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Subject 7. Regressions with More Than One Time Series PDF Download

Occasionally an analyst will run a regression using two time series i.e. time series utilizing two different variables. For example, using the market model to estimate the equity beta for a stock, an analyst regresses a time series of the stock's returns (yt) on a time series of returns for the market (xt). Cointegration means that two time series are economically linked (related to the same macro variable) or follow the same trend and that relationship is not expected to change.

yt = b0 + b1 xt + ε

In this case, we have two different time series, yt and xt. Either one of the time series is subject to non-stationarity.

  • If neither data series has a unit root : VALID
  • If only one data series has a unit root: INVALID
  • If both data series have unit root & they are cointegrated : VALID
  • If both data series have unit root & they are not cointegrated : INVALID

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