Yanis NASSI

The chart compares the normalized price of Bitcoin with the S&P 500 index over the full observation period. While Bitcoin remains significantly more volatile, its medium-term movements often mirror those of the equity market, especially during periods of macroeconomic stress or euphoria.

This partial correlation has strengthened in recent years, suggesting that Bitcoin is increasingly reacting to traditional market drivers such as monetary policy, central bank announcements, or global economic indicators. The spread highlights periods of divergence between the two assets.

Recent crossovers between the normalized curves mark potential turning points. The latest instance, where the S&P 500 overtakes Bitcoin, could indicate a phase of consolidation for crypto, depending on how broader market conditions evolve.

This chart compares the normalized evolution of the DXY (US Dollar Index) and Bitcoin over the full analysis period. A general inverse relationship can be observed : when the DXY rises, Bitcoin tends to stagnate or decline, and vice versa.

This inverse correlation reflects a common macroeconomic pattern: a strong dollar is typically associated with global risk aversion, weighing on alternative assets such as Bitcoin. Conversely, a weakening dollar often signals increased liquidity and a shift toward risk-on sentiment.

Cross-movements and divergence phases between the two curves highlight key moments when Bitcoin either reacts sharply to changes in dollar strength or temporarily decouples. The chart reinforces the role of the DXY as a key macro driver in Bitcoin price dynamics.

BTC Dominance is a relevant indicator for anticipating early-stage bull markets. A rising dominance typically reflects a rotation of capital toward Bitcoin as a safer crypto asset before risk spreads to altcoins. This behavior often marks the beginning of a new bullish cycle centered on Bitcoin.

The indicator is calculated based on the estimated market capitalization of the top cryptocurrencies — BTC, ETH, BNB, USDT, and XRP.

The dominance metric is calculated as:

In the chart, we observe that phases of rising dominance often coincide with or even precede Bitcoin price increases, making it a potential leading indicator. Conversely, declining dominance during price rallies can signal a more speculative or late-cycle phase. This makes BTC Dominance a key variable to monitor alongside price action.

The Fear & Greed Index is a composite indicator that measures overall market sentiment based on various signals such as volatility, volume, social media trends, and Bitcoin dominance. It ranges from 0 (extreme fear) to 100 (extreme greed), providing a synthetic view of investor emotion.

In the chart, we observe that sharp increases in the Fear & Greed Index often precede or accompany Bitcoin price rallies. These periods of renewed optimism are aligned with clear upward momentum. Conversely, drops in sentiment generally correlate with phases of consolidation or temporary pullbacks.

This visual correlation suggests that the index can act as a trend signal, capturing growing investor confidence at the early stages of bullish cycles. It appears to function more as a momentum companion than a reversal indicator, making it a valuable behavioral metric for tracking the strength of price trends.

The Grayscale Bitcoin Trust (GBTC) is a publicly traded financial product that offers investors access to the Bitcoin market through a regulated vehicle. It serves as an alternative to direct crypto ownership and is widely used by institutional participants.

The chart shows a largely parallel evolution between GBTC and Bitcoin’s price. Both curves follow broadly similar trends over the entire period, although some short-term deviations can be observed.

This behavior suggests that GBTC may be a relevant variable to consider in a predictive model, as a proxy for institutional interest and engagement with Bitcoin-related investment products.

The price of gold is traditionally viewed as a safe-haven asset, used by investors to hedge against inflation, economic uncertainty, or geopolitical risk. It is often compared to Bitcoin, especially in debates about long-term value preservation.

In the chart, we observe that gold and Bitcoin sometimes exhibit parallel trends, particularly during certain synchronized bullish phases. However, frequent divergences also appear, highlighting distinct behaviors in response to market cycles and investor sentiment.

These differences suggest that gold may not consistently track Bitcoin, but it could still serve as a complementary variable when analyzing how capital moves between traditional and digital assets during different market regimes.

Public interest in Bitcoin is often measured through the frequency of Google searches. This behavioral indicator helps capture how much attention the asset is receiving from the general public, particularly during periods of strong volatility or bullish momentum.

The chart shows that Google search spikes often align with Bitcoin price peaks, and sometimes precede them slightly. These patterns tend to emerge during bull markets, reflecting a growing wave of mainstream interest.

This correlation suggests that search trends may be a valuable signal for predictive modeling, as a proxy for market sentiment and public engagement with Bitcoin.

