a period of foreign and economic upheaval for the Bush administration wherein the presidency enjoyed high approval ratings over the Gulf crisis but faced increasing criticism from the press over economic policy. Empirical results are reported in "Recession Headline News, Consumer Sentiment, the State of the Economy and Presidential Popularity: A Time Series Analysis 1989-1993" (with D. J. Blood), International Journal of Public Opinion Research, 1995.
     (Supported by NSF Grant No. SBR 94-22922)
(iv) Nonstationary Economic Time Series
Recent and ongoing work cover a variety of topics: inter alia, efficient quasi-differencing (QD) and trend estimation procedures; robust methods of estimation and inference for nonstationary time series; simultaneous equations cointegrating estimation; foreign exchange market unbiasedness tests; FM-regression methods and extensions; nonlinear I(1) analysis; kernel regression asymptotics, asymptotic policy analysis for cointegrated VAR's.
     (Supported by NSF Grant Nos. SBR 97-30295 and SES 00-92509)
(v) Nonstationary Panel Data
A general asymptotic theory for panel data applications with nonstationary data has been obtained in joint work in Econometrica, 1999, with Hyungsik Moon, "Linear Regression Limit Theory for Nonstationary Panel Data". This paper considers the general problem of multidimensional asymptotics, where more than one index may pass to infinity. Both sequential and joint limits are obtained. In a related work, we have shown how consistent estimation of local to unity parameters is possible using panel data. Research on several aspects of this general topic is continuing. Some of these papers may be downloaded from this website.
     (Supported by NSF Grant Nos. SBR 97-30295 and SES 00-92509)
(vi) Developments of Hannan Regression
Second order asymptotics for Hannan and periodogram regression methods have been developed in joint work with Zhijie Xiao. We have also developed expansions for Wald tests in cointegrated regression models. Asymptotics for time detrended spectral regressions have been obtained and shown to have unexpected biases, even asymptotically, in joint work in Econometrica, 2001, with Dean Corbae and Sam Ouliaris "Band Spectral Regression with Trending Data".
     (Supported by NSF Grant No. SBR 97-30295 and SES 00-92509)
(vii) Descriptive Statistics for Nonstationary Data
While there are many techniques of descriptive statistics for stationary time series, few techniques have been developed for doing descriptive statistics for nonstationary time series. In ongoing research, new methods for describing the features of time series that behave in a nonstationary way have been developed by the author. Some of these methods are discussed and illustrated in an empirical application to interest rate data on measuring the Fisher effect that the author presented at the Yale/Cowles Foundation Irving Fisher Conference in May 1998 (downloadable from this website). Ongoing empirical work on this problem is being conducted with Yixiao Sun.
     (Supported by NSF Grant No. SBR 97-30295 and SES 00-92509)

Watch this site for regular updates.