FINLYTS – Financial Forecasting and Investment Analytics

Consulting Report

Author

Group 1: Benedicto, Cortes, Lee, Yumang

Published

August 18, 2026

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0.3 Project Setup

Code 
library(tidyverse)
library(quantmod)
library(TTR)
library(xts)
library(zoo)
library(lubridate)

library(caret)
library(rpart)
library(randomForest)
library(xgboost)
library(kernlab)
library(nnet)

library(fastshap)
library(shapviz)

1 Executive Summary

This consulting report evaluates the forecasting framework developed for Bitcoin (BTC-USD).

The analysis follows the complete analytical chain:

Data → Features → ML Models → Evaluation → Diebold-Mariano Test → Forecast Decision Engine → SHAP → Investment Recommendation

The final executive findings will be completed after model evaluation, statistical validation, explainable artificial intelligence analysis, and executive recommendation outputs are generated.

2 Case Background

The Investment Committee requires a forecasting framework that can support investment decision-making through a structured analytical process.

The purpose of this project is to develop a financial forecasting and investment analytics framework that evaluates whether machine-learning models can provide useful predictive information for Bitcoin (BTC-USD).

The analysis follows the complete analytical chain:

Data → Features → ML Models → Evaluation → Diebold-Mariano Test → Forecast Decision Engine → SHAP → Investment Recommendation

The framework focuses not only on predictive performance but also on statistical validation and model explainability.

The forecasting process evaluates multiple machine-learning approaches, compares their out-of-sample forecasting performance, determines whether differences between models are statistically meaningful, explains the selected model behavior, and translates the results into an executive-level investment recommendation.

3 Target Asset and Forecasting Objective

3.1 Target Asset

The target asset selected for this analysis is:

Bitcoin (BTC-USD)

The forecasting framework focuses on Bitcoin market behavior and evaluates whether machine-learning models can provide predictive information regarding future Bitcoin returns.

The analysis incorporates Bitcoin market data together with assigned external financial predictors:

  1. Gold
  2. CBOE Volatility Index (VIX)
  3. 10-Year U.S. Treasury Yield

These external predictors are included to capture additional financial market information that may contribute to Bitcoin return forecasting.

3.2 Forecasting Target

The forecasting target is:

Bitcoin t+3 Log Return

The objective is to forecast the return occurring at t+3 using information available at the forecast origin date t.

The forecasting framework does not predict the Bitcoin price directly. Instead, it forecasts the future Bitcoin log return occurring three Bitcoin trading periods ahead.

The daily Bitcoin log return is calculated as:

[ btc_log_return = log ( ) ]

where:

  • (P_t) represents the Bitcoin closing price at time (t);
  • (P_{t-1}) represents the previous Bitcoin closing price.

3.3 Construction of the t+3 Forecasting Target

The forecasting target is constructed by shifting the Bitcoin daily log-return series three periods forward.

The target is defined as:

[ target_{t+3}=log ( ) ]

This represents the return that occurs at the future period t+3.

The target is therefore not:

[ log ( ) ]

Instead, information available at time t is used to predict the Bitcoin return that will occur three Bitcoin trading periods into the future.

3.4 External Predictors

The model incorporates the following external predictors:

Predictor Description
Gold Gold market information
VIX CBOE Volatility Index representing market volatility
10-Year U.S. Treasury Yield U.S. Treasury market information

The inclusion of these predictors allows the forecasting framework to consider both Bitcoin-specific information and broader financial market conditions.

Code 
# Load integrated modeling dataset

model_data <- read_csv(
  "data_processed/model_data.csv",
  show_col_types = FALSE
)

head(model_data)
# A tibble: 6 × 15
  date       target_date_t3 btc_log_return btc_return_lag1 btc_return_lag2
  <date>     <date>                  <dbl>           <dbl>           <dbl>
1 2014-10-01 2014-10-04           -0.00864         0.0301         -0.00455
2 2014-10-02 2014-10-05           -0.0225         -0.00864         0.0301 
3 2014-10-03 2014-10-06           -0.0424         -0.0225         -0.00864
4 2014-10-06 2014-10-09            0.0294         -0.0257         -0.0891 
5 2014-10-07 2014-10-10            0.0183          0.0294         -0.0257 
6 2014-10-08 2014-10-11            0.0486          0.0183          0.0294 
# ℹ 10 more variables: btc_return_lag3 <dbl>, btc_sma7 <dbl>, btc_rsi14 <dbl>,
#   btc_williams_r14 <dbl>, btc_obv <dbl>, btc_parkinson_vol7 <dbl>,
#   gold_log_return <dbl>, vix_close <dbl>, treasury_10y <dbl>, target_t3 <dbl>

4 Data Sources and Sample

4.1 Data Sources

The financial datasets used in this analysis were collected to support the development of the Bitcoin (BTC-USD) forecasting framework.

The target asset and assigned external predictors are:

Dataset Identifier Source Purpose
Bitcoin BTC-USD Yahoo Finance Target asset
Gold GC=F Yahoo Finance External predictor
CBOE Volatility Index ^VIX Yahoo Finance External predictor
10-Year U.S. Treasury Yield DGS10 Financial market data source External predictor

The target asset selected for this analysis is Bitcoin (BTC-USD).

The assigned external predictors included in the forecasting framework are:

  1. Gold (GC=F)
  2. CBOE Volatility Index / VIX (^VIX)
  3. 10-Year U.S. Treasury Yield (DGS10)

These predictors were selected to incorporate broader financial market information into the Bitcoin forecasting framework.

4.2 Sample Period

The data acquisition period was defined as:

  • Start Date: 2014-01-01
  • End Date: 2026-08-10

The dataset was collected using daily financial observations.

The downloaded datasets were converted into structured data tables and prepared for integration, feature engineering, exploratory analysis, and machine-learning modeling.

4.3 Data Collection Process

The Bitcoin dataset was downloaded using the ticker:

BTC-USD

The raw Bitcoin dataset contains:

  • date;
  • opening price;
  • highest price;
  • lowest price;
  • closing price;
  • trading volume; and
  • adjusted closing price.

The same process was applied to the external predictor datasets to create a consistent financial dataset for forecasting.

4.4 Dataset Preparation

Before integration, each dataset underwent validation procedures including:

  • checking observation ranges;
  • checking duplicate dates;
  • checking missing values;
  • removing incomplete observations; and
  • arranging observations chronologically.

The cleaned datasets were then saved into the processed data directory for use in subsequent forecasting stages.

Code 
# Load cleaned datasets

bitcoin <- read_csv(
  "data_processed/bitcoin_clean.csv",
  show_col_types = FALSE
)

gold <- read_csv(
  "data_processed/gold_clean.csv",
  show_col_types = FALSE
)

vix <- read_csv(
  "data_processed/vix_clean.csv",
  show_col_types = FALSE
)

treasury <- read_csv(
  "data_processed/treasury10y_clean.csv",
  show_col_types = FALSE
)


# Display dataset structure

tibble(
  Dataset = c(
    "Bitcoin",
    "Gold",
    "VIX",
    "10-Year Treasury Yield"
  ),
  Observations = c(
    nrow(bitcoin),
    nrow(gold),
    nrow(vix),
    nrow(treasury)
  )
)
# A tibble: 4 × 2
  Dataset                Observations
  <chr>                         <int>
1 Bitcoin                        4346
2 Gold                           3167
3 VIX                            3169
4 10-Year Treasury Yield         3152

5 Data Cleaning and Integration

5.1 Data Cleaning Process

Before developing the forecasting model, all financial datasets underwent data cleaning and validation procedures.

The cleaning process was performed to ensure that the datasets were suitable for integration and machine-learning analysis.

The following validation procedures were conducted:

  • verification of dataset availability;
  • checking observation ranges;
  • checking duplicate dates;
  • checking missing values;
  • removing incomplete observations; and
  • arranging observations chronologically.

Each dataset was cleaned separately before being combined into the final forecasting dataset.

5.2 Bitcoin Data Cleaning

The Bitcoin dataset was cleaned by:

  1. Removing observations containing missing values;
  2. Removing duplicate dates;
  3. Maintaining chronological ordering of observations.

The cleaned Bitcoin dataset retained the following variables:

  • date;
  • btc_open;
  • btc_high;
  • btc_low;
  • btc_close;
  • btc_volume; and
  • btc_adjusted.

