Sample Thesis Paper
Granger causality is a technique for determining whether one time series is useful in forecasting another. A time series X is said to Granger-cause Y if it can be shown, usually through a series of F-tests on lagged values of X (and with lagged values of Y also known), that those X values provide statistically significant information about future values of Y.
The test works by first doing a regression of ΔY on lagged values of ΔY. Once the appropriate lag interval for Y is proved significant (t-stat or p-value), subsequent regressions for lagged levels of ΔX are performed and added to the regression provided that they 1) are significant in and of themselves and 2) add explanatory power to the model.
This can be repeated for multiple ΔX’s (with each ΔX being tested independently of other ΔX’s, but in conjunction with the proven lag level of ΔY). More than 1 lag level of a variable can be included in the final regression model, provided it is statistically significant and provides explanatory power.
We are often looking for a clear story, such as X granger-causes Y but not the other way around. In the real world, often, difficult results are found such as neither granger-causes the other, or that each granger-causes the other. Furthermore, Granger causality does not imply true causality. If both X and Y are driven by a common third process, but with a different lag, there would be Granger causality. Yet, manipulation of one process would not change the other.
Finally, Engel Granger Techniques is utilized to explore the following relationship
ILTMit =α + ∑βj*Ln(ILTMit-k) + ∑γj*Ln(ILTMit-k) ………………………1
ILTSit =α + ∑βj*Ln(ILTSit-k) + ∑γj*Ln(ILTSit-k) ………………………2
ILTS= α + ∑βj*Ln(IBit-k) + ∑γj*Ln(IBit-k) …………………………………3