The NVT Ratio (Network Value to Transactions) is a fundamental metric used to assess whether Bitcoin is overvalued or undervalued relative to its transaction volume. It is often compared to the traditional P/E ratio in equity markets: a high NVT may signal speculative overvaluation, while a low ratio might suggest stronger fundamental usage.

In the chart, the visual relationship between the NVT Ratio and Bitcoin's price appears relatively weak. Peaks in the NVT do not consistently align with major turning points in price, and at times the two indicators move in opposite directions or remain disconnected.

This suggests that the NVT Ratio may provide more structural insights than short-term signals. Its inclusion in a predictive model could still be valuable, but its true utility will need to be assessed through empirical testing rather than visual inspection alone.

Interest rates, particularly those set by the Federal Reserve, are among the most influential macroeconomic variables. Rate hikes tend to tighten financial conditions and reduce market liquidity, while lower rates encourage borrowing, investment, and risk-taking — all of which can influence crypto markets.

The chart shows a notable inverse relationship between interest rates and the price of Bitcoin. Periods of low or falling rates — such as in 2020 and 2021 — coincided with strong upward movements in Bitcoin. In contrast, the tightening cycle that began in 2022 aligned with a decline in crypto valuations.

This visual correlation reinforces the idea that Bitcoin is behaving more like a macro-sensitive asset. As such, interest rates are a key input in any predictive model aiming to capture shifts in market sentiment or liquidity cycles.

The CSI 300 Index tracks the performance of the 300 largest stocks on the Shanghai and Shenzhen stock exchanges. It is widely used as a proxy for Chinese equity markets and serves as a macroeconomic signal reflecting investor sentiment in Asia.

The chart shows periods of both alignment and divergence between the CSI 300 and Bitcoin. While Bitcoin remains more volatile, some medium-term trends appear to be partially synchronized, especially during broad global risk-on or risk-off movements.

However, it is important to note that CSI 300 data is only available from 2021 onward, creating a missing segment for the first year of the study (March 2020 to March 2021). This data gap may limit the ability to fully assess long-term interactions and should be considered carefully when incorporating this variable into predictive modeling.

The mining difficulty represents the level of computational effort required to validate a new block on the Bitcoin blockchain. It automatically adjusts approximately every two weeks to maintain a regular block creation rate (about every 10 minutes), regardless of fluctuations in the total hash power on the network.

The chart shows a generally upward trend in difficulty over the full period, with occasional dips or plateaus. While some difficulty increases coincide with Bitcoin price rises, the short-term correlation appears inconsistent, suggesting a more structural than reactive behavior.

As a structural indicator, mining difficulty captures network confidence and miner activity. Its slow-moving nature makes it a valuable long-term signal, potentially useful in predictive models as a stability feature rather than a short-term driver of Bitcoin price fluctuations.

The M2 Money Supply represents the amount of money circulating in the U.S. economy, including cash, checking accounts, savings, and other forms of liquidity. It is a key macroeconomic indicator for assessing monetary policy and the availability of liquidity in financial markets.

The chart shows a clear upward trend in M2, with a notable surge during 2020–2021. This spike coincides with a major rally in Bitcoin, suggesting a potential relationship between monetary expansion and crypto performance. However, after 2022, the visual correlation becomes less consistent and harder to interpret.

M2 is a valuable feature for modeling Bitcoin behavior, particularly to capture macro liquidity cycles. However, it is important to note that recent values for late 2025 have been extrapolated using a regression based on a correlated macroeconomic variable. This allows the dataset to be extended but warrants close monitoring of its reliability during modeling.

Bitcoin’s daily trading volume represents the total value of coins exchanged on the market during a given day. It is commonly used to assess liquidity and market activity, offering insight into the level of investor participation and potential interest in the asset.

The graph shows several notable peaks in trading volume, many of which coincide with sharp movements in the Bitcoin price—either upward or downward. However, some volume spikes appear disconnected from major price shifts, suggesting the relationship is not perfectly linear or consistent over time.

BTC volume remains a valuable complementary indicator for modeling purposes. It can help detect moments of increased market engagement, such as during trend reversals or breakout phases. While it may not independently predict price movements, its inclusion in a multivariate model could enhance predictive robustness when combined with other variables.