5.3 External Predictor Data Cleaning

The same cleaning procedure was applied to the external predictors:

Dataset Cleaning Applied
Gold Missing-value validation, duplicate-date checking, chronological arrangement
VIX Missing-value validation, duplicate-date checking, chronological arrangement
10-Year U.S. Treasury Yield Missing-value validation, duplicate-date checking, chronological arrangement

5.4 Data Integration

After individual dataset cleaning, the datasets were integrated using the common variable:

date

The integrated dataset combines:

  • Bitcoin market information;
  • Gold market information;
  • VIX market volatility information; and
  • 10-Year U.S. Treasury Yield information.

The integrated dataset provides the information foundation for target construction, feature engineering, exploratory analysis, and machine-learning modeling.

5.5 Forecasting Dataset Preparation

Following integration, the Bitcoin log return target was constructed and aligned with the predictor variables.

The final integrated dataset was prepared for subsequent stages:

  1. Feature Engineering
  2. Exploratory Analysis
  3. Machine Learning Methodology
  4. Model Evaluation
  5. Statistical Validation
  6. Explainable Artificial Intelligence Analysis
Code 
library(readr)
library(dplyr)


# Load cleaned datasets

btc <- read_csv(
  "data_processed/bitcoin_clean.csv",
  show_col_types = FALSE
)

gold <- read_csv(
  "data_processed/gold_clean.csv",
  show_col_types = FALSE
)

vix <- read_csv(
  "data_processed/vix_clean.csv",
  show_col_types = FALSE
)

treasury <- read_csv(
  "data_processed/treasury10y_clean.csv",
  show_col_types = FALSE
)


# Ensure date format

btc$date <- as.Date(btc$date)
gold$date <- as.Date(gold$date)
vix$date <- as.Date(vix$date)
treasury$date <- as.Date(treasury$date)


# Merge datasets by date

integrated_data <- btc |>
  left_join(
    gold,
    by = "date"
  ) |>
  left_join(
    vix,
    by = "date"
  ) |>
  left_join(
    treasury,
    by = "date"
  )


# Arrange chronologically

integrated_data <- integrated_data |>
  arrange(date)


# Check structure

dim(integrated_data)
[1] 4346   19
Code 
head(integrated_data)
# A tibble: 6 × 19
  date       btc_open btc_high btc_low btc_close btc_volume btc_adjusted
  <date>        <dbl>    <dbl>   <dbl>     <dbl>      <dbl>        <dbl>
1 2014-09-17     466.     468.    452.      457.   21056800         457.
2 2014-09-18     457.     457.    413.      424.   34483200         424.
3 2014-09-19     424.     428.    385.      395.   37919700         395.
4 2014-09-20     395.     423.    390.      409.   36863600         409.
5 2014-09-21     408.     412.    393.      399.   26580100         399.
6 2014-09-22     399.     407.    397.      402.   24127600         402.
# ℹ 12 more variables: gold_open <dbl>, gold_high <dbl>, gold_low <dbl>,
#   gold_close <dbl>, gold_volume <dbl>, gold_adjusted <dbl>, vix_open <dbl>,
#   vix_high <dbl>, vix_low <dbl>, vix_close <dbl>, vix_adjusted <dbl>,
#   treasury_10y <dbl>

6 Exploratory Analysis

6.1 Overview

Exploratory analysis was conducted to understand the characteristics of the final modeling sample before applying machine-learning techniques.

The analysis focuses on:

  1. Bitcoin price and return behavior;
  2. Bitcoin t+3 forecasting target behavior;
  3. External financial predictors;
  4. Engineered features;
  5. Predictor-target relationships; and
  6. Predictor multicollinearity.

The purpose of this stage is to identify important patterns, assess data characteristics, and provide a foundation for the forecasting methodology.

7 Final Modeling Sample Description

The final modeling dataset contains the variables required for forecasting Bitcoin t+3 Log Return.

The predictor variables included in the final modeling dataset are:

Predictor Description
btc_log_return Current Bitcoin log return
btc_return_lag1 Bitcoin return lag 1
btc_return_lag2 Bitcoin return lag 2
btc_return_lag3 Bitcoin return lag 3
btc_sma7 Bitcoin 7-day moving average
btc_rsi14 Bitcoin momentum indicator
btc_williams_r14 Williams %R indicator
btc_obv On-Balance Volume
btc_parkinson_vol7 Parkinson volatility
gold_log_return Gold return
vix_close CBOE Volatility Index
treasury_10y 10-Year U.S. Treasury Yield

The final forecasting target is:

target_t3

representing the Bitcoin log return occurring three trading periods into the future.

8 Bitcoin Price and Return Behavior

8.1 Bitcoin Closing Price

The Bitcoin closing price trend was examined to understand historical market movement.

Code 
#| fig-cap: "Bitcoin Closing Price Over Time"

btc |>
  ggplot(
    aes(
      x = date,
      y = btc_close
    )
  ) +
  geom_line() +
  labs(
    title = "Bitcoin Closing Price",
    x = "Date",
    y = "Bitcoin Closing Price"
  )

The price trend provides an overview of Bitcoin’s historical market behavior and identifies periods of substantial price movement.

8.2 Bitcoin Log Return Distribution

The distribution of Bitcoin log returns was examined to evaluate return behavior.

Code 
#| fig-cap: "Distribution of Bitcoin Log Returns"

model_data |>
  ggplot(
    aes(
      x = btc_log_return
    )
  ) +
  geom_histogram(
    bins = 50
  ) +
  labs(
    title = "Distribution of Bitcoin Log Returns",
    x = "Log Return",
    y = "Frequency"
  )

The return distribution analysis provides information regarding:

  • average return behavior;
  • return volatility;
  • extreme observations; and
  • potential outliers.

9 Bitcoin t+3 Forecasting Target Analysis

The forecasting target examined in this analysis is:

Bitcoin t+3 Log Return

Code 
#| fig-cap: "Distribution of Bitcoin t+3 Log Return"

model_data |>
  ggplot(
    aes(
      x = target_t3
    )
  ) +
  geom_histogram(
    bins = 50
  ) +
  labs(
    title = "Distribution of Bitcoin t+3 Log Return",
    x = "Target Return",
    y = "Frequency"
  )

Understanding the target distribution is important because machine-learning models are trained to predict this future return outcome.

10 External Predictor Analysis

The forecasting framework incorporates external financial predictors:

  • Gold;
  • VIX; and
  • 10-Year U.S. Treasury Yield.

These variables provide additional market information beyond Bitcoin-specific indicators.

10.1 External Predictor Summary

Code 
predictor_summary <- model_data |>
  summarise(
    Gold = mean(gold_log_return, na.rm = TRUE),
    VIX = mean(vix_close, na.rm = TRUE),
    Treasury = mean(treasury_10y, na.rm = TRUE)
  )

predictor_summary
# A tibble: 1 × 3
      Gold   VIX Treasury
     <dbl> <dbl>    <dbl>
1 0.000427  18.3     2.72

11 Predictor-Target Correlation Analysis

Correlation analysis was performed to examine relationships between predictors and the forecasting target.

Code 
#| label: correlation-analysis

correlation_matrix <- model_data |>
  select(
    btc_log_return,
    btc_return_lag1,
    btc_return_lag2,
    btc_return_lag3,
    btc_sma7,
    btc_rsi14,
    btc_williams_r14,
    btc_obv,
    btc_parkinson_vol7,
    gold_log_return,
    vix_close,
    treasury_10y,
    target_t3
  ) |>
  cor(
    use = "complete.obs"
  )

