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Full-Text Articles in Social and Behavioral Sciences
Multiple Regression With Integrated Time Series, Peter C.B. Phillips
Multiple Regression With Integrated Time Series, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Recent work on the theory of regression with integrated process is reviewed. This work is particularly relevant in economics where many financial series and macroeconomic time series exhibit nonstationary characteristics and are often well modeled individually as simple ARIMA processes. The theory makes extensive use of weak convergence methods and allows for integrated processes that are driven by quite general weakly dependent and possibly heterogeneously distributed innovations. The theory also includes near integrated time series, which have roots near unity, and cointegrated series, which move together over time but are individually nonstationary. A general framework for asymptotic analysis is given …
Weak Convergence Of Sample Covariance Matrices To Stochastic Integrals Via Martingale Approximations, Peter C.B. Phillips
Weak Convergence Of Sample Covariance Matrices To Stochastic Integrals Via Martingale Approximations, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral from zero to one of ∫ 0 1 BdB ’, where B is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a similar result obtains. In this case, the limit is ∫ 0 1 BdB ’ + Λ and involves a constant matrix Λ, of bias terms whose magnitude depends on the serial correlation properties of the sequence. This note gives a simple proof of the result using martingale approximations.