Technically speaking, Phillips proved that parameter estimates will not converge in probabilitythe intercept will diverge and the slope will have a non-degenerate distribution as the sample size increases.
In particular, Monte Carlo simulations show that one will get a very high R squaredvery high individual t-statistic and a low Durbin-Watson statistic. Ordinary least squares will no longer be consistent and commonly used test-statistics will be non-valid.
Yule and Granger and Newbold were the first to draw attention to the problem of spurious correlation and find solutions on how to address it in time series analysis. Thus ECMs directly estimate the speed at which a dependent variable returns to equilibrium after a change in other variables. The term error-correction relates to the fact that last-period's deviation from a long-run equilibrium, the errorinfluences its short-run dynamics. ECMs are a theoretically-driven approach useful for estimating both short-term and long-term effects of one time series on another. An error correction model ECM belongs to a category of multiple time series models most commonly used for data where the underlying variables have a long-run stochastic trend, also known as cointegration.