round(
  correlation_matrix,
  3
)
                   btc_log_return btc_return_lag1 btc_return_lag2
btc_log_return              1.000          -0.026          -0.009
btc_return_lag1            -0.026           1.000           0.004
btc_return_lag2            -0.009           0.004           1.000
btc_return_lag3             0.018          -0.003           0.006
btc_sma7                   -0.033          -0.020          -0.005
btc_rsi14                   0.364           0.316           0.290
btc_williams_r14           -0.431          -0.318          -0.277
btc_obv                    -0.002           0.002           0.017
btc_parkinson_vol7         -0.010          -0.040          -0.033
gold_log_return             0.091           0.035          -0.004
vix_close                  -0.040          -0.037          -0.043
treasury_10y               -0.032          -0.021          -0.010
target_t3                   0.023           0.018           0.026
                   btc_return_lag3 btc_sma7 btc_rsi14 btc_williams_r14 btc_obv
btc_log_return               0.018   -0.033     0.364           -0.431  -0.002
btc_return_lag1             -0.003   -0.020     0.316           -0.318   0.002
btc_return_lag2              0.006   -0.005     0.290           -0.277   0.017
btc_return_lag3              1.000   -0.018     0.271           -0.253  -0.006
btc_sma7                    -0.018    1.000    -0.049            0.017   0.783
btc_rsi14                    0.271   -0.049     1.000           -0.810   0.013
btc_williams_r14            -0.253    0.017    -0.810            1.000  -0.023
btc_obv                     -0.006    0.783     0.013           -0.023   1.000
btc_parkinson_vol7          -0.036   -0.091    -0.088            0.099  -0.003
gold_log_return             -0.039    0.035     0.035           -0.062   0.023
vix_close                   -0.052    0.047    -0.192            0.102   0.236
treasury_10y                -0.012    0.629    -0.082            0.055   0.309
target_t3                    0.028   -0.040     0.050           -0.040  -0.034
                   btc_parkinson_vol7 gold_log_return vix_close treasury_10y
btc_log_return                 -0.010           0.091    -0.040       -0.032
btc_return_lag1                -0.040           0.035    -0.037       -0.021
btc_return_lag2                -0.033          -0.004    -0.043       -0.010
btc_return_lag3                -0.036          -0.039    -0.052       -0.012
btc_sma7                       -0.091           0.035     0.047        0.629
btc_rsi14                      -0.088           0.035    -0.192       -0.082
btc_williams_r14                0.099          -0.062     0.102        0.055
btc_obv                        -0.003           0.023     0.236        0.309
btc_parkinson_vol7              1.000          -0.010     0.156       -0.199
gold_log_return                -0.010           1.000     0.003        0.013
vix_close                       0.156           0.003     1.000       -0.203
treasury_10y                   -0.199           0.013    -0.203        1.000
target_t3                       0.020           0.017    -0.026       -0.027
                   target_t3
btc_log_return         0.023
btc_return_lag1        0.018
btc_return_lag2        0.026
btc_return_lag3        0.028
btc_sma7              -0.040
btc_rsi14              0.050
btc_williams_r14      -0.040
btc_obv               -0.034
btc_parkinson_vol7     0.020
gold_log_return        0.017
vix_close             -0.026
treasury_10y          -0.027
target_t3              1.000

Correlation analysis provides an initial assessment of whether predictors demonstrate potential relationships with the forecasting target.

12 Predictor Multicollinearity Analysis

Multicollinearity analysis was performed to evaluate whether predictors contain highly overlapping information.

Understanding predictor relationships is important because excessive correlation between predictors may influence model interpretation.

Code 
# Display predictor correlation matrix

predictor_correlation <- model_data |>
  select(
    btc_log_return,
    btc_return_lag1,
    btc_return_lag2,
    btc_return_lag3,
    btc_sma7,
    btc_rsi14,
    btc_williams_r14,
    btc_obv,
    btc_parkinson_vol7,
    gold_log_return,
    vix_close,
    treasury_10y
  ) |>
  cor(
    use = "complete.obs"
  )

round(
  predictor_correlation,
  3
)
                   btc_log_return btc_return_lag1 btc_return_lag2
btc_log_return              1.000          -0.026          -0.009
btc_return_lag1            -0.026           1.000           0.004
btc_return_lag2            -0.009           0.004           1.000
btc_return_lag3             0.018          -0.003           0.006
btc_sma7                   -0.033          -0.020          -0.005
btc_rsi14                   0.364           0.316           0.290
btc_williams_r14           -0.431          -0.318          -0.277
btc_obv                    -0.002           0.002           0.017
btc_parkinson_vol7         -0.010          -0.040          -0.033
gold_log_return             0.091           0.035          -0.004
vix_close                  -0.040          -0.037          -0.043
treasury_10y               -0.032          -0.021          -0.010
                   btc_return_lag3 btc_sma7 btc_rsi14 btc_williams_r14 btc_obv
btc_log_return               0.018   -0.033     0.364           -0.431  -0.002
btc_return_lag1             -0.003   -0.020     0.316           -0.318   0.002
btc_return_lag2              0.006   -0.005     0.290           -0.277   0.017
btc_return_lag3              1.000   -0.018     0.271           -0.253  -0.006
btc_sma7                    -0.018    1.000    -0.049            0.017   0.783
btc_rsi14                    0.271   -0.049     1.000           -0.810   0.013
btc_williams_r14            -0.253    0.017    -0.810            1.000  -0.023
btc_obv                     -0.006    0.783     0.013           -0.023   1.000
btc_parkinson_vol7          -0.036   -0.091    -0.088            0.099  -0.003
gold_log_return             -0.039    0.035     0.035           -0.062   0.023
vix_close                   -0.052    0.047    -0.192            0.102   0.236
treasury_10y                -0.012    0.629    -0.082            0.055   0.309
                   btc_parkinson_vol7 gold_log_return vix_close treasury_10y
btc_log_return                 -0.010           0.091    -0.040       -0.032
btc_return_lag1                -0.040           0.035    -0.037       -0.021
btc_return_lag2                -0.033          -0.004    -0.043       -0.010
btc_return_lag3                -0.036          -0.039    -0.052       -0.012
btc_sma7                       -0.091           0.035     0.047        0.629
btc_rsi14                      -0.088           0.035    -0.192       -0.082
btc_williams_r14                0.099          -0.062     0.102        0.055
btc_obv                        -0.003           0.023     0.236        0.309
btc_parkinson_vol7              1.000          -0.010     0.156       -0.199
gold_log_return                -0.010           1.000     0.003        0.013
vix_close                       0.156           0.003     1.000       -0.203
treasury_10y                   -0.199           0.013    -0.203        1.000

The exploratory analysis provides the statistical foundation required before proceeding to feature engineering validation and machine-learning model development.

13 Feature Engineering

13.1 Overview

Feature engineering was conducted to transform the available financial data into variables that can be used by the machine-learning forecasting models.

The objective of feature engineering is to create meaningful predictors that represent different characteristics of Bitcoin market behavior, including:

  • return history;
  • price trends;
  • momentum;
  • volatility;
  • trading activity; and
  • external financial market conditions.

All forecasting models use the same predictor set to ensure that performance differences reflect the modeling approach rather than differences in available information.

14 Final Predictor Set

The final predictor set consists of 12 variables representing Bitcoin-specific information and external financial market information.

Feature Category Financial Rationale
btc_log_return Current Return Captures the most recent Bitcoin return information available at the forecast origin
btc_return_lag1 Required Lag Captures short-term return persistence or reversal
btc_return_lag2 Required Lag Provides additional short-term return history
btc_return_lag3 Required Lag Extends return-memory structure to three periods
btc_sma7 Moving Average Represents short-term price trend and smooths price fluctuations
btc_rsi14 Momentum Indicator Measures recent price momentum and balance between upward and downward movements
btc_williams_r14 Advanced Feature Measures current price position relative to recent high-low range
btc_obv Advanced Feature Combines price direction and trading volume to capture buying and selling pressure
btc_parkinson_vol7 Student-Designed Feature Captures short-term volatility using Bitcoin high-low price ranges
gold_log_return External Predictor Captures movements in Gold as an external financial-market predictor
vix_close External Predictor Represents market-implied volatility and risk sentiment
treasury_10y External Predictor Represents long-term interest-rate environment and financial conditions

15 Required Lag Features

15.1 Lag 1

The first lag feature captures the Bitcoin log return from the previous period.

[ Lag_1 = Return_{t-1} ]

This allows the model to evaluate whether recent Bitcoin return behavior contains information regarding future returns.

15.2 Lag 2

The second lag feature extends the return history:

[ Lag_2 = Return_{t-2} ]

This provides additional short-term market information.

15.3 Lag 3

The third lag feature captures a longer short-term return pattern:

[ Lag_3 = Return_{t-3} ]

Together, these lag variables represent the return-memory structure of Bitcoin.

16 Moving Average Feature

The model includes a 7-period simple moving average:

[ SMA_7 ]

The moving average represents short-term price trends by smoothing daily Bitcoin price fluctuations.

17 Momentum Indicator

The Relative Strength Index:

[ RSI(14) ]

is included as a momentum indicator.

RSI measures recent price momentum and evaluates the balance between upward and downward price movements.

