Arch, Cointegration and Common Features: Theory and Application

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This is an accomplishment based renewal of a project that developed ARCH and related models and tests for cointegration. Models of ARCH and cointegration are now used in almost every area of economics to test for economic relationships among different economic variables using time series data. These studies typically use univariate time series models or multivariate models with at most two or three different time series. This is a major drawback for most economic applications. This grant will permit the investigator to continue the research started under the previous grant on multivariate ARCH and cointegration analysis. In addition the project develops and applies a new statistical procedure called common features to problems in economics and finance. A conference will be held in April, 1992 in La Jolla, California on new developments in volatility models and applications to finance. Economic time series have many distinctive characteristics. Generally, they exhibit serial correlation, trends, seasonality, often heteroskedasticity, skewness, kurtosis, and various other features. In order to detect each of these features in a data set, a variety of tests are available each of which takes the particular feature in question as the alternative to the null hypothesis that the feature is not present in the data. Under its previous NSF grant, the investigator developed a new statistical procedure called common features that permits the analyst to determine if two or more data sets share the same distinctive characteristics. This procedure was used to show that there was empirical evidence of a common international business cycle for the major industrial countries. The procedure will be extended and generalized. It will be used to examine sectoral output in the U.S. to see whether sectors move together over the business cycle. The procedure will be used to determine whether regions within the U.S. move together. International data on capital markets will be analyzed to determine what features are common to the equity markets for several blocks of countries. This research should provide new insights into the nature of the volatility in international capital markets.