Detecting Forex Cycles with Moving Averages and Finite Differences
Summary
The article surveys ways to identify recurring structure in Forex prices, including spectral methods, periodograms, autocorrelation, moving averages, and dot mapping. It explains how moving averages can reveal cycles and trends, but may miss one-sided waves or fail when noise is too large. Dot mapping plots each observation against the previous one to examine dependence; examples contrast a logistic series, a pseudo-random series, and real prices, where trend may obscure cycles.
The main analysis develops finite differences as a way to detect cyclic behavior around an estimated level. A second difference sampled at a hypothesized period can cancel stable cycles and sufficiently long trends; summing recent differences may highlight disturbances such as a new trend or a cycle changing. The discussion also introduces custom differences and their use in comparing historical price movements. These are exploratory analysis techniques, not evidence of a dependable trading signal: cycles can be masked by trend and noise, oscillator methods have limits, and market patterns may change.
Key ideas
- Moving averages can help separate trend and cyclic components, but their resolution and noise tolerance are limited.
- Dot mapping compares adjacent observations to reveal dependence or recurring structure in a time series.
- Finite differences sampled at a candidate period can help assess whether price fluctuations are repeating consistently.
- Deviations in accumulated differences may indicate a disturbance in an otherwise stable cycle or trend.
- Market cycles are uncertain and may change, so these methods require further validation before trading use.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.