Granger-causality is a popular definition of causality that permits a statistical test to determine the direction of a causal relation between two variables. In this work special attention has been given to the context in which the definitions of and tests for Granger-causality were first introduced. The modern applications of Granger's tests have strayed far from their introduction in the context cross-spectral analysis. The mathematics of the spectral representations used by Granger to introduce his definitions of causality have their foundation in the discrete Fourier transform, which is an analysis technique that was found to deal with identifying the underlying frequency components of time series. In the univariate case this is called spectral analysis, and it deals with the frequency components of one time series. In the multivariate case, or cross-spectral analysis, this deals with the frequency components of the relationship between two or more time series. In this investigation, Matlab code was written in accordance with both the estimates used in spectral and cross-spectral analysis, Granger's definitions of causality and feedback, as well as the statistics required to run multiple Granger-causality tests. Data for most examples in this work was generated in Matlab, with the exception of the example in chapter 6, which uses data on the daily percent change in stock prices of Apple Inc. and Samsung Electronics Co. to perform an example test for Granger-causality. However, what this investigation deals with the most is the application of Fourier analysis to time series.


Hartman, Jim




causality, spectral analysis, fourier transform, granger causality, matlab

Publication Date


Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis



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