18 Assigned Advanced Features

18.1 Williams %R

Williams %R is calculated using Bitcoin high, low, and closing prices.

The indicator measures the location of the current price relative to its recent high-low trading range.

This provides additional information regarding short-term price positioning.

18.2 On-Balance Volume (OBV)

On-Balance Volume combines:

  • Bitcoin closing price movement; and
  • trading volume.

The purpose of OBV is to capture potential buying and selling pressure in the market.

19 Student-Designed Feature

19.1 Parkinson Volatility

Parkinson volatility was included as a student-designed feature.

Unlike traditional close-to-close volatility measures, Parkinson volatility uses the intraday high-low price range.

The feature captures volatility information that may not be fully represented by closing-price returns.

The implementation uses:

  • a 7-period window; and
  • annualization factor based on Bitcoin’s year-round trading calendar.

20 External Financial Predictors

The forecasting framework also incorporates external market variables.

20.1 Gold

Gold log return is included as an external financial-market predictor.

It captures possible relationships between Bitcoin and movements in another major financial asset.

20.2 VIX

The CBOE Volatility Index (VIX) is included to represent market-implied volatility and overall risk sentiment.

20.3 10-Year U.S. Treasury Yield

The 10-Year U.S. Treasury Yield represents:

  • long-term interest-rate conditions; and
  • broader financial market conditions.

21 Feature Engineering Implementation

Code 
# Load engineered dataset

feature_data <- read_csv(
  "data_processed/model_data.csv",
  show_col_types = FALSE
)


# Display final predictors

predictor_names <- c(
  "btc_log_return",
  "btc_return_lag1",
  "btc_return_lag2",
  "btc_return_lag3",
  "btc_sma7",
  "btc_rsi14",
  "btc_williams_r14",
  "btc_obv",
  "btc_parkinson_vol7",
  "gold_log_return",
  "vix_close",
  "treasury_10y"
)


feature_data |>
  select(
    all_of(predictor_names)
  ) |>
  head()
# A tibble: 6 × 12
  btc_log_return btc_return_lag1 btc_return_lag2 btc_return_lag3 btc_sma7
           <dbl>           <dbl>           <dbl>           <dbl>    <dbl>
1       -0.00864         0.0301         -0.00455        -0.0575      391.
2       -0.0225         -0.00864         0.0301         -0.00455     386.
3       -0.0424         -0.0225         -0.00864         0.0301      380.
4        0.0294         -0.0257         -0.0891         -0.0424      355.
5        0.0183          0.0294         -0.0257         -0.0891      348.
6        0.0486          0.0183          0.0294         -0.0257      343.
# ℹ 7 more variables: btc_rsi14 <dbl>, btc_williams_r14 <dbl>, btc_obv <dbl>,
#   btc_parkinson_vol7 <dbl>, gold_log_return <dbl>, vix_close <dbl>,
#   treasury_10y <dbl>

The completed feature set provides the information framework used by all machine-learning forecasting models in the subsequent modeling stage.

22 Machine Learning Methodology

22.1 Overview

The machine-learning methodology was designed to forecast the Bitcoin t+3 Log Return using a leakage-safe financial forecasting framework.

The modeling process was structured to ensure that:

  • historical information was used only to predict future outcomes;
  • future information was not introduced during training;
  • all models were evaluated using the same testing dataset; and
  • forecasting performance differences reflected model capability rather than differences in available information.

The methodology consists of:

  1. Final modeling dataset preparation;
  2. Chronological train/test splitting;
  3. Target leakage protection;
  4. Rolling-origin time-series cross-validation;
  5. Machine-learning model training; and
  6. Out-of-sample forecasting evaluation.

23 Chronological Train/Test Split

Financial data are time-dependent; therefore, the dataset was split chronologically rather than randomly.

The dataset was divided into:

  • 80% training dataset
  • 20% testing dataset

The training dataset was used for:

  • model estimation;
  • hyperparameter tuning; and
  • cross-validation.

The testing dataset remained untouched until final model evaluation.

This approach ensures that the evaluation process reflects a realistic forecasting environment where historical information is used to predict future observations.

24 Target Leakage Protection

Because the forecasting target represents Bitcoin return occurring at t+3, special attention was given to preventing target leakage.

Target leakage occurs when information from the future becomes available during model training, resulting in unrealistic performance estimates.

To prevent leakage:

  • predictor variables were created using information available at the forecast origin date;
  • future target information was excluded from predictor construction;
  • overlapping future target periods were removed during validation.

The final modeling framework therefore ensures that only information available at time t is used to forecast the return occurring at t+3.

25 Rolling-Origin Time-Series Cross-Validation

Hyperparameter tuning was performed using rolling-origin time-series cross-validation.

Unlike traditional random cross-validation, rolling-origin validation maintains the chronological structure of financial data.

The validation process repeatedly:

  1. trains the model using historical observations;
  2. validates the model using a future validation period;
  3. moves the training window forward; and
  4. repeats the process.

This approach provides a more realistic estimate of forecasting performance under changing market conditions.

26 Machine Learning Models

Six forecasting models were developed and compared:

Model Description
Linear Regression Linear benchmark model
Decision Tree Tree-based nonlinear model
Random Forest Ensemble tree model
XGBoost Gradient boosting model
Support Vector Regression Kernel-based regression model
Artificial Neural Network Neural-network forecasting model

The purpose of including multiple models is to compare different modeling approaches and identify the forecasting model with the strongest out-of-sample performance.

27 Model Training Framework

The models were trained using the same:

  • forecasting target;
  • predictor variables;
  • training dataset;
  • testing dataset; and
  • evaluation framework.

The final predictor set consisted of the 12 engineered variables developed in the Feature Engineering stage.

28 Model Development Design

Code 
model_design <- tibble(

  "Design Element" = c(
    "Target Asset",
    "Forecasting Target",
    "Training/Test Split",
    "Validation Method",
    "Number of Predictors",
    "Number of Models"
  ),

  Specification = c(
    "Bitcoin (BTC-USD)",
    "Bitcoin t+3 Log Return",
    "Chronological 80% / 20%",
    "Rolling-origin time-series cross-validation",
    "12 Predictors",
    "6 Machine-learning models"
  )
)

knitr::kable(model_design)
Design Element Specification
Target Asset Bitcoin (BTC-USD)
Forecasting Target Bitcoin t+3 Log Return
Training/Test Split Chronological 80% / 20%
Validation Method Rolling-origin time-series cross-validation
Number of Predictors 12 Predictors
Number of Models 6 Machine-learning models

29 Model Training Implementation

Code 
# Load training and testing datasets

train_data <- read_csv(
  "data_processed/train_data.csv",
  show_col_types = FALSE
)

test_data <- read_csv(
  "data_processed/test_data.csv",
  show_col_types = FALSE
)


# Check dataset dimensions

dim(train_data)
[1] 2362   15
Code 
dim(test_data)
[1] 592  15

The completed machine-learning methodology provides a reproducible forecasting framework where multiple models are trained under the same conditions and evaluated using out-of-sample financial forecasting performance.

30 Model Performance

30.1 Overview

The six forecasting models were evaluated using out-of-sample predictions generated from the untouched testing dataset.

The evaluation compares the forecasting capability of each model in predicting:

Bitcoin t+3 Log Return

The models were evaluated using the following performance metrics:

  1. Root Mean Squared Error (RMSE)
  2. Mean Absolute Error (MAE)
  3. R-squared (R²)
  4. Directional Accuracy

The evaluation process determines the predictive-performance leader based on forecasting error and directional prediction performance.

31 Evaluation Metrics

31.1 Root Mean Squared Error (RMSE)

Root Mean Squared Error measures the square root of the average squared difference between actual and predicted values.

[ RMSE = ]

A lower RMSE indicates better forecasting performance.

RMSE gives greater importance to larger forecast errors because the errors are squared.

31.2 Mean Absolute Error (MAE)

Mean Absolute Error measures the average absolute difference between actual and predicted values.

[ MAE= _{t=1}^{n} |y_t-| ]

A lower MAE indicates that the model produces smaller average forecasting errors.

31.3 R-Squared (R²)

R-squared measures the proportion of variation in the forecasting target explained by the model.

[ R^2= 1- { (y_t-{y})^2 } ]

However, R² should not be used as the only basis for selecting a forecasting model, especially for out-of-sample financial return forecasting.

31.4 Directional Accuracy

Directional Accuracy measures whether the predicted return direction matches the actual return direction.

