# Exponential Regression Rainbow

## Overview

Historically, the HEX price has hit local price minima (key "bottom" regions) on the exponential fit defined by R*exp(ρ*t), where:

R = 0.0002009889556

ρ = 0.010475051

t = time [in days]

If we fit the entire history of HEX daily price data to a similar exponential curve G*exp(γ*t), we get the following parameters:

G = 0.00007152730947

γ = 0.01005249327

Finally, by fitting only local price maxima (key "top" regions), we arrive at the exponential curve B*exp(β*t), where:

B = 0.001359205336

β = 0.008829454716

Because these exponential curves (which we can refer to as simply R, G, & B) are simply least-squares fits, we can visualize important metrics such as % error as symmetrical "tolerance bands" around each respective curve (labeled with +/-).

## Diminishing Returns:

Many assets oftentimes experience the burden of diminishing returns over their lifetimes. If we want to express diminishing returns mathematically, we can apply dampening coefficients to our steepest curves (namely R & G) - we'll define dr and dg as yearly % diminishing returns for our respective curves and for now use:

dr = 13.7%

dg = 10.0%

Now we can define our dampening coefficients as:

Δr = ( 1 - ( ( t / 365 ) * dr ) )

Δg = ( 1 - ( ( t / 365 ) * dg ) )

The application of these coefficients turns our Regression Rainbow model into a set of 9 equations, the main 3 being:

Δr * R*exp(ρ*t)

Δg * G*exp(γ*t)

B*exp(β*t)

## Curve Convergence:

Depending on the values of Δr and Δg, the exponential curves R, G, & B converge at different points in the future. As the years continue to give us more price data, we can continue to fine-tune Δr and Δg with community feedback to best fit the reality of the price chart.

## Charts

The first chart plots all three exponential curves (R, G, & B), each curve's associated pair of tolerance curves (R-, R+), (G-, G+), & (B-, B+), and the price of HEX over time.

The second chart takes all of the data from the first chart and normalizes it to the curve R. This gives us a better visualization of how price is performing relative to our model.

## How To Use

Long term HEX investors can monitor the daily price relative to the regression rainbow.

Periods when the HEX price has reached the lower regions (red) have been great historical opportunities to buy HEX. When the HEX price has entered the middle regions (green), price has often seen high volatility shortly thereafter. The few times we've see the HEX price enter the upper regions (blue), it has been rejected.

## Created By

Gerardo - @gerawrdog