A finite, empirically useless and almost sure VAR representation for all minimal transition equations

Saccal, Alessandro (2023): A finite, empirically useless and almost sure VAR representation for all minimal transition equations.

Abstract

Does there exist a systematic manner to derive a finite vector autoregression (VAR) representation for any minimal transition equation? While the good news be that any transition equation of a minimal linear time invariant (LTI) state space representation in discrete time admits a VAR representation of finite order of the non-minimal states in the (minimal) measurement equation’s outputs, the bad news are that such a representation, on account of the procedure underlying its derivation, is both the probabilistically surest and empirically useless, ranging from linear combinations of non-minimal states in principle, equal to shifted white noises, to output nullity, thereby presenting negative repercussions with particular regard to first order linear rational expectations (LRE) models of optimising representative agents.

• Item Type: MPRA Paper
• Language: English
• Keywords: DSGE models; LRE models; minimality; state space; VMA representation; VAR representation.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models

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