The S&P 500 volume reflects the total number of shares traded on the index during a given day. It is commonly used as a measure of market liquidity and can indicate shifts in investor sentiment or market stress.

The chart compares the normalized S&P 500 trading volume with Bitcoin’s price. While occasional spikes in trading activity coincide with market turning points in Bitcoin, the alignment is not consistent over time.

As a result, the S&P 500 volume appears to act more as a contextual variable than a direct predictor. It may prove useful when considered alongside other macro indicators, particularly during high-volatility periods.

Bitcoin volatility refers here to the realized standard deviation of daily returns, capturing the magnitude of price fluctuations over time, regardless of direction.

The chart displays repeated volatility spikes, often aligned with major price movements. Some of these peaks precede key turning points, while others appear to be reactive, following rapid market movements. Periods of low volatility tend to coincide with consolidations or slow upward trends.

Volatility is a structural market behavior indicator that can help detect regime changes. While it does not predict direction, it provides alert signals that can help adjust model sensitivity or feature weightings. It is therefore a valuable complementary variable in predictive modeling.

The visualizations below examine the potential relationship between the daily count of violent conflicts (resulting in more than 10 deaths) and the price of Bitcoin. These figures are sourced from the ACLED global conflict database, which tracks geopolitical violence across countries. Two indicators are considered: the number of daily conflict events and the total number of deaths associated with them.

Visually, there appears to be no clear or consistent correlation. While some periods of heightened geopolitical tension seem to coincide with Bitcoin volatility, such patterns are not easily generalizable. Bitcoin's response to conflict appears to be highly context-dependent, rather than directly tied to the frequency or severity of global unrest.

It is also important to note that conflict-related data is only available for approximately three out of the five years in the full dataset. As a result, these variables will be included in exploratory regressions, but their final inclusion in the predictive model will depend on their statistical significance. Their relevance will be assessed rigorously, without assuming explanatory power upfront.

The Aggregate Finance to the Real Economy (China) indicator reflects the volume of financial resources allocated to the Chinese economy, including loans, bonds, and other credit instruments. It is widely used as a proxy for domestic credit stimulus and economic policy interventions in China.

These data were initially available on a monthly basis and were interpolated to daily frequency by replicating each monthly value across all days of the corresponding month. Although this method limits daily variability, some upward movements in aggregate finance appear to coincide with periods of rising Bitcoin prices, especially after 2021.

Due to China's importance in the crypto ecosystem, this macroeconomic signal remains relevant for modeling. However, because of its low granularity and smoothing method, this variable should be interpreted with caution and is flagged as one to monitor carefully during the forecasting phase.

The regression results confirm a strong and highly significant positive relationship between the normalized S&P500 index and the normalized Bitcoin price. The coefficient is close to 1.07, indicating that when the S&P500 increases by one unit (normalized scale), Bitcoin tends to rise by a similar magnitude. With an R² of 0.75, the model explains a large portion of the variance in Bitcoin prices.

This strong relationship aligns with our visual analysis and confirms that macroeconomic conditions reflected in the S&P500 index play a significant role in Bitcoin’s price fluctuations. The hypothesis is clearly validated by this univariate regression.

The univariate regression between the DXY (Dollar Index) and Bitcoin (normalized close) reveals a statistically significant but weak relationship, with an R² of 3%. This means the DXY only explains a small fraction of Bitcoin's price movements in a direct, daily comparison.

This result echoes the visual analysis, which suggested a potential lagged inverse relationship between the two. These findings justify a deeper investigation using optimal lag structures in the multivariate phase.

Notably, a structural shift in correlation appears around late 2023, suggesting that Bitcoin's sensitivity to macroeconomic indicators such as the DXY might be evolving. This change will be revisited during the final interpretation stage.

The univariate regression between BTC Dominance and Bitcoin price (normalized) confirms a strong and significant relationship. With an R² of 55%, this variable alone explains over half of the price variation of Bitcoin, making it a key macro indicator in the crypto ecosystem.

The positive coefficient (0.7772) supports the hypothesis that a rising BTC Dominance typically aligns with price increases. This result reinforces the visual patterns observed earlier and confirms BTC Dominance as a strong candidate for predictive modeling.

Further tests with lag structures will help verify the temporal dynamics of this relationship. The variable will be retained for multivariate modeling phases.

