We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then 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

: a fractionally-integrated Gaussian vector autoregression (VAR) . Importantly, our approach explicitly permits measurement errors in the realized volatilities. Comparing the resulting volatility forecasts to those obtained from currently popular daily volatility models and more complicated high

has k unit roots and n- k distinct stationary linear combinations. Our proposed tests can be viewed alternatively as tests of the number of common trends, linearly independent cointegrating vectors, or autoregressive unit roots of the vector process. Both of the proposed tests are asymptotically

This paper suggests that the interactions of security trades and quote revisions be modeled as a vector autoregressive system. Within this framework, a trade's information effect may be meaningfully measured as the ultimate price impact of the trade innovation. Estimates for a sample of NYSE

finite-sample inference

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This chapter discusses econometric techniques for vector autoregressions (VAR). In most cases, the variables in VAR are assumed to be stationary. 1 Let yt be an n-dimensional vector stochastic process that is covariance stationary. Because yt is covariance stationary, it has a Wold representation

Various types of impulse responses have been used for interpreting finite order vector autoregessive (VAR) models in the stationary as well as the nonstationary cointegrated case. In practice, finite order VAR processes are regarded as rough approximations to the actual data generation process

Ce cahier a également été publié par le Centre interuniversitaire de recherche en économie quantitative (CIREQ) sous le numéro 12-2000.

and distribution theory allow for the joint consideration of nonlinearity Ž thresholds. and nonstationary Žunit roots.. Our limit theory is based on a new set of tools that combine unit root asymptotics with empirical process methods. We work with a particular two-parameter empirical process that converges weakly