[Pandora][Swarm] Rapid Exponential Moving Average

ENVISIONING POSSIBILITY
What is the theoretical pinnacle of possibility? The current state of algorithmic affairs falls far short of my aspirations for achievable feasibility. I'm lifting the lid off of Pandora's box once again, very publicly this time, as a brute force challenge to conventional 'wisdom'. The unfolding series of time mandates a transcendental systemic alteration...


THE MOVING AVERAGE ZOO:
The realm of digital signal processing for trading is filled with familiar antiquated filtering tools. Two families of filtration, being 'infinite impulse response' (EMA, RMA, etc.) and 'finite impulse response' (WMA, SMA, etc.), are prevalently employed without question. These filter types are the mules and donkeys of data analysis, broadly accepted for use in finance.

At first glance, they appear sufficient for most tasks, offering a basic straightforward way to reduce noise and highlight trends. Yet, beneath their simplistic facade lies a constellation of limitations and impediments, each having its own finicky quirks. Upon closer inspection, identifiable drawbacks render them far from ideal for many real-world applications in today's volatile markets.


KNOWN FUNDAMENTAL FLAWS:
Despite commonplace moving average (MA) popularity, these conventional filters suffer from an assortment of fundamental flaws. Most of them don't genuinely address core challenges of how to preserve the true dynamics of a signal while suppressing noise and retaining cutoff frequency compliance. Their simple cookie cutter structures make them ill-suited in actuality for dynamic market environments. In reality, they often trade one problem for another dilemma, forsaking analytics to choose between distortion and delay.

A deeper seeded issue remains within frequency compliance, how adequately a filter respects (or disrespects) the underlying signal’s spectral properties according to it's assigned periodic parameter. Traditional MAs habitually distort phase relationships, causing delayed reactions with surplus lag or exaggerations with excessive undershoot/overshoot. For applications requiring timely resilience, such as algorithmic trading, these shortcomings are often functionally unacceptable. What’s needed is vigorous filters that can more accurately retain signal behaviors while minimizing lag without sacrificing smoothness and uniformity. Until then, the public MA zoo remains as a collection of corny compromises, rather than a favorable toolbelt of solutions.

P.S.: In PSv7+, in my opinion, many of these geriatric MAs deserve no future with ease of access for the naive, simply not knowing these filters are most likely creating bigger problems than solving any.


R.E.M.A.
What is this? I prefer to think of it as the "radical EMA", definitely along my lines of a retire everything morte algorithm. This isn't your run of the mill average from the petting zoo. I would categorize it as a paradigm shifting rampant economic masochistic annihilator, sufficiently good enough to begin ruthlessly executing moving averages left and right. Um, yeah... that kind of moving average destructor as you may soon recognize with a few 'Filters+' settings adjustments, realizing ordinary EMA has been doing us an injustice all this time.

Does it possess the capability to relentlessly exterminate most averaging filters in existence? Well, it's about time we find out, by uncaging it on the loose into the greater economic wilderness. Only then can we truly find out if it is indeed a radical exponential market accelerant whose time has come. If it is, then it may eventually become a reality erasing monolithic anomaly destined for greatness, ultimately changing the entire landscape of trading in perpetuity.


UNLEASHING NEXT-GEN:
This lone next generation exoweapon algorithm is intended to initiate the transformative beginning stages of mass filtration deprecation. However, it won't be the only one, just the first arrival of it's alien kind from me. Welcome to notion #1 of my future filtration frontier, on this episode of the algorithmic twilight zone. Where reality takes a twisting turn one dimension beyond practical logic, after persistent models of mindset disintegrate into insignificance, followed by illusory perception confronted into cognitive dissonance.

An evolutionary path to genuine advancement resides outside the prison of preconceptions, manifesting only after divergence from persistent binding restrictions of dogmatic doctrines. Such a genesis in transformative thinking will catalyze unbounded cognitive potential, plowing the way for the cultivation of total redesigns of thought. Futuristic innovative breakthroughs demand the surrender of legacy and outmoded understandings.

Now that the world's largest assembly of investors has been ensembled, there are additional tasks left to perform. I'm compelled to deploy this mathematical-weapon of mass financial creation into it's rightful destined hands, to "WE THE PEOPLE" of TV.


SCRIPT INTENTION:
Deprecate anything and everything as any non-commercial member sees desirably fit. This includes your existing code formulations already in working functional modes of operation AND/OR future projects in the works. Swapping is nearly as simple as copying and pasting with meager modifications, after you have identified comparable likeness in this indicators settings with a visual assessment. Results may become eye opening, but only if you dare to look and test.

Where you may suspect a ta.filter() is lacking sufficient luster or may be flat out majorly deficient, employing rema, drema, trema, or qrema configurations may be a more suitable replacement. That's up to you to discern. My code satire already identifies likely bottom of the barrel suspects that either belong in the extinction record or have already been marked for deprecation. They are ordered more towards the bottom by rank where they belong. SuperSmoother is a masterpiece here to stay, being my original go-to reference filter. Everything you see here is already deprecated, including REMA...


REMA CHARACTERISTICS
- VERY low lag
- No overshoot
- Frequency compliant
- Proper initialization at bar_index==0
- Period parameter accepts poitive floating point numerics (AND integers!)
- Infinite impulse response (IIR) filter
- Compact code footprint
- Minimized computational overhead