I have a timeseries dataset of a quantity measured over the period of a week. I want to verify if the data is varying in a diurnal fashion with the help of some mathematical measure. Does any such measure exist?
If you want to find periodic behaviors of your data, you should use the Fourier transform, which decomposes your data into a linear combination of cyclic waveforms. If you have a guess on the actual period, as in your case, you can try something simpler. For each hour during the day, compute the mean $\mu$ and variance $\sigma^2$ of your data, and plot the intervals $[\mu-\sigma,\mu+\sigma]$ for each hour. That should give you an idea regarding your hunch. (More generally, you can try a sophisticated method like ANOVA.)
Perhaps you should ask your question over in stats.se.