The univariate regression between the Fear & Greed Index and Bitcoin (normalized close) reveals a statistically significant positive relationship, with a coefficient of 0.0026 and a p-value below 0.001. However, the R² remains moderate at 10.7%, suggesting that this behavioral metric only explains a limited portion of Bitcoin’s daily price movements.

This outcome partially confirms the visual analysis, where the index tends to move in tandem with Bitcoin price but doesn’t appear as a dominant explanatory factor in a direct, daily relationship. The predictive power might increase when optimal lags are introduced — especially considering that some peaks in "greed" precede major price increases.

As a result, this indicator remains relevant for behavioral modeling, although its role will need to be reassessed with lag structures in the multivariate regression phase.

The univariate regression between GBTC and Bitcoin's normalized price shows a statistically significant but very weak relationship, with a coefficient of 0.1245 and a p-value of 0.043. However, the explained variance is minimal, with an R² of just 0.3%.

This result confirms the limitations observed during the visual analysis: while GBTC may reflect broader market sentiment or institutional activity, it does not appear to directly influence Bitcoin’s daily price movements in a linear, unlagged setup.

It is likely that the value of this variable lies in more complex or delayed dynamics, which will be further explored in the multivariate modeling phase with lag structure.

La régression univariée entre le prix de l’or (Gold_Price) et le cours du Bitcoin (Close) met en évidence une relation positive forte et statistiquement significative. Le R² de 59,2% indique que le prix de l’or explique à lui seul plus de la moitié des variations du Bitcoin sur la période étudiée.

Ce résultat semble confirmer l’hypothèse d’une corrélation partielle entre les deux actifs, possiblement en tant que valeurs alternatives dans certains contextes macroéconomiques. Cependant, il faudra approfondir cette relation en testant différents retards temporels (lags) lors de la modélisation multivariée, et en tenant compte d'autres variables influentes.

The univariate regression between Google Search Interest and Bitcoin (normalized close) shows a statistically significant positive relationship, with an R² of 14.4%. This suggests that public attention, as reflected in search trends, plays a moderate role in explaining Bitcoin's price fluctuations.

The estimated coefficient (0.5560) confirms a positive correlation: increases in search volume are associated with price increases. While this result supports our initial assumption, further analysis is needed to evaluate whether a lagged effect might enhance predictive power.

The univariate regression between the NVT Ratio and Bitcoin normalized close reveals a weak but statistically significant relationship, with an R² of 2.5%. This suggests the NVT Ratio explains a small portion of Bitcoin’s short-term fluctuations.

This aligns with the visual analysis, which hinted at a possible relationship without clear, consistent alignment. Such a metric may gain predictive power when combined with other variables or when modeled using optimal lags, to be explored in the multivariate analysis phase.

The univariate regression between the interest rate and Bitcoin’s normalized closing price reveals a positive and statistically significant relationship. The coefficient is 0.1263 with a p-value well below 0.001.

However, this result contradicts the initial hypothesis suggesting that rising interest rates should negatively affect Bitcoin by reducing liquidity and risk appetite. With an R² of just 5.6%, the explanatory power remains modest.

The sign of the relationship may evolve when lag structures are introduced, as the effects of monetary policy tend to unfold over time. This will be explored further in the multivariate phase of the analysis.

The univariate regression between the CSI 300 index and Bitcoin (normalized close) shows a very weak but statistically significant negative relationship, with a coefficient of -0.0625 and a p-value of 0.017.

This suggests that drops in the CSI 300 could coincide with minor upward moves in Bitcoin. However, the explanatory power of the model remains extremely low (R² = 0.6%), and the dataset for this variable starts only in 2021, limiting the reliability of the analysis.

Further investigation with lag structures and a multivariate model will be required to assess the true predictive power of this variable. At this stage, no robust conclusion can be drawn.

Cette régression simple examine le lien entre la difficulté du minage de Bitcoin (difficulty) et le prix du Bitcoin (Close_norm). Le modèle révèle une corrélation positive significative, avec un coefficient de 0.5316 et un R² de 0.489, indiquant que près de 49% de la variance du prix du Bitcoin est expliquée par la difficulté.

Ce résultat soutient l’hypothèse selon laquelle une augmentation de la difficulté — reflet d’une intensification de l’activité sur le réseau et d’un engagement accru des mineurs — tend à accompagner ou précéder des hausses du prix du BTC.

