Wavelet Denoising and ARMA Forecasts for Stock Trading

Summary

The article proposes reducing noise in stock prices with wavelet decomposition, fitting ARMA models to the resulting coefficient series, forecasting those coefficients, and reconstructing a one-step-ahead price estimate. Its denoising explanation relies on the idea that signal energy is concentrated in relatively few wavelet coefficients, while noise is spread across many small coefficients. It outlines hard and soft thresholding, and notes that ARMA modeling assumes a stationary linear series.

For an example, it selects Ping An Bank, applies a symmetric db4 wavelet with two decomposition levels to the preceding 100 trading days, and reconstructs a forecast for the next day. The stated trading rule buys at the open when the forecast exceeds that day’s opening price by more than 1% and there is no existing position; it sells an existing position when the forecast is below the open. A backtest period and initial capital are stated, but the supplied excerpt gives no numerical performance results or risk assessment, and the single-stock example limits generalization.

Key ideas

• Wavelet thresholding is used to reduce noise before modeling a stock price series.
• Separate ARMA models forecast the decomposed wavelet coefficient series, whose forecasts are reconstructed into a price estimate.
• The example uses Ping An Bank prices, a db4 wavelet, two decomposition levels, and 100 prior trading days.
• The rule buys when the forecast is more than 1% above the open without a current position and sells when the forecast is below the open while holding.
• The excerpt states a backtest period and starting capital but does not include performance figures or risk analysis.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.