1 Introduction
Stocks rise and fall, creating patterns and movements that are as unpredictable as ocean waves. However, just as scientists predict the movement of waves by understanding the currents beneath them, we can use similar tools to decipher some of the patterns in the stock market.
By harnessing the power of wavelet transforms, we go beneath the surface in an attempt to uncover the underlying causes driving stock prices. This journey is not just about numbers and data; It's about turning the abstract into something tangible, taking advantage of a stock's seemingly erratic behavior and finding the rhythm and reason.
2. Wavelet transform theory
In essence, a wavelet is a short-lived oscillation whose energy is concentrated in time, ensuring that it is short-lived and limited in duration. Think of beating a drum: the sound produced is intense, but fades away quickly. This transient nature of wavelets makes them ideal for analyzing financial signals that are non-stationary (i.e. their statistical properties change over time). The wavelet transform is akin to providing a microscope to view the intricate details of stock data, capturing its large trends and tiny fluctuations.
2.1 Why not use Fourier transform?
Many people may be thinking, why not just use the Fourier transform, which is a very popular signal analysis tool? The Fourier transform decomposes a signal into its component sinusoids. However, its fatal weakness is its inability to provide time and frequency information simultaneously. While it can tell us how often they exist, it often ignores when they occur. Unlike the Fourier transform, the wavelet transform captures frequency and time, providing a time-frequency representation of the signal.
2.2 The essence of wavelet transform
Mathematically, wavelet transform can be expressed as:
where：
W is the result of our comparison, giving us