Cette relation relativement forte, en comparaison des autres variables étudiées, suggère que la difficulty pourrait constituer un bon candidat pour être intégrée à un modèle prédictif. Une analyse complémentaire avec des lags pourrait affiner encore cette lecture.

The regression between the M2 money supply and Bitcoin's normalized price reveals a moderately strong and statistically significant relationship. With an R² of 23.8% and a positive coefficient (~0.53), the results suggest that Bitcoin is positively correlated with increases in M2.

This supports the idea that Bitcoin may benefit from expansionary monetary policies, which inject more liquidity into the system. However, M2 data was partially extrapolated for late periods, so this variable should be treated with caution and re-evaluated with lag structures during multivariate modeling.

Compared to interest rates (which showed a weaker and contradictory relationship), M2 appears to be a more structurally relevant predictor of Bitcoin price movements, possibly capturing broader liquidity effects.

The simple regression between Bitcoin transaction volume and Close_norm reveals a statistically significant and moderately strong relationship, with an R² of 16.2%.

The positive coefficient suggests that higher trading activity is generally associated with higher Bitcoin prices, potentially reflecting investor interest or speculative momentum.

However, volume may also respond after price movements rather than anticipate them. Further analysis with lag structures will be necessary to clarify its predictive value in multivariate models.

The univariate regression between Bitcoin's volatility and its normalized price shows no statistically significant relationship, with an R² near zero and a non-significant p-value (≈ 0.29). The slight negative coefficient is not meaningful in this context.

This result contradicts our initial hypothesis, which expected a clear link between volatility spikes and price movements. It suggests that the relationship may be nonlinear or involve lagged effects not captured in this simple regression.

Further exploration using lag structures or alternative modeling techniques will be necessary to assess the true role of volatility in Bitcoin pricing.

The univariate regression between S&P500 trading volume and Bitcoin's normalized price shows a statistically significant but weak negative relationship, with an R² of 3.8%.

The negative coefficient suggests a potential capital reallocation dynamic: during periods of increased activity on traditional markets, interest in Bitcoin might diminish. However, this remains a tentative interpretation given the limited explanatory power of the variable.

This result warrants further exploration with optimal lag testing to determine if the relationship persists over time or under specific market conditions.

The regression between the number of global conflicts (with more than 10 deaths/day) and Bitcoin's normalized price shows a statistically significant and relatively strong relationship, with R² = 21.9%. The positive coefficient suggests that periods with more geopolitical instability may coincide with upward movements in Bitcoin's price, possibly reflecting investor demand for alternative assets.

The total number of fatalities also shows a significant, though weaker, relationship (R² = 10.9%). However, in the combined model, only the conflict count remains statistically significant, confirming it as the more relevant explanatory variable.

These insights will need to be re-evaluated with lagged versions of the variables during the multivariate modeling phase, especially considering that conflict data was only available for part of the study period.

The univariate regression between Aggregate Financing on the Real Economy in China and Bitcoin normalized price shows a statistically significant but weak inverse relationship, with an R² of 3%. This suggests that increases in aggregate financing are slightly associated with decreases in Bitcoin price.

However, caution is needed in interpretation. The variable is available only at a monthly frequency and has been applied to daily data, potentially reducing precision. Additionally, China’s complex regulatory stance toward Bitcoin might distort the economic link over time.

This variable should therefore be flagged for closer analysis during the multivariate phase, especially after recalculating optimal lags on unnormalized data.

The optimal lag analysis reveals that some variables exert an immediate influence on Bitcoin's price. Variables like CLOSES&P500, difficulty, and Volume all reach their highest explanatory power with a lag of 0 days, suggesting a near-instantaneous market reaction to these indicators.

Other factors, including BTC Dominance, Gold Price, and Fear & Greed Index, show better predictive power with short to mid-term lags (30 to 60 days), which likely reflects delayed market adaptation or indirect influence mechanisms. Notably, macroeconomic and structural indicators like Interest rate, CSI300, or Aggregate financing (China) tend to require longer lags (90 days) to reach their full effect.

Overall, the distribution of optimal lags appears economically coherent: technical or direct financial indicators react quickly, while sentiment or macro-financial variables exhibit delayed effects. This lag structure will guide us in constructing a more robust multivariate forecasting model.

The multivariate regression V7 explores the influence of macroeconomic, market and sentiment variables on the price of Bitcoin, without using spread variables. This specification confirms several key univariate findings, while also revealing the specific contribution of each factor when controlling for the others.

