A Band Spectral Density Regression of Exports on the Gross Domestic Product of the Kenyan Economy

The aim of this study is to be able to find the relationship between two time series variables applying the spectral analysis techniques. The spectral analysis techniques would enable the study explain this relationship in a more advanced way particularly in the frequency domain. Since the study will be focusing on two time series, we shall use the cross spectral density function which shall be estimated based on the cross periodogram function. The Cross spectral density function would give the power distribution of the two times series across the frequency domain. In this case each power will be associated with a frequency. Then we shall apply the square coherence function to find whether there is any association or the presence of a seasonality effect between the two series signals at each frequency. This would help us determine whether these two series are dependent or independent. Once the association has been established, we shall apply the Frequency Response Function (FRF) to estimate the effect the input variable in this case the independent variable has on the output in this case the dependent variable across the frequency domain. Finally, the study would use an <i>F Test </i>to determine which of the input frequencies are significant in explaining the output or the output variable.