The unilateral shift operator T unifies stationary process invertibility with algebraic invertibility of transfer functions f(T) in the Wiener algebra, where f(T) is the Toeplitz operator with matching norm.
Time Series Analysis
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Proposes L² norm for stationary ARMA models from Wold decomposition and derives MSPE bounds for AR(1) approximating MA(1), with empirical checks.
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Stationary Process Invertibility and the Unilateral Shift Operator
The unilateral shift operator T unifies stationary process invertibility with algebraic invertibility of transfer functions f(T) in the Wiener algebra, where f(T) is the Toeplitz operator with matching norm.
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On an $L^2$ norm for stationary ARMA processes
Proposes L² norm for stationary ARMA models from Wold decomposition and derives MSPE bounds for AR(1) approximating MA(1), with empirical checks.