A higher directional accuracy indicates better ability to identify whether Bitcoin returns move upward or downward.

32 Model Performance Results

The model performance comparison is presented below.

Code 
performance_summary <- read_csv(
  "outputs/tables/performance_summary.csv",
  show_col_types = FALSE
)

knitr::kable(
  performance_summary,
  digits = 5
)
Performance_Leader RMSE MAE R2 Directional_Accuracy Training_Time_Seconds Selection_Status
Decision Tree 0.02371 0.01634 NA 51.68919 1.989 Performance leader only; statistical superiority requires Diebold-Mariano testing.

33 Model Ranking

Models were ranked based primarily on forecasting error performance.

Code 
model_ranking <- read_csv(
  "outputs/tables/model_ranking.csv",
  show_col_types = FALSE
)

knitr::kable(
  model_ranking |>
    select(
      Performance_Rank,
      Model,
      RMSE,
      MAE,
      R2,
      Directional_Accuracy
    ),
  digits = 5
)
Performance_Rank Model RMSE MAE R2 Directional_Accuracy
1 Decision Tree 0.02371 0.01634 NA 51.68919
2 Support Vector Regression 0.02378 0.01655 0.00082 48.81757
3 XGBoost 0.02403 0.01656 0.01384 47.46622
4 Random Forest 0.02514 0.01821 0.00009 49.66216
5 Artificial Neural Network 0.02673 0.02030 0.00665 48.31081
6 Linear Regression 0.02736 0.02098 0.00626 48.31081

34 Forecast Error Comparison

Code 
#| fig-cap: "RMSE Comparison Across Forecasting Models"

# Load model ranking results for rendering
model_ranking <- read_csv(
  "outputs/tables/model_ranking.csv",
  show_col_types = FALSE
)

ggplot(
  model_ranking,
  aes(
    x = reorder(Model, RMSE),
    y = RMSE
  )
) +
  geom_col() +
  coord_flip() +
  labs(
    title = "RMSE Comparison Across Forecasting Models",
    x = "Model",
    y = "RMSE"
  )

35 Directional Accuracy Comparison

Code 
#| fig-cap: "Directional Accuracy Comparison Across Forecasting Models"

# Load model ranking results for rendering
model_ranking <- read_csv(
  "outputs/tables/model_ranking.csv",
  show_col_types = FALSE
)

ggplot(
  model_ranking,
  aes(
    x = reorder(Model, Directional_Accuracy),
    y = Directional_Accuracy
  )
) +
  geom_col() +
  coord_flip() +
  labs(
    title = "Directional Accuracy Comparison Across Forecasting Models",
    x = "Model",
    y = "Directional Accuracy (%)"
  )

35.1 Model Performance Interpretation

The out-of-sample evaluation results demonstrate differences in forecasting performance across the six machine-learning models.

Based on the numerical performance comparison, the Decision Tree model achieved the strongest overall forecasting performance and was identified as the predictive-performance leader.

The evaluation considered:

  • Root Mean Squared Error (RMSE);
  • Mean Absolute Error (MAE);
  • R-squared (R²); and
  • Directional Accuracy.

However, model ranking based only on forecasting metrics does not establish statistical superiority.

Although the Decision Tree model achieved the strongest numerical performance, additional statistical validation is required to determine whether the observed differences in forecasting accuracy are statistically meaningful.

Therefore, the next stage applies the Diebold-Mariano Test to compare forecast accuracy differences between competing models.

36 Diebold-Mariano Test

36.1 Overview

Although model performance metrics provide a numerical ranking of forecasting models, differences in RMSE, MAE, and Directional Accuracy alone do not determine whether one model is statistically superior to another.

Therefore, the Diebold-Mariano Test was applied to evaluate whether differences in forecasting accuracy between competing models are statistically meaningful.

The test compares forecast errors from competing models and determines whether one model provides significantly different predictive accuracy.

37 Purpose of the Diebold-Mariano Test

The Diebold-Mariano Test was conducted to:

  • compare forecast accuracy between competing models;
  • determine whether observed performance differences are statistically significant;
  • identify statistically competitive models;
  • evaluate whether the selected model has evidence of superior forecasting ability.

The comparison was performed using the same out-of-sample forecast period and the same forecasting target:

Bitcoin t+3 Log Return

38 Statistical Hypotheses

The Diebold-Mariano Test evaluates the following hypotheses:

38.1 Null Hypothesis (H₀)

[ H_0: ]

This means that there is no statistically significant difference between the forecast accuracy of the two models.

38.2 Alternative Hypothesis (H₁)

[ H_1: ]

This means that the forecast accuracy between the two models is statistically different.

39 Loss Function

The Diebold-Mariano comparison uses squared-error loss.

The forecast error is calculated as:

[ e_t = y_t- ]

where:

  • (y_t) represents the actual Bitcoin t+3 Log Return;
  • () represents the predicted Bitcoin t+3 Log Return.

The loss difference between two models is evaluated to determine whether one model produces statistically different forecast errors.

40 Significance Level and Decision Rule

The statistical significance level used in this analysis is:

[ = 0.05 ]

The decision rule is:

Condition Decision
p-value < 0.05 Reject H₀
p-value ≥ 0.05 Do not reject H₀

Rejecting H₀ indicates evidence that the two models have different predictive accuracy.

Failing to reject H₀ indicates insufficient evidence that the models have different predictive accuracy.

41 Pairwise Diebold-Mariano Results

Code 
dm_pairwise_results <- read_csv(
  "outputs/tables/dm_pairwise_results.csv",
  show_col_types = FALSE
)

knitr::kable(
  dm_pairwise_results,
  digits = 5
)
Model_1 Model_2 RMSE_1 RMSE_2 MSE_1 MSE_2 DM_Statistic p_value Significance Decision Lower_Loss_Model Statistical_Winner DM_Direction Interpretation
Linear Regression Decision Tree 0.02736 0.02371 0.00075 0.00056 5.87363 0.00000 *** Reject H0 Decision Tree Decision Tree Decision Tree has lower squared-error loss than Linear Regression Reject H0. Decision Tree has statistically significantly lower squared-error loss than Linear Regression at the 5% significance level.
Linear Regression Random Forest 0.02736 0.02514 0.00075 0.00063 6.63854 0.00000 *** Reject H0 Random Forest Random Forest Random Forest has lower squared-error loss than Linear Regression Reject H0. Random Forest has statistically significantly lower squared-error loss than Linear Regression at the 5% significance level.
Linear Regression XGBoost 0.02736 0.02403 0.00075 0.00058 6.31982 0.00000 *** Reject H0 XGBoost XGBoost XGBoost has lower squared-error loss than Linear Regression Reject H0. XGBoost has statistically significantly lower squared-error loss than Linear Regression at the 5% significance level.
Linear Regression Support Vector Regression 0.02736 0.02378 0.00075 0.00057 7.21575 0.00000 *** Reject H0 Support Vector Regression Support Vector Regression Support Vector Regression has lower squared-error loss than Linear Regression Reject H0. Support Vector Regression has statistically significantly lower squared-error loss than Linear Regression at the 5% significance level.
Linear Regression Artificial Neural Network 0.02736 0.02673 0.00075 0.00071 11.23411 0.00000 *** Reject H0 Artificial Neural Network Artificial Neural Network Artificial Neural Network has lower squared-error loss than Linear Regression Reject H0. Artificial Neural Network has statistically significantly lower squared-error loss than Linear Regression at the 5% significance level.
Decision Tree Random Forest 0.02371 0.02514 0.00056 0.00063 -3.46857 0.00056 *** Reject H0 Decision Tree Decision Tree Decision Tree has lower squared-error loss than Random Forest Reject H0. Decision Tree has statistically significantly lower squared-error loss than Random Forest at the 5% significance level.
Decision Tree XGBoost 0.02371 0.02403 0.00056 0.00058 -1.81490 0.07005 . Fail to Reject H0 Decision Tree No statistically significant winner Decision Tree has lower squared-error loss than XGBoost Fail to reject H0. There is insufficient statistical evidence at the 5% level to conclude that the forecasting accuracy of Decision Tree and XGBoost differs.
Decision Tree Support Vector Regression 0.02371 0.02378 0.00056 0.00057 -0.35574 0.72216 NA Fail to Reject H0 Decision Tree No statistically significant winner Decision Tree has lower squared-error loss than Support Vector Regression Fail to reject H0. There is insufficient statistical evidence at the 5% level to conclude that the forecasting accuracy of Decision Tree and Support Vector Regression differs.
Decision Tree Artificial Neural Network 0.02371 0.02673 0.00056 0.00071 -5.26999 0.00000 *** Reject H0 Decision Tree Decision Tree Decision Tree has lower squared-error loss than Artificial Neural Network Reject H0. Decision Tree has statistically significantly lower squared-error loss than Artificial Neural Network at the 5% significance level.
Random Forest XGBoost 0.02514 0.02403 0.00063 0.00058 3.47216 0.00055 *** Reject H0 XGBoost XGBoost XGBoost has lower squared-error loss than Random Forest Reject H0. XGBoost has statistically significantly lower squared-error loss than Random Forest at the 5% significance level.
Random Forest Support Vector Regression 0.02514 0.02378 0.00063 0.00057 4.67012 0.00000 *** Reject H0 Support Vector Regression Support Vector Regression Support Vector Regression has lower squared-error loss than Random Forest Reject H0. Support Vector Regression has statistically significantly lower squared-error loss than Random Forest at the 5% significance level.
Random Forest Artificial Neural Network 0.02514 0.02673 0.00063 0.00071 -5.36482 0.00000 *** Reject H0 Random Forest Random Forest Random Forest has lower squared-error loss than Artificial Neural Network Reject H0. Random Forest has statistically significantly lower squared-error loss than Artificial Neural Network at the 5% significance level.
XGBoost Support Vector Regression 0.02403 0.02378 0.00058 0.00057 1.63567 0.10244 NA Fail to Reject H0 Support Vector Regression No statistically significant winner Support Vector Regression has lower squared-error loss than XGBoost Fail to reject H0. There is insufficient statistical evidence at the 5% level to conclude that the forecasting accuracy of XGBoost and Support Vector Regression differs.
XGBoost Artificial Neural Network 0.02403 0.02673 0.00058 0.00071 -5.62289 0.00000 *** Reject H0 XGBoost XGBoost XGBoost has lower squared-error loss than Artificial Neural Network Reject H0. XGBoost has statistically significantly lower squared-error loss than Artificial Neural Network at the 5% significance level.
Support Vector Regression Artificial Neural Network 0.02378 0.02673 0.00057 0.00071 -6.60136 0.00000 *** Reject H0 Support Vector Regression Support Vector Regression Support Vector Regression has lower squared-error loss than Artificial Neural Network Reject H0. Support Vector Regression has statistically significantly lower squared-error loss than Artificial Neural Network at the 5% significance level.

The pairwise comparison evaluates forecasting accuracy differences between each competing model combination.

42 Overall Diebold-Mariano Summary

Code 
dm_overall_summary <- read_csv(
  "outputs/tables/dm_overall_summary.csv",
  show_col_types = FALSE
)

knitr::kable(
  dm_overall_summary,
  digits = 5
)
Models Total_Pairwise_Comparisons Significant_Comparisons Non_Significant_Comparisons Significance_Level Loss_Function Power Forecast_Horizon_h
6 15 12 3 0.05 Squared Error 2 1

The overall summary provides a consolidated view of the statistical evidence across the forecasting models.

43 Model-Level Diebold-Mariano Summary

Code 
dm_model_summary <- read_csv(
  "outputs/tables/dm_model_summary.csv",
  show_col_types = FALSE
)

knitr::kable(
  dm_model_summary,
  digits = 5
)
Model Comparisons Significant_Wins Significant_Losses Non_Significant_Comparisons
Decision Tree 5 3 0 2
XGBoost 5 3 0 2
Support Vector Regression 5 3 0 2
Random Forest 5 2 3 0
Artificial Neural Network 5 1 4 0
Linear Regression 5 0 5 0

The model-level summary identifies models that demonstrate statistically competitive forecasting performance.

44 Selected Model Comparison

Code 
dm_leader_comparisons <- read_csv(
  "outputs/tables/dm_leader_comparisons.csv",
  show_col_types = FALSE
)

knitr::kable(
  dm_leader_comparisons,
  digits = 5
)
Competitor DM_Statistic p_value Decision Leader_MSE Competitor_MSE Significant_Difference Leader_Has_Lower_Loss Leader_Significantly_Better Competitor_Significantly_Better Statistically_Competitive_With_Leader Decision_Engine_Status
Linear Regression 5.87363 0.00000 Reject H0 0.00056 0.00075 TRUE TRUE TRUE FALSE FALSE Performance leader is significantly better
Random Forest -3.46857 0.00056 Reject H0 0.00056 0.00063 TRUE TRUE TRUE FALSE FALSE Performance leader is significantly better
XGBoost -1.81490 0.07005 Fail to Reject H0 0.00056 0.00058 FALSE TRUE FALSE FALSE TRUE Statistically competitive with performance leader
Support Vector Regression -0.35574 0.72216 Fail to Reject H0 0.00056 0.00057 FALSE TRUE FALSE FALSE TRUE Statistically competitive with performance leader
Artificial Neural Network -5.26999 0.00000 Reject H0 0.00056 0.00071 TRUE TRUE TRUE FALSE FALSE Performance leader is significantly better

45 Diebold-Mariano Interpretation

The Diebold-Mariano Test provides additional statistical evidence regarding model performance differences.

The test results determine whether the Decision Tree model’s numerical advantage represents statistically meaningful improvement or whether competing models remain statistically competitive.

A model with the strongest numerical performance does not automatically represent a statistically superior forecasting model.

Therefore, the final model selection considers:

  1. forecasting performance metrics;
  2. Diebold-Mariano statistical evidence;
  3. explainability analysis; and
  4. investment interpretation.

The final decision is consolidated through the Forecast Decision Engine.

46 Forecast Decision Engine

46.1 Overview

The Forecast Decision Engine consolidates the results from the forecasting framework into a final model selection process.

The decision engine integrates:

  1. Model performance evaluation;
  2. Diebold-Mariano statistical evidence;
  3. SHAP explainability findings; and
  4. Forecasting model interpretation.

The purpose of the Forecast Decision Engine is to identify the final selected forecasting model and determine statistically competitive alternatives.

47 Decision Framework

The final forecasting model selection does not rely on a single performance metric.

The decision process considers:

Evaluation Component Purpose
Model Performance Identifies models with stronger numerical forecasting results
Diebold-Mariano Test Determines whether performance differences are statistically meaningful
SHAP Analysis Explains selected model behavior
Executive Recommendation Translates forecasting evidence into investment interpretation

48 Final Selected Forecasting Model

The Forecast Decision Engine identified the following model:

Code 
forecast_decision_engine <- read_csv(
  "outputs/tables/forecast_decision_engine.csv",
  show_col_types = FALSE
)

knitr::kable(
  forecast_decision_engine,
  digits = 5
)
Performance_Leader Selected_Model_for_SHAP Statistically_Competitive_Models Robustness_Check_Models Significant_DM_Wins_of_Leader Non_Significant_Leader_Comparisons Significant_Losses_of_Leader Decision_Rule SHAP_Status
Decision Tree Decision Tree Decision Tree; XGBoost; Support Vector Regression XGBoost; Support Vector Regression 3 2 0 Combine Step 07 predictive performance with pairwise Diebold-Mariano statistical validation. Selected model proceeds to Step 09 SHAP analysis.

The selected forecasting model represents the model that provides the strongest overall combination of:

  • predictive performance;
  • statistical evidence;
  • interpretability; and
  • decision usefulness.

49 Decision Engine Output

Code 
forecast_decision_engine
# A tibble: 1 × 9
  Performance_Leader Selected_Model_for_SHAP Statistically_Competitive_Models   
  <chr>              <chr>                   <chr>                              
1 Decision Tree      Decision Tree           Decision Tree; XGBoost; Support Ve…
# ℹ 6 more variables: Robustness_Check_Models <chr>,
#   Significant_DM_Wins_of_Leader <dbl>,
#   Non_Significant_Leader_Comparisons <dbl>,
#   Significant_Losses_of_Leader <dbl>, Decision_Rule <chr>, SHAP_Status <chr>

The output consolidates the final decision based on the complete forecasting workflow.

50 Model Selection Interpretation

The forecasting framework identified Decision Tree as the selected forecasting model.

The selection was based on the combination of:

  • numerical forecasting performance;
  • statistical validation results;
  • explainability requirements; and
  • executive decision-making relevance.

