1987 Cointegration Correction Error
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long-run stochastic trend, also known as cointegration. ECMs are a theoretically-driven approach useful for estimating both short-term and long-term effects of one time series on another. The term error-correction relates to the fact
Cointegration And Error Correction Representation Estimation And Testing
that last-periods deviation from a long-run equilibrium, the error, influences its short-run dynamics. Thus cointegration and error correction model ECMs directly estimate the speed at which a dependent variable returns to equilibrium after a change in other variables. Contents 1 error correction mechanism cointegration History of ECM 2 Estimation 2.1 Engel and Granger 2-Step Approach 2.2 VECM 2.3 An example of ECM 3 Further reading History of ECM[edit] Yule (1936) and Granger and Newbold (1974) were the first
Engle And Granger 1987 Cointegration
to draw attention to the problem of spurious correlation and find solutions on how to address it in time series analysis. Given two completely unrelated but integrated (non-stationary) time series, the regression analysis of one on the other will tend to produce an apparently statistically significant relationship and thus a researcher might falsely believe to have found evidence of a true relationship between these variables. Ordinary least squares
Granger 1981
will no longer be consistent and commonly used test-statistics will be non-valid. In particular, Monte Carlo simulations show that one will get a very high R squared, very high individual t-statistic and a low Durbin–Watson statistic. Technically speaking, Phillips (1986) proved that parameter estimates will not converge in probability, the intercept will diverge and the slope will have a non-degenerate distribution as the sample size increases. However, there might a common stochastic trend to both series that a researcher is genuinely interested in because it reflects a long-run relationship between these variables. Because of the stochastic nature of the trend it is not possible to break up integrated series into a deterministic (predictable) trend and a stationary series containing deviations from trend. Even in deterministically detrended random walks walks spurious correlations will eventually emerge. Thus detrending doesn't solve the estimation problem. In order to still use the Box–Jenkins approach, one could difference the series and then estimate models such as ARIMA, given that many commonly used time series (e.g. in economics) appear to be stationary in first differences. Forecasts from such a model will still reflect cycles and seasonality that are present in the data. However, any information about long-run adjustments that the data
instructions
Johansen 1988
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