A time series is an observation recorded at a succession of time intervals. The stock market is a time series.
Each bar on this chart of the S&P 500 represents a trading day. I have placed green dots at some low points on this time series. Notice that the dots are NOT equally spaced.
What may not be apparent to your eye is that a time series (including this one of the S&P 500) can show periodic behavior. Often times, periodic behavior can be very complex.
Spectral analysis is a technique that allows a mathematician to discover the periodic patterns in a time series. To perform spectral analysis, a mathematician will transform (using Fourier mathematics) the data from a time series to a frequency series. That is to say, what is the frequency over time of various interval patterns in the data?
A Covariance calculation then helps to highlight the points of greatest variation in the data. The covariance of a time series can be represented by a function known as the spectral density. The spectral density can be estimated using a periodogram function.
Long story short, embedded in the OPTUMA market data program is a Periodogram function. Running this function will help one determine the most predominant cycles in a time series. Once these cycles are determined, a market trader/investor can be alert to times when the trend might change.
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