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Full-Text Articles in Social and Behavioral Sciences
Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips
Weak Convergence To The Matrix Stochastic Integral Bdb, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form ∫ 0 1 WdW , where W ( r ) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes the theory involves weak convergence to matrix stochastic integrals of the form ∫ 0 1 BdB ’, where B ( r ) is vector Brownian motion with non scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to ∫ 0 1 BdB ’ under quite general conditions. The theory is …
Testing For A Unit Root In Time Series Regression, Peter C.B. Phillips, Pierre Perron
Testing For A Unit Root In Time Series Regression, Peter C.B. Phillips, Pierre Perron
Cowles Foundation Discussion Papers
This paper proposes some new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory …