Cointegrated linear processes in Bayes Hilbert space

Seo, Won-Ki; Beare, Brendan K.

doi:10.1016/j.spl.2018.11.032

Cited by 11 publications

(13 citation statements)

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“…In this article, we provide representation theorems for I(1) and I(2) vector autoregressive processes taking values in an arbitrary complex separable Hilbert space. This more general setting is of central relevance for statistical applications involving functional time series (Hörmann and Kokoszka, 2012), and was first studied by Chang, Kim, and Park (2016) in the case of I(1) probability densityvalued time series; see also Beare (2017) and Seo and Beare (2019). Our results here build on those we obtained in an earlier article with J. Seo ) establishing a representation theorem for the I(1) case.…”

Section: Introductionsupporting

confidence: 67%

Representation of I(1) and I(2) Autoregressive Hilbertian Processes

Beare

Seo

2019

Econom. Theory

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We develop versions of the Granger-Johansen representation theorems for I(1) and I(2) vector autoregressive processes that apply to processes taking values in an arbitrary complex separable Hilbert space. This more general setting is of central relevance for statistical applications involving functional time series. An I(1) or I(2) solution to an autoregressive law of motion is obtained when the inverse of the autoregressive operator pencil has a pole of first or second order at one. We obtain a range of necessary and sufficient conditions for such a pole to be of first or second order. Cointegrating and attractor subspaces are characterized in terms of the behavior of the autoregressive operator pencil in a neighborhood of one.

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Section: Introductionsupporting

confidence: 67%

Representation of I(1) and I(2) Autoregressive Hilbertian Processes

Beare

Seo

2019

Econom. Theory

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“…One notable special case is given by H-valued processes x t = ψ( f t ), where f t is a generic probability density function (pdf) and ψ is an invertible transformation, see Petersen and Müller (2016), Beare (2017), and Seo and Beare (2019). 1 Modeling dynamics of an entire density or parts of a density is of practical interest in modeling income distributions, see, e.g., Bourguignon, Ferreira, and Lustig (2005), Piketty (2014), and Chang, Kim, and Park (2016b).…”

Section: Introductionmentioning

confidence: 99%

“…Density functions do not form a vector space with the standard addition and multiplication operations. This difficulty can be overcome by the transformation approach ofPetersen and Müller (2016) and/or by redefining the basic operations of addition and multiplication, as inSeo and Beare (2019) and references thereof.…”

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confidence: 99%

Cointegration in Functional Autoregressive Processes

Franchi

Paruolo

2019

Econom. Theory

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This paper defines the class of H-valued autoregressive (AR) processes with a unit root of finite type, where H is an infinite dimensional separable Hilbert space, and derives a generalization of the Granger-Johansen Representation Theorem valid for any integration order d = 1, 2, . . . . An existence theorem shows that the solution of an AR with a unit root of finite type is necessarily integrated of some finite integer d and displays a common trends representation with a finite number of common stochastic trends of the type of (cumulated) bilateral random walks and an infinite dimensional cointegrating space. A characterization theorem clarifies the connections between the structure of the AR operators and (i) the order of integration, (ii) the structure of the attractor space and the cointegrating space, (iii) the expression of the cointegrating relations, and (iv) the Triangular representation of the process. Except for the fact that the number of cointegrating relations that are integrated of order 0 is infinite, the representation of H-valued ARs with a unit root of finite type coincides with that of usual finite dimensional VARs, which corresponds to the special case H = R p .

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“…Benefits of employing the Bayes space context in spatial data analysis are also illustrated in environmental applications, e.g., by Menafoglio et al (2014Menafoglio et al ( , 2016b; Álvarez Vázquez et al (2020); Talská et al (2020). The approach has also been used to model cointegrated linear processes of densities (Seo and Beare, 2019). Note that the choice of the space within which the analysis is embedded (also termed as the feature space) is critical in Object Oriented Spatial Statistics (O2S2) -and, more generally, in Object Oriented Data Analysis -because it has a key impact on the results and on their interpretation.…”

Section: Problem Settingmentioning

confidence: 99%