Time-Varying Price Visualization of the Periodic Components of the NASDAQ Composite Index Since 2010 Using Non-Harmonic Analysis

Analysis of stock prices has been widely studied because of the strong demand among private investors and financial institutions. However, it is difficult to accurately capture the factors that cause fluctuations in stock prices, as they are affected by a variety of factors. Therefore, we used non-harmonic analysis, a frequency technique with at least
${10}^{4}$
to
${10}^{10}$
more accurately than conventional analysis methods, to visualize the periodicity of the Nasdaq Composite Index stock price from January 4, 2010, to September 8, 2023. We classified periods with intense periodic fluctuations as ROI1, ROI2, and ROI3, and conducted a detailed analysis by comparing the results of short-time Fourier transform (STFT), continuous wavelet transform (CWT), and non-harmonic analysis (NHA). The results showed that NHA effectively suppressed side lobes and captured subtle changes in periodic fluctuations, enabling us to decompose the complex state of stock prices into multiple waveforms. Furthermore, we confirmed the potential for these waveforms to correspond to causal relationships arising from events. Moreover, the results of this experiment could be used to understand the relationship between periodic fluctuations and incidents or events and to use deep learning to predict stock prices.