The S&P500 has the strongest effect on Bitcoin, with a 1-point increase in the index associated with a $19.4 rise in BTC price. Other variables such as gold, interest rates, fear/greed index and monetary aggregates (M2) also show strong and significant effects. The dominance of BTC, while economically meaningful, remains only marginally significant in this specification.

Overall, this model reaches an adjusted R² of 93.4%, suggesting that the combined set of variables explains most of the variance in Bitcoin prices, even without spreads. This reinforces the relevance of a diversified and lag-adjusted explanatory framework for cryptoasset modeling.

This regression confirms that Bitcoin is highly reactive to macro-financial dynamics, especially equity markets, interest rates, and liquidity metrics. It also reveals the importance of sentiment (Fear/Greed, Google Search) and crypto-specific fundamentals (dominance, difficulty). While this version omits spreads, it already captures over 93% of Bitcoin's price variance, making it a solid foundation before testing more advanced models.

The residuals exhibit an approximately normal distribution, particularly in the central region which is enough for inference under a HAC-robust regression framework. Some deviations appear in the tails, a common occurrence in financial time series due to volatility clustering and extreme movements.

These tail discrepancies are not alarming for the current analysis, but they should be acknowledged when performing inference procedures that rely strictly on normality assumptions.

This version of the multivariate model introduces refined lags and includes spread variables to better capture the relative dynamics between Bitcoin and key market indicators. The inclusion of spreads helps isolate the "excess performance" of BTC compared to macroeconomic drivers, offering a more robust framework for price explanation.

Compared to model v7, several lags have been adjusted to improve significance in a multivariate context, and non-significant variables were removed. Additionally, spread features were added to measure the deviation between BTC and reference assets (e.g. gold, sentiment, volatility), which improves both interpretability and fit.

While this specification achieves a remarkable R² of 99%, suggesting excellent explanatory power, this performance should be interpreted with caution due to potential mechanical effects from spreads being derived from the target. Therefore, this model should be used for interpretation and feature selection, but not for pure prediction tasks without careful validation.

Below is a summary of the most impactful changes introduced in model v11. We focus on newly added spread variables and those whose coefficients changed significantly compared to v7.

Model v11 integrates additional features (spreads and lag adjustments) that improve interpretability and performance. It confirms the importance of relative positioning of Bitcoin versus traditional assets and sentiment metrics. However, spreads derived from the dependent variable may inflate explanatory power if not used carefully.

Overall, v11 offers a refined and theoretically coherent model structure. Still, it should be complemented with predictive performance tests and out-of-sample validation to confirm its generalizability, especially in volatile market regimes.

Autocorrelation:
The Durbin-Watson test returns a very low statistic (0.400), indicating strong positive autocorrelation in the residuals. While the predicted values follow the actual BTC prices closely, this result suggests persistent time-dependent structures not fully captured by the explanatory variables.

Heteroskedasticity:
The Breusch-Pagan test confirms the presence of significant heteroskedasticity (p < 0.001). This reinforces the importance of using HAC robust standard errors, which were already applied to this model to mitigate the potential bias in inference.

Multicollinearity:
VIF values are elevated for several predictors, especially for Spread_NVT_Ratio_Close, difficulty, and Fear_Greed_Index. These results highlight redundancy between features, which could affect the precision and reliability of individual coefficients. While not invalidating the model, it emphasizes the need for careful interpretation.

Visual Diagnostics:
The predicted values from model v11 follow the actual Bitcoin closing price very closely, with minimal divergence throughout the observed period. This suggests a strong in-sample fit and improved responsiveness to price fluctuations compared to model v7. The residuals are notably tighter and exhibit fewer clustered deviations, especially during periods of high volatility. Compared to v7, where residuals showed more pronounced autocorrelation and large spikes during high-volatility phases, model v11 demonstrates better stability and smoother adjustment. While some residual spikes remain (e.g., around index 600 and 1050), they are of lower magnitude and less frequent. This confirms the added value of spread variables and refined lag structures in capturing short-term dislocations.

The residual normality is generally respected in model v11. The histogram displays a bell-shaped and centered distribution, with density well concentrated around zero. The Q-Q plot confirms this trend: most points align closely with the theoretical line, indicating a good Gaussian approximation, especially in the central range where most observations are located.

