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I recently learned about moving averages, and the use of the intersection of a "slow" moving average with a "fast" moving average to predict significant long term-shifts in stochastic data.

An example application of this technique is the technical analysis of stocks, where it appears standard to use a 200-day window for the slow moving average and a 50-day window for the fast moving average, and when the fast crosses the slow it is known as a golden cross (or a death cross, depending on direction). This is taken by analysts to indicate that a turning point is imminent and the long term trend is about to change.

Here's a visual example of such a construction applied to stocks (but I am not interested in the stock market in particular.)

enter image description here

I'm interested in the more general use of moving averages to gain insight into stochastic data (from a somewhat more rigorous statistical perspective rather than technical analysis). Please note this is indeed a general mathematical consideration, as moving averages of stochastic data are a type of convolution and smoothing function, and also find application in fields such as signal processing where they represent low-pass frequency filters.

In my naivete, it seems arbitrary to pick two particular window sizes for the pair of moving averages when attempting to quantify a turning point. It begs the question how the predicted turning point would behave if the window sizes were varied, and whether more general information could be extracted by examining a spectrum of window size pairs. More specifically, if a 3D plot was prepared, with two independent axes for the moving average window sizes, and the dependent axis for the resulting crossover point (a value in "time"), would it yield meaningful data? Could this collection of all possible "golden crosses" have some asymptote, extremum or other feature that provides a fuller picture, which an arbitrary pair of windows only approximates?

Question: Does this sort of analysis have a name, and is it used? Is there a reason it should or shouldn't be used?

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    $\begingroup$ Day-trading heuristics and rules of thumb are commonly known as 'technical analysis'. These have little to no mathematical or scientific basis, and are widely discredited in academia. For more information ask on the quant se. $\endgroup$
    – Snoop
    Oct 31, 2022 at 11:26
  • $\begingroup$ @Snoop Thanks. My interest is more in the theoretical aspect of quantify trends in arbitrary stochastic data. I would be remiss not to mention the stock application, but I'm hoping to view this from the perspective of statistics (rather than dubious technical analysis). Surely the crossing of different moving averages has some usefulness as a statistical descriptor of the data? $\endgroup$ Nov 1, 2022 at 10:47
  • $\begingroup$ I understand! Then, I would suggest rephrasing the question, leaving the finance application as an example, and focusing on the purely mathematical formulation of what you're asking. $\endgroup$
    – Snoop
    Nov 1, 2022 at 11:20
  • $\begingroup$ @Snoop Thank you, I improved the question. I can format relevant definition in LaTeX if necessary, but they are straightforward and included in the linked Wikipedia page. $\endgroup$ Nov 1, 2022 at 13:24

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