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Continuous time autoregressive models with common stochastic trends. (English) Zbl 0647.62104

Summary: A multivariate continuous time model is presented in which an n- dimensional process is represented as the sum of k stochastic trends plus an n-dimensional stationary term, assumed to obey a system of higher- order autoregressive stochastic differential equations. When \(k<n\), the variables are cointegrated and can be represented as linear combinations of a reduced number of common trends. An algorithm to estimate the parameters of the model is presented for the case that the trend and stationary disturbances are uncorrelated. This algorithm is used to extract a common (continuous time) stochastic trend from postwar U.S. GNP and consumption.

MSC:

62P20 Applications of statistics to economics
91B84 Economic time series analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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