As observed in model v7, slight deviations appear at the distribution's tails, suggesting mild leptokurtosis (i.e., more extreme values than under normality). This implies that a few outliers are less well captured. However, these deviations remain acceptable within the framework of a model estimated using HAC covariance, which specifically adjusts for such non-standard residual behavior.

Compared to v7, the residual distribution in v11 appears slightly more regular and symmetric overall, confirming a more stable fit and improved model robustness.

Both multivariate regressions present strong explanatory power. Model v7 achieves an adjusted R² of 93.4% using macro-financial and sentiment indicators, without any spread-based features. In contrast, model v11 reaches an impressive 99.0% adjusted R² by integrating spread variables and more precisely tuned lags.

While v11 outperforms v7 in terms of raw fit, part of this performance could be mechanical, as the spreads are derived from the target variable (Close). This raises concerns regarding overfitting and emphasizes the importance of robustness checks and predictive validation.

To prepare for the next phase ( predictive modeling using Ridge regression and Random Forest ) we select a structurally sound, flexible, and interpretable specification.

Model v11 is chosen as the reference base due to:

1. Its ability to capture relative dynamics (via spreads) between Bitcoin and explanatory factors.
2. Improved fit and residual regularity.
3. Better compatibility with trend-based variables and lagged interactions.

However, to avoid potential overfitting:

1. Spread variables will be tested carefully in predictive scenarios.
2. Strict train/test segmentation will be used for validation.

This approach ensures we benefit from the explanatory richness of v11 without compromising predictive reliability.

After building a robust analytical foundation through classical econometric regressions (OLS) and careful variable selection, this section marks a turning point in the project: the experimentation of supervised machine learning models to predict Bitcoin price dynamics.

This is my first in-depth implementation of predictive algorithms in a real-world financial context, aiming to test their relevance for anticipating BTC movements. Rather than focusing solely on final outcomes, I made the choice to document the entire thought process (including inconclusive attempts and progressive adjustments) as part of my learning journey.

This initial Ridge model aimed to explain the current price of Bitcoin (Close_t) using contemporary macroeconomic and crypto-financial indicators (including spread variables constructed from the same target). While the model achieved an extremely high R² (>98%), it suffers from serious methodological flaws:

1. High risk of data leakage: Many variables (e.g., spreads) were derived directly from the target variable.
2. No temporal causality: All variables are contemporaneous (T), so this model cannot be used for real predictive tasks.
3. Over-optimistic performance: Even with a valid train/test split, the setup inflates metrics due to construction bias.

Despite these flaws, this step played a key role in shaping the project's methodology. It helped identify core variables and confirmed the necessity of lagged, forward-looking designs for proper ML forecasting.

A revised version (df_ridge_v5) was also tested with fewer variables, removing some spreads and multicollinear features. Despite a slight drop in performance, the same core limitations persisted.

This attempt was useful as a methodological checkpoint but does not provide any realistic predictive power. It helped clarify the importance of variable construction and justified our shift toward models predicting the change in BTC price (e.g., ΔClose_t+1) using only lagged features.

As a first predictive step, we attempted to model the variation in Bitcoin price one day ahead (ΔClose_t+1) using Ridge Regression. This marks a shift from explanatory modeling to true forecasting, based only on features available at time t.

We created five distinct datasets (A to E), each progressively enriched with macroeconomic lags, sentiment indicators, spread-based variables, and technical signals (e.g., moving averages, MACD, RSI). All spreads were computed at time t to avoid any data leakage.

Across all datasets, Ridge regression failed to produce a meaningful predictive model for ΔClose_t+1. All R² scores are negative, indicating the model performs worse than a simple mean predictor. This confirms the inherent challenge of predicting raw price changes in Bitcoin, due to its high volatility and low signal-to-noise ratio.

Despite this, the process provided key learnings regarding feature interactions and model sensitivity. It also reinforces the importance of exploring non-linear methods and alternative targets such as directional prediction.

The Random Forest model was tested as a more flexible alternative to Ridge regression for predicting the future variation of Bitcoin price (ΔClose_t+1). Due to the asset’s extreme volatility, this task represents a classic challenge in financial data science. The goal here is not to predict exact values, but to build a robust model capable of adapting to the noisy, nonlinear dynamics of the crypto market.

Several dataset versions were constructed to test the incremental addition of features: starting with all contemporaneous variables, then transitioning to lagged versions with or without trend indicators.