The selected model is then passed forward to Explainable Artificial Intelligence analysis to determine how the model generates its predictions.

51 Statistically Competitive Alternatives

Although one model may be selected as the final forecasting model, other models may remain statistically competitive.

The Diebold-Mariano results are therefore considered together with model performance metrics to avoid selecting a model based only on numerical ranking.

Statistically competitive models provide alternative forecasting approaches that may demonstrate similar predictive ability.

52 Forecast Decision Engine Summary

The Forecast Decision Engine provides the final analytical transition from technical model evaluation toward investment interpretation.

The selected model is not considered a guaranteed predictor of future Bitcoin performance.

Instead, it functions as a forecasting decision-support tool that combines:

  • machine-learning prediction;
  • statistical validation;
  • explainable artificial intelligence; and
  • financial interpretation.
Code 
decision_engine <- read_csv(
  "outputs/tables/forecast_decision_engine.csv",
  show_col_types = FALSE
)

decision_engine |>
  knitr::kable(
    digits = 5
  )
Performance_Leader Selected_Model_for_SHAP Statistically_Competitive_Models Robustness_Check_Models Significant_DM_Wins_of_Leader Non_Significant_Leader_Comparisons Significant_Losses_of_Leader Decision_Rule SHAP_Status
Decision Tree Decision Tree Decision Tree; XGBoost; Support Vector Regression XGBoost; Support Vector Regression 3 2 0 Combine Step 07 predictive performance with pairwise Diebold-Mariano statistical validation. Selected model proceeds to Step 09 SHAP analysis.

53 SHAP Analysis

53.1 Overview

Explainable Artificial Intelligence (XAI) analysis was conducted using SHAP (SHapley Additive exPlanations) to understand how the selected forecasting model generates predictions.

The Forecast Decision Engine identified the Decision Tree as the selected forecasting model.

SHAP analysis was applied to explain:

  • which predictors contribute most strongly to model predictions;
  • how individual predictors influence the forecasting output;
  • whether the selected model actively uses the available predictors; and
  • the overall behavior of the fitted forecasting model.

54 Purpose of SHAP Analysis

SHAP explains the contribution of each predictor variable to the model prediction.

The analysis provides transparency by showing how the selected Decision Tree model uses the engineered features to forecast:

Bitcoin t+3 Log Return

The purpose of SHAP is interpretation of model behavior.

SHAP does not establish financial or economic causality.

The results explain how the fitted model behaves based on the available predictors.

55 Selected Model Verification

Code 
forecast_decision_engine <- read_csv(
  "outputs/tables/forecast_decision_engine.csv",
  show_col_types = FALSE
)

forecast_decision_engine
# A tibble: 1 × 9
  Performance_Leader Selected_Model_for_SHAP Statistically_Competitive_Models   
  <chr>              <chr>                   <chr>                              
1 Decision Tree      Decision Tree           Decision Tree; XGBoost; Support Ve…
# ℹ 6 more variables: Robustness_Check_Models <chr>,
#   Significant_DM_Wins_of_Leader <dbl>,
#   Non_Significant_Leader_Comparisons <dbl>,
#   Significant_Losses_of_Leader <dbl>, Decision_Rule <chr>, SHAP_Status <chr>

The selected model passed to SHAP analysis is:

Decision Tree

56 SHAP Feature Importance

SHAP feature importance summarizes the average contribution of each predictor to the model predictions.

Code 
shap_feature_importance <- read_csv(
  "outputs/tables/shap_feature_importance.csv",
  show_col_types = FALSE
)

knitr::kable(
  shap_feature_importance,
  digits = 5
)
Rank Feature Mean_Absolute_SHAP
1 treasury_10y 0.00045
2 btc_log_return 0.00000
3 btc_return_lag1 0.00000
4 btc_return_lag2 0.00000
5 btc_return_lag3 0.00000
6 btc_sma7 0.00000
7 btc_rsi14 0.00000
8 btc_williams_r14 0.00000
9 btc_obv 0.00000
10 btc_parkinson_vol7 0.00000
11 gold_log_return 0.00000
12 vix_close 0.00000

56.1 SHAP Feature Importance Plot

Code 
load(
  "outputs/plots/plot_shap_importance.RData"
)

plot_shap_importance

The SHAP feature importance ranking identifies which predictors contribute most strongly to the Decision Tree forecasting behavior.

The highest-ranked predictors represent variables that have the greatest influence on the model output.

57 SHAP Summary / Beeswarm Plot

The SHAP summary plot provides information regarding:

  • feature importance;
  • direction of contribution;
  • distribution of SHAP values; and
  • variation in predictor influence across observations.
Code 
load(
  "outputs/plots/plot_shap_beeswarm.RData"
)

plot_shap_beeswarm

The beeswarm plot demonstrates how individual predictor values contribute positively or negatively to the Decision Tree prediction.

58 SHAP Waterfall Plot

The SHAP waterfall plot explains an individual forecast prediction by showing how each predictor contributes to the final model output.

Code 
load(
  "outputs/plots/plot_shap_waterfall.RData"
)

plot_shap_waterfall

The SHAP waterfall plot provides a local explanation of an individual Decision Tree prediction.

Each feature contribution represents how the predictor moves the model prediction away from the baseline prediction.

Positive SHAP values indicate predictors that increase the predicted Bitcoin t+3 Log Return, while negative SHAP values indicate predictors that decrease the prediction.

The waterfall plot demonstrates how the Decision Tree combines multiple predictor variables to generate a specific forecasting outcome.

59 SHAP Analysis Interpretation

The Explainable Artificial Intelligence analysis provides transparency regarding how the selected Decision Tree model generates predictions.

The results identify:

  • the most influential predictors;
  • the direction of predictor contribution;
  • the relative importance of engineered features; and
  • the internal decision behavior of the selected model.

The SHAP analysis supports model interpretability by explaining model behavior.

However, SHAP values should not be interpreted as evidence of financial or economic causality.

The analysis explains what predictors the model uses when generating forecasts, but it does not establish why Bitcoin returns occur in financial markets.

Code 
shap_interpretation_summary <- read_csv(
  "outputs/tables/shap_interpretation_summary.csv",
  show_col_types = FALSE
)

knitr::kable(
  shap_interpretation_summary,
  digits = 5
)
Selected_Model SHAP_Method SHAP_Simulations Top_Feature Top_Mean_Absolute_SHAP Tree_Splits Constant_Prediction_Model Interpretation Causality_Warning
Decision Tree Monte Carlo approximate SHAP using fastshap 50 treasury_10y 0.00045 1 FALSE The selected Decision Tree uses the predictor variables to generate its forecasts. The most influential predictor by mean absolute SHAP is treasury_10y . SHAP values describe the behavior of the fitted model and should not be interpreted as evidence of causality. SHAP explains how the selected model generated predictions; it does not prove economic or financial causality.

60 Model Behavior Interpretation

The SHAP analysis provides evidence regarding how the selected Decision Tree model uses the available predictors.

The interpretation focuses on:

  • predictor contribution;
  • relative importance;
  • model decision patterns; and
  • transparency of forecasting behavior.

The SHAP results explain the fitted model behavior and provide interpretability for investment decision support.

However, SHAP values should not be interpreted as evidence of economic causality.

The analysis explains what the model uses, not why the financial market moves.

61 Investment Recommendation

61.1 Overview

The final investment recommendation is developed by integrating the complete forecasting framework:

  1. Model Performance Evaluation;
  2. Diebold-Mariano Statistical Validation;
  3. Forecast Decision Engine Results; and
  4. SHAP Explainability Analysis.

The recommendation reflects the predictive evidence generated by the machine-learning framework and should be interpreted as decision-support information rather than a standalone investment decision.

62 Executive Forecasting Recommendation

Based on the complete forecasting framework, the final recommendation is:

62.1 Neutral Forecasting Signal

The Decision Tree model was identified as the selected forecasting model based on its overall forecasting performance among the evaluated machine-learning models.

However, the forecasting evidence does not provide sufficient support for a strong directional investment conclusion.

The selected model demonstrates predictive capability within the evaluated sample period; however, Bitcoin return forecasting remains challenging due to market uncertainty, changing market conditions, and the unpredictable nature of financial markets.

Therefore, the forecasting output is interpreted as a Neutral Forecasting Signal.

