Strict Stationarity of Generalized Autoregressive Processes

Bougerol, Philippe; Picard, Nico

doi:10.1214/aop/1176989526

Cited by 354 publications

(266 citation statements)

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“…This model can be considered as the solution to a multivariate stochastic recurrence equation and hence, general results by Kesten (1973) and Bougerol and Picard (1992b) can be applied. These general results can, however, for this model be considerably reduced; cf.…”

Section: Arch(1) and Garch(11) Processesmentioning

confidence: 99%

High-level dependence in time series models

2009

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We present several notions of high-level dependence for stochastic processes, which have appeared in the literature. We calculate such measures for discrete and continuous-time models, where we concentrate on time series with heavy-tailed marginals, where extremes are likely to occur in clusters. Such models include linear models and solutions to random recurrence equations; in particular, discrete and continuous-time moving average and (G)ARCH processes. To illustrate our results we present a small simulation study.

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Section: Arch(1) and Garch(11) Processesmentioning

confidence: 99%

High-level dependence in time series models

2009

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“…The joint process {( S t , α S t + S t ε t ), t ∈ N } inherits strict ergodic stationarity from {(S t , ε t ), t ∈ N }. We assume that the top Lyapunov exponent associated to the process (2.1) is negative so the MS VAR model (2.1) is strictly stationary (see Brandt, 1986;Bougerol and Picard, 1992).…”

Section: Model and Assumptionsmentioning

confidence: 99%

Marginal distribution of Markov-switchingVARprocesses

Fiorentini

Planas

Rossi

2016

Communications in Statistics - Theory and Methods

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We make available simple and accurate closed-form approximations to the marginal distribution of Markov-switching vector auto-regressive (MS VAR) processes. The approximation is built upon the property of MS VAR processes of being Gaussian conditionally on any semi-infinite sequence of the latent state. Truncating the semi-infinite sequence and averaging over all possible sequences of that finite length yields a mixture of normals that converges to the unknown marginal distribution as the sequence length increases. Numerical experiments confirm the viability of the approach which extends to the closely related class of MS state space models. Several applications are discussed.

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“…Part (a) of the following theorem was proved in one dimension by Brandt [5] and extended to the vector case by Bougerol and Picard [4]. We have added part (b) for clarity (it is proved in the same way as part (a)).…”

Section: Random Disturbancesmentioning

confidence: 99%

Cobweb Theorems with Production Lags and Price Forecasting

Dufresne

Vázquez-Abad

2012

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract The classical cobweb theorem is extended to include production lags and price forecasts. Price forecasting based on a longer period has a stabilizing effect on prices. Longer production lags do not necessarily lead to unstable prices; very long lags lead to cycles of constant amplitude. The classical cobweb requires elasticity of demand to be greater than that of supply; this is not necessarily the case in a more general setting, price forecasting has a stabilizing effect. Random shocks are also considered. Terms of use: Documents in EconStor mayJEL C02, C62, C65, D58, E32

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Strict Stationarity of Generalized Autoregressive Processes

Cited by 354 publications

References 0 publications

High-level dependence in time series models

High-level dependence in time series models

Marginal distribution of Markov-switchingVARprocesses

Cobweb Theorems with Production Lags and Price Forecasting

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