4.2.1. Model Assumptions

A few assumptions were made in this VAR model in an effort to use real market data to forecast just over six months. First, the model assumes that the relationship between the variables is static. A variety of timelines were tested accordingly in order to understand differences in behavior. The following are the timeframes selected for analysis:

Experiment A: Full timeframe: [04-01-2009, 22-11-2016], Post-boom timeframe: [10-12-2013, 22-11-2016], the Year of 2016 timeframe: [01-01-2016, 22-11-2016]. Experiment B: Full timeframe: [01-01-2011, 01-08-2020], Post-boom timeframe: [01-01-2017, 01-08-2020], the Year of 2020 timeframe: [01-01-2020, 01-08-2020]. For both Experiments A and B, the second assumption made in the model was the segregation of endogenous and exogenous variables. The decision-making process yielded a qualitative and intuitive measure for the variables.

### 4.2.2. Model Validation and Verifications

The process of validating the model was among the most difficult tasks throughout the entire process. Ultimately, the selected set of endogenous variable contained the BTC exchange rate, a variable for supply, and a variable for demand. Collectively, these variables help represent the market mechanics of Bitcoin. Based on the selected endogenous and exogenous variables, the following parameters were used:


The resulting selection of a timeframe was selected according to Akaike Information Criterion (AIC), Schwarz Criterion (SC), Hannan Quinn (HQ), and Forecast Prediction Error (FPE). This screening

process served as a deterministic selection of the timeframe for the forecasting by encompassing summary statistics such as *p*-value and R<sup>2</sup> to verify the accuracy of the relationship that was being estimated. Additionally, other combinations of variables were attempted with exceptionally poor results. Most of the other variables that were included as an aggregate to those used in the model projected dramatic market crashes with negative asset value.

### *4.3. Bayesian Vector Autoregression (BVAR) Model*

The classical VAR model may have over-parameterization problems because of the large number of parameters and limited availability of time-series datasets (Sims 1980); alternatively, the Bayesian vector autoregression model can be used. The BVAR model applies Bayesian methods to estimate a VAR and treats the VAR model parameters as random variables. It also assigns and updates the prior probabilities of both observed and unobserved parameters based on available data (Miranda-Agrippino and Ricco 2018). The BVAR model in this paper uses the same variables of interest in the VAR model as described in Section 4.2. Let *Yt* be a list of variables used in this BVAR model, such that:

$$Y\_t = \langle \text{MKPRU}, \text{ MWNUS}, \text{ TOTBC} \rangle \tag{6}$$

As in the VAR model, the BVAR model also assumes the chosen variables have static relationships and uses several different timelines to observe forecasting outputs. The BVAR model uses the same timeframes (Experiment A and Experiment B) used in the VAR model in order to compare their forecasting abilities.