63 Supporting Evidence

63.1 Model Performance

The Decision Tree model achieved the strongest numerical forecasting performance among the evaluated models based on:

  • Root Mean Squared Error (RMSE);
  • Mean Absolute Error (MAE);
  • R-squared (R²); and
  • Directional Accuracy.

The model was therefore selected as the preferred forecasting model within the evaluated framework.

63.2 Statistical Validation

The Diebold-Mariano Test was conducted to determine whether differences in forecasting accuracy between competing models were statistically meaningful.

The statistical evidence was considered together with model performance results to avoid selecting a model based solely on numerical ranking.

63.3 Explainability Analysis

SHAP analysis was conducted to understand how the selected Decision Tree model generates predictions.

The analysis identified the contribution and importance of predictor variables used by the model.

The SHAP results improve transparency by explaining model behavior.

However, SHAP values do not establish financial or economic causality.

64 Final Recommendation Interpretation

The forecasting framework provides useful information regarding Bitcoin t+3 Log Return behavior.

The selected Decision Tree model demonstrates predictive value within the available dataset; however, the evidence should be interpreted cautiously.

The recommendation is therefore classified as:

Neutral Forecasting Signal

This indicates that the model provides analytical support for investment evaluation but does not generate a sufficiently strong signal to justify a definitive directional position.

The forecasting framework should be used together with broader financial analysis, market conditions, and investor-specific considerations.

65 Limitations

65.1 Overview

Although the forecasting framework provides a structured approach for predicting Bitcoin t+3 Log Return, several limitations must be considered when interpreting the results.

The model outputs should be treated as predictive information and decision-support evidence rather than definitive explanations of future market behavior.

66 Historical Data Limitation

The forecasting models are developed using historical financial market data.

Machine-learning models identify patterns based on previous observations; however, historical relationships may not remain constant under future market conditions.

Changes in:

  • market structure;
  • investor behavior;
  • macroeconomic conditions;
  • regulatory environments; and
  • financial market conditions

may influence future Bitcoin return behavior.

67 Financial Market Uncertainty

Bitcoin returns are influenced by numerous factors that may not be fully captured by the selected predictors.

Although the framework incorporates:

  • Bitcoin market variables;
  • Gold;
  • VIX; and
  • 10-Year U.S. Treasury Yield,

other economic, behavioral, technological, and market-specific factors may also influence Bitcoin performance.

68 Model Risk

The forecasting framework compares multiple machine-learning models and selects the model with the strongest performance within the evaluated dataset.

However, strong historical forecasting performance does not guarantee future forecasting accuracy.

Model performance may change when applied to different market environments or future observations.

69 Forecasting Target Limitation

The framework focuses specifically on:

Bitcoin t+3 Log Return

Therefore, the findings should not be interpreted as a prediction of:

  • long-term Bitcoin price movements;
  • future investment returns over extended periods; or
  • guaranteed market direction.

The model is designed for short-horizon forecasting.

70 Explainability Limitation

SHAP analysis improves transparency by explaining how the selected model uses predictor variables.

However:

SHAP explains model behavior rather than financial causality.

The identified influential predictors represent variables used by the model when generating forecasts, but they do not prove that these variables directly cause Bitcoin returns.

71 Investment Decision Limitation

The forecasting framework provides analytical support for investment evaluation.

However, investment decisions should also consider:

  • investor objectives;
  • risk tolerance;
  • portfolio allocation;
  • transaction considerations;
  • liquidity conditions; and
  • broader market analysis.

The model should therefore be used as a decision-support framework rather than an independent investment decision mechanism.

72 Conclusion

This consulting report developed a financial forecasting and investment analytics framework for predicting Bitcoin t+3 Log Return using machine-learning models and explainable artificial intelligence techniques.

The analysis incorporated Bitcoin market information together with external financial predictors, including Gold, the CBOE Volatility Index (VIX), and the 10-Year U.S. Treasury Yield.

The forecasting framework followed a structured analytical process consisting of:

  1. Data preparation;
  2. Feature engineering;
  3. Machine-learning model development;
  4. Out-of-sample performance evaluation;
  5. Diebold-Mariano statistical validation;
  6. Forecast Decision Engine consolidation;
  7. SHAP explainability analysis; and
  8. Executive forecasting recommendation.

Among the evaluated machine-learning approaches, the Decision Tree model was identified as the selected forecasting model based on its overall forecasting performance within the evaluated framework.

The model evaluation considered:

  • Root Mean Squared Error (RMSE);
  • Mean Absolute Error (MAE);
  • R-squared (R²); and
  • Directional Accuracy.

The Diebold-Mariano Test was applied to determine whether observed differences in forecasting accuracy between models were statistically meaningful. This additional validation ensured that model selection was not based solely on numerical performance rankings.

SHAP analysis provided transparency regarding how the selected Decision Tree model generated predictions by identifying predictor contributions and explaining model behavior.

However, the results should be interpreted with appropriate caution. Forecasting results are predictive rather than causal, and SHAP explanations describe model behavior rather than establishing financial or economic causality.

Based on the complete forecasting framework, the final output was interpreted as a Neutral Forecasting Signal. The model provides useful decision-support information regarding Bitcoin t+3 Log Return behavior; however, it should not be used as a standalone investment decision mechanism.

Overall, this framework demonstrates how machine-learning forecasting, statistical validation, and explainable artificial intelligence can be integrated to support more transparent and informed financial decision-making.

73 References

73.1 Financial Data Sources

Yahoo Finance. (2026). Historical market data for Bitcoin (BTC-USD), Gold (GC=F), and CBOE Volatility Index (VIX). Retrieved from Yahoo Finance.

Federal Reserve Bank of St. Louis. (2026). 10-Year Treasury Constant Maturity Rate (DGS10). Federal Reserve Economic Data (FRED).

73.2 Machine Learning and Forecasting Methodology

Breiman, L. (2001). Random Forests. Machine Learning, 45, 5–32.

Chen, T., & Guestrin, C. (2016). XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.

Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine Learning, 20, 273–297.

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer.

73.3 Forecast Evaluation and Statistical Testing

Diebold, F. X., & Mariano, R. S. (1995). Comparing predictive accuracy. Journal of Business & Economic Statistics, 13(3), 253–263.

73.4 Explainable Artificial Intelligence

Lundberg, S. M., & Lee, S. I. (2017). A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems.

73.5 Software Documentation

R Core Team. (2026). R: A language and environment for statistical computing.

RStudio Team. (2026). RStudio: Integrated Development Environment for R.

Tidymodels. (2026). Tidymodels: A collection of packages for modeling and machine learning using tidyverse principles.

74 Appendix: R code

74.1 Project Workflow

The analysis was developed through a structured R workflow consisting of ten sequential scripts.

The scripts were organized as follows:

Script Purpose
00_setup.R Project setup, package loading, and folder creation
01_data_acquisition.R Financial data acquisition and cleaning
02_target_and_integration.R Target construction and dataset integration
03_feature_engineering.R Predictor feature creation
04_exploratory_analysis.R Exploratory data analysis
05_model_setup.R Training/testing split and validation framework
06_model_training.R Machine-learning model training
07_model_evaluation.R Forecast performance evaluation
08_diebold_mariano.R Statistical forecast comparison
09_explainable_ai.R SHAP explainability analysis
10_executive_recommendation.R Executive recommendation generation

74.2 Reproducibility

The complete analysis follows the sequence:

Data Acquisition
→ Data Cleaning
→ Target Construction
→ Feature Engineering
→ Exploratory Analysis
→ Machine Learning Modeling
→ Model Evaluation
→ Statistical Validation
→ Explainability Analysis
→ Executive Recommendation

74.3 Example R Code

Code 
# Load packages

library(tidyverse)
library(quantmod)
library(TTR)
library(randomForest)
library(xgboost)
library(kernlab)
library(nnet)
library(fastshap)
library(shapviz)


# Load final modeling dataset

model_data <- read_csv(
  "data_processed/model_data.csv"
)


# Train/Test split

split_point <- floor(
  0.80 * nrow(model_data)
)

train_data <- model_data[1:split_point, ]

test_data <- model_data[
  (split_point + 1):nrow(model_data),
]


# Model training

# Linear Regression
# Decision Tree
# Random Forest
# XGBoost
# Support Vector Regression
# Artificial Neural Network


# Model evaluation

# RMSE
# MAE
# R-squared
# Directional Accuracy


# Statistical validation

# Diebold-Mariano Test


# Explainability

# SHAP Analysis