# INFERENCE IN LINEAR TIME SERIES MODELS WITH SOME UNIT ROOTS

@article{Sims1990INFERENCEIL, title={INFERENCE IN LINEAR TIME SERIES MODELS WITH SOME UNIT ROOTS}, author={Christopher A. Sims and James H. Stock and Mark W. Watson}, journal={Econometrica}, year={1990}, volume={58}, pages={113-144} }

This paper considers estimation and hypothesis testing in linear time series when some or all of the variables have (possibly multiple) unit roots. The motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. Parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distribution, converging at the rate of T(superscript "one-half") In general, the…

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## References

SHOWING 1-10 OF 18 REFERENCES

### Time series regression with a unit root

- Mathematics
- 1987

This paper studies the random walk in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression…

### Multiple Time Series Regression with Integrated Processes

- Mathematics
- 1986

This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory includes vector autoregressions and multivariate regressions amongst…

### Asymptotic normality, when regressors have a unit root

- Mathematics, Economics
- 1988

Under fairly general conditions, ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables.…

### Distribution of the Estimators for Autoregressive Time Series with a Unit Root

- Mathematics
- 1979

Abstract Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with…

### Co-integration and error correction: representation, estimation and testing

- Economics
- 1987

The relationship between cointegration and error correction models, first suggested by Granger, is here extended and used to develop estimation procedures, tests, and empirical examples. A vector of…

### Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors

- Mathematics, Economics
- 1987

Time series variables that stochastically trend together form a cointegrated system. OLS and NLS estimators of the parameters of a cointegrating vector are shown to converge in probability to the…

### Asymptotic properties of multivariate nonstationary processes with applications to autoregressions

- Mathematics
- 1990

Asymptotic properties of multivariate time series with characteristic roots on the unit circle are considered. For a vector autoregressive moving average process, we derive the limiting distributions…