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Advatages of Cointegration over Regression

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Submitted By muna
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There are two types of models that can be fitted to a given time series set of data; Regression Models (RM) and Time-Series Models (TSM). Let us initially consider the limitations of using regression as a tool to model building: * There are some practical barriers which need to be overcome when fitting a RM model such as multicollinearity and/or hetroscedasticity. These two limitations are extensively discussed by the academic community, and multicollinearity will not be lengthily discussed as it’s not the main focus of this study.

* Apart from the above two common setbacks, a RM has certain assumptions that need to be satisfied.

3.2.2.6 Assumptions regarding errors in regression modeling

A typical RM will estimate its parameters using ordinary least square (OLS) approach. An OLS estimate requires the errors to be white noise. That is the errors are assumed to have a distribution with mean zero and constant variance, hence the errors must be stationery. In other words is white noise in the model: where and are the two time series in concern.

But in time series data of limited length, this assumption of errors is violated if a relationship between and is insignificant; that is if β1 = 0. If so the model will reduce to, with following the same distribution of .
If is non stationary (as is the case most of the time) too will be non stationary, hence will not be white noise; violating the above assumption of stationary errors. This limitation will lead to erroneous conclusions that have been researched extensively as discussed in the literature review (see chapter 2.3 ). This drawback in RM’s is known as spurious regression.

A probable solution for spurious regression was proposed by Granger and Newbold in 1974. They recommended that an OLS RM be fitted for differenced, that is non stationary, variables. The idea was that this…...

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