Extraction of Periodic Characteristics and Long-Term Stock Price Forecasting Using Non-Harmonic Analysis With Over 14 Years of NASDAQ Data Before and After COVID-19

Stock price forecasting is a critical challenge in financial markets, and methods capable of accurately capturing the complex long-term dynamics of the market remain underdeveloped. Moreover, traditional methods such as short-time fourier transform (stft) and continuous wavelet transform (CWT) suffer from time-frequency resolution trade-offs. To address these challenges, this study applies non-harmonic analysis (NHA) to extract periodic components from the NASDAQ Composite Index over the past 14.5 years. This novel approach provides a more accurate representation of stock price periodicities. By applying bandpass filtering and multi-windowing techniques, this study identifies key periodic components ranging from one week to four years. Furthermore, an autoregressive moving average (ARMA) model is employed to predict the amplitudes of these periodic components, enabling the construction of long-term price waveforms. Compared with conventional techniques, including Ichinose’s method, long short-term memory (LSTM) networks, and the autoregressive integrated moving average (ARIMA) model, the proposed method demonstrates a superior predictive performance with lower mean absolute percentage error (MAPE). These findings provide new insights into stock market dynamics and suggest broader applications of NHA in financial time-series analysis.