Geodesic
On random processes as an implicit solution of equations
Kybernetika, Tome 53 (2017) no. 6, pp. 985-991 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Random processes with convenient properties are often employed to model observed data, particularly, coming from economy and finance. We will focus our interest in random processes given implicitly as a solution of a functional equation. For example, random processes AR, ARMA, ARCH, GARCH are belonging in this wide class. Their common feature can be expressed by requirement that stated random process together with incoming innovations must fulfill a functional equation. Functional dependence is linear for AR, ARMA. We consider a general functional dependence, but, existence of a forward and a backward equivalent rewritings of the given functional equation is required. We present a concept of solution construction giving uniqueness of assigned solution. We introduce a class of implicit models where forward and backward equivalent rewritings exist. Illustrative examples are included.
Random processes with convenient properties are often employed to model observed data, particularly, coming from economy and finance. We will focus our interest in random processes given implicitly as a solution of a functional equation. For example, random processes AR, ARMA, ARCH, GARCH are belonging in this wide class. Their common feature can be expressed by requirement that stated random process together with incoming innovations must fulfill a functional equation. Functional dependence is linear for AR, ARMA. We consider a general functional dependence, but, existence of a forward and a backward equivalent rewritings of the given functional equation is required. We present a concept of solution construction giving uniqueness of assigned solution. We introduce a class of implicit models where forward and backward equivalent rewritings exist. Illustrative examples are included.
DOI : 10.14736/kyb-2017-6-0985
Classification : 62M10, 91B70
Keywords: econometric models; ARMA process; implicit definition 
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Lachout, Petr. On random processes as an implicit solution of equations. Kybernetika, Tome 53 (2017) no. 6, pp. 985-991. doi: 10.14736/kyb-2017-6-0985

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