Journal ArticleDOI
Likelihood Analysis of the I(2) Model
TLDR
The I(2) model as discussed by the authors is defined as a submodel of the general vector autoregressive model, by two reduced rank conditions, and describes stochastic processes with stationary second difference.Abstract:
The I(2) model is defined as a submodel of the general vector autoregressive model, by two reduced rank conditions. The model describes stochastic processes with stationary second difference. A parametrization is suggested which makes likelihood inference feasible. Consistency of the maximum likelihood estimator is proved, and the asymptotic distribution of the maximum likelihood estimator is given. It is shown that the asymptotic distribution is either Gaussian, mixed Gaussian or, in some cases, even more complicated.read more
Citations
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The cointegrated VAR model : methodology and applications
TL;DR: In this paper, a model and relations in economics and economics and Econometrics are discussed. But the authors focus on the Cointegration rank and do not discuss the relationship between the model and the model.
Journal ArticleDOI
A representation theory for a class of vector autoregressive models for fractional processes
TL;DR: In this paper, a new vector autoregressive model defined from the fractional lag operator 1 − (1 − L)d was proposed and conditions in terms of the coefficients for the model to generate processes that are fractional of order zero.
Journal ArticleDOI
Likelihood analysis of seasonal cointegration
Søren Johansen,Ernst Schaumburg +1 more
TL;DR: In this article, the error correction model for seasonal cointegration is analyzed and conditions are found under which the process is integrated of order 1 and cointegrated at seasonal frequency, and a representation theorem is given.
Journal ArticleDOI
An Econometric Analysis of I(2) Variables
TL;DR: A survey of the recent literature dealing with I(2) variables in economic time series, that is, processes that require to be differenced twice in order to become stationary, can be found in this paper.
OtherDOI
Vector autoregressive models
TL;DR: In this article, the authors consider the problem of separating long-run and short-run components of the data generation process (DGP) in a vector autoregressive model, where cointegration relations are not modelled explicitly although they may be present.
References
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Journal ArticleDOI
Statistical analysis of cointegration vectors
TL;DR: In this paper, the authors consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors, and derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimensions.
Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models / Søren Johansen
TL;DR: In this paper, the authors present the likelihood methods for the analysis of cointegration in VAR models with Gaussian errors, seasonal dummies, and constant terms, and show that the asymptotic distribution of the maximum likelihood estimator is mixed Gausssian.
Journal ArticleDOI
Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models
TL;DR: In this article, the authors derived the likelihood analysis of vector autoregressive models allowing for cointegration and showed that the asymptotic distribution of the maximum likelihood estimator of the cointegrating relations can be found by reduced rank regression and derives the likelihood ratio test of structural hypotheses about these relations.
Journal ArticleDOI
A simple estimator of cointegrating vectors in higher order integrated systems
James H. Stock,Mark W. Watson +1 more
TL;DR: In this paper, an efficient estimator of cointegrating vectors is presented for systems involving deterministic components and variables of differing, higher orders of integration. But the estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x 2 distributions.
Posted Content
Likelihood-Based Inference in Cointegrated Vector Autoregressive Models
TL;DR: In this paper, the authors give a detailed mathematical and statistical analysis of the cointegrated vector autoregresive model, which has gained popularity because it can capture the short-run dynamic properties as well as the long-run equilibrium behaviour of many non-stationary time series.