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==History of ECM==
Yule (1936) and Granger and Newbold (1974) were the first 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]] will no longer be consistent and commonly used test-statistics will be non-valid. In particular, [[Monte Carlo method|Monte Carlo simulations]] show that one will get a very high [[coefficient of determination|R squared]], very high individual [[t-statistic]] and a low [[Durbin–Watson statistic]]. Technically speaking, Phillips (1986) proved that parameter estimates will not [[Convergence in probability|converge in probability]], the [[Y-intercept|intercept]] will diverge and the slope will have a non-degenerate distribution as the sample size increases. However, there might a common [[cointegration|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 stationary|trend]] and a stationary series containing deviations from trend. Even in deterministically detrended [[random walk]]s walks spurious correlations will eventually emerge. Thus detrending doesn't solve the estimation problem.
In order to still use the [[Box–Jenkins| 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 in levels may contain is omitted and longer term forecasts will be unreliable.
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