Measuring Volatility Through the Fourier Transform
The next step is to take a look at how the Fourier Transform can be applied to securities. Consider the figure shown. It is an upwards linear trend with two cosines added. Now this is starting to look more like an actual stock progression. The key difference is that this chart has fundamental frequencies to it.
These fundamental frequencies shine through in the Fourier Transform. One can see the linear trend causes a high amplitude at lower frequencies. However, the two fundamental frequencies show up clearly in the Fourier Transform. The issue is that real stock returns do not have underlying frequencies, like sounds does. However, there should still be higher amplitudes in the Fourier Transform to account for the increasing oscillatory behavior of volatile stocks.
The next step is to take a look at how the Fourier Transform can be applied to securities. Consider the figure shown. It is an upwards linear trend with two cosines added. Now this is starting to look more like an actual stock progression. The key difference is that this chart has fundamental frequencies to it.
These fundamental frequencies shine through in the Fourier Transform. One can see the linear trend causes a high amplitude at lower frequencies. However, the two fundamental frequencies show up clearly in the Fourier Transform. The issue is that real stock returns do not have underlying frequencies, like sounds does. However, there should still be higher amplitudes in the Fourier Transform to account for the increasing oscillatory behavior of volatile stocks.