Solution for f(n) in recurrence equation

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SUMMARY

The discussion centers on finding a solution for the Parabolic Stop and Reverse (SAR) equation, specifically SAR(n+1). The user seeks to eliminate SAR(n) from the equation and successfully derives the formula SAR(n) = (1-α)ⁿSAR₀ + (1-(1-α)ⁿ)EP, where SAR₀ is the initial value and EP is the extreme point. This formula demonstrates the recursive nature of the SAR calculation, emphasizing the impact of the smoothing factor α on the SAR values over time.

PREREQUISITES
  • Understanding of Parabolic SAR and its application in trading
  • Familiarity with recurrence relations in mathematics
  • Knowledge of the smoothing factor α in time series analysis
  • Basic grasp of extreme points (EP) in financial indicators
NEXT STEPS
  • Research the mathematical properties of recurrence relations
  • Explore advanced applications of Parabolic SAR in trading strategies
  • Learn about the implications of different values of α on SAR calculations
  • Investigate the relationship between SAR and other technical indicators
USEFUL FOR

Quantitative analysts, algorithmic traders, and anyone interested in technical analysis of financial markets will benefit from this discussion.

Bruno Tolentino
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Exist solution for SAR(n+1) in this equation:

5d3067fc0eb6fe426183193d6e3c0cb5.png


https://en.wikipedia.org/wiki/Parabolic_SAR

?

I want to eliminate SAR(n), but I never saw this kind of equation before...
 
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If you substitute ##SAR_n## by ##SAR_n = SAR_{n-1}+\alpha (EP-SAR_{n-1})## and so on, you will get the following (where I substituted ##n+1## by ##n## and if I made no mistake):
$$SAR_{n}=(1-\alpha)^{n}SAR_0+(1-(1-\alpha)^{n})EP$$
 
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