Studies on the Bitcoin Generalized Stock-to-Flow (S2F-G) Model: (i) Error-bars (ii) Training & Validation

By Bitcoin.Modeling ( https://twitter.com/Bitcoin_Model ), 4th May 2023

The Bitcoin Generalized Stock-to-Flow Model (or “Generalized Model”) was introduced in 2022 [1] as a modification to the Original Stock-to-Flow Model (or “Original Model”) [2] by independently modeling the Stock and Flow variables. The primary model equation governing the Generalized Model was presented as:

The Original Model is recovered from the above equation by substituting m = n = k.

In the first paper on the Generalized Model [1], the Mean values (μ or 10^μ) of the Constant (C) and the parameters (m and n) were provided. Here, the Upper and Lower Limits have been calculated using the Standard Deviations from their respective Mean values, as shown in Table 1.

Table 1. Upper and Lower Limits for the scaling parameters of the Bitcoin Generalized Stock-to-Flow Model.

Using the above values, the graph of the Generalized Model with Error-bars is plotted in Fig. 1 below.

Fig. 1. Bitcoin Generalized Stock-to-Flow Model with Error-bars.

The Upper Limit of the Generalized Model is determined to be $480K and the Lower Limit as $60K, with a Geometric Mean of $170K, for the next halving cycle beginning in 2024. The projection of $500K or higher for the same cycle by the Original Model is definitely outside the limits of the Generalized Model.

In Statistical Analysis, a part of the data-set is often used as Training to create a Model, and another part is used as Validation of the constructed Model [3]. In the present study, the Bitcoin Price until the end of 2018 is considered to be the Training data-set, while the rest of the data through May 2023 is used for Validation. The data-to-model fit between 2019–2023 as shown in Fig. 2 is in visually good agreement for the Generalized Model with an R2-fit of 97%, whereas only moderately so for the Original Model which has an R2-fit of 95.7%.

Fig. 2. Bitcoin Original and Generalized Stock-to-Flow Models with Training and Validation data-sets.

Thus, the Generalized Model fits the existing data differently as well as makes predictions at odds with the Original Model:

1) The data-to-model fit for the Generalized Model is superior to that of the Original Model.

2) The Upper Limit of the Bitcoin Price for the 2024–28 cycle projected by the Generalized Model is $480K, which is lower than the Mean value of the Original Model at $500K.

As to which model is correct remains to be seen!

References:-

[1] “Bitcoin Generalized Stock-to-Flow (S2F-G) Model”, by ‘Bitcoin.Modeling’, on the Medium publishing platform, dated 5th September 2022: https://medium.com/@bitcoin.modeling/bitcoin-generalized-stock-to-flow-s2f-g-model-867953687b33

[2] “Modeling Bitcoin Value with Scarcity”, by ‘Plan B’, on the Medium publishing platform, dated 22nd March 2019: https://medium.com/@100trillionUSD/modeling-bitcoins-value-with-scarcity-91fa0fc03e25

[3] “Training, validation, and test data sets”, Wikipedia article: https://en.wikipedia.org/wiki/Training,_validation,_and_test_data_sets

(Disclaimer: Not Financial Advice. Invest at your own risk.)