Below are the results of each Random Forest version, including performance metrics and prediction graphs.

Despite Bitcoin’s high volatility, Random Forest models proved generally more effective than Ridge regressions across all tested scenarios. Their ability to handle nonlinear relationships and incorporate a large number of variables without excessive multicollinearity makes them a solid option for financial forecasting tasks.

To evaluate their robustness, we developed four successive dataset versions, ranging from a configuration including all t or (t0) features (V1) to stricter lagged setups enriched with trend indicators, both basic and advanced (V4 and V5). The spreads used, although derived from the Close variable, were constructed using values available at time T. They are therefore suitable for forecasting ΔClose_t+1 without introducing any information leakage.

The performance results show that V3 offers the best methodological compromise. It achieves:

1. The lowest RMSE among rigorous versions,
2. The R² closest to zero (indicating lower residual variance),
3. And a more stable architecture under extreme market movements.

In summary, V3 stands out as the most robust and interpretable configuration for real-world or out-of-sample applications. Yet, even with this setup, the predictive performance remains limited: all models show negative R² values, meaning they fail to outperform a naive baseline. This underlines the inherent difficulty of predicting short-term price variations for a highly volatile asset like Bitcoin.

For this reason, the next part of our analysis will explore alternative prediction targets (including directional classification of price movement (bullish vs. bearish) and horizon extensions (e.g., ΔClose_t+3 or ΔClose_t+7)) to better align with real-world strategy design.

Given the challenges observed with direct regression on Bitcoin price variations (ΔClose_t+1), a more pragmatic approach consists in predicting only the direction of the movement: will the price go up or down the next day?

This binary classification task (bullish vs. bearish) better reflects real-world trading decisions and is more tolerant to noise. Several model versions were tested using a Random Forest classifier, with or without optimal lag transformation and class balancing via SMOTE.

Among the four tested models, Version 3 (Lagged) stands out with the best recall on bullish days (0.67) and the highest ROC AUC (0.5381). This confirms the added value of individual lag optimization in capturing early signals in macro and crypto indicators.

Conversely, SMOTE-based balancing methods, although sometimes helpful in highly imbalanced settings, appeared inefficient or even detrimental in this context. This may be due to the low class imbalance (~52/48) and the distortion SMOTE introduces in temporal data.

Overall, these findings suggest that the asymmetric dynamics of Bitcoin (e.g., sharp bullish recoveries) can be better detected using lags rather than rebalancing strategies.

In conclusion, predicting short-term direction at t+1 remains difficult, but some promising signals emerge from a lag-based approach. The signal, however, remains weak and noisy – especially for next-day movement – suggesting the need to explore:

1. Longer prediction horizons such as t+3 or t+7, where short-term noise may smooth out,
2. Other model families such as boosting or neural networks, better suited for capturing nonlinear patterns.

After observing limited predictive performance at horizon T+1, we extended our directional classification approach to a weekly timeframe: T+7. The objective was to determine whether macro-financial signals, volatility indicators, and trend measures gain relevance over a slightly longer period.

This experiment also tests whether lagged features—individually optimized per variable—help reveal delayed causal relationships that are difficult to detect at shorter horizons.

Results show that the use of lagged variables significantly improves model performance compared to the raw (T) version. The lagged model achieves a stable prediction quality, with strong recall on upward trends and no need for SMOTE-based resampling.

The presence of a few lag-0 variables (e.g., BTC_Dominance_lag0, difficulty_lag0) does not appear to compromise generalization, as they are not among the most important features. Temporal dynamics are well distributed across lags and variable types.

The top-ranked features reflect the relevance of trend indicators (SMA_20_lag40), macro factors (M2usa_lag22, Interest_rate_lag35), equity markets (CLOSES&P500_lag9), and crypto-specific indicators such as BTC_Dominance_lag0 and Google_srch_lag24.

Overall, the lagged model at T+7 shows meaningful predictive value, with accuracy approaching 60% and a ROC AUC near 0.59. These results suggest that incorporating temporal dynamics improves the model’s robustness, while maintaining interpretability.

This confirms the hypothesis introduced in the previous section: lag selection outperforms SMOTE rebalancing when directional signal quality is sufficient.

In the next step, we will use a XGBoost classifier model to see if it improves performance.

After testing logistic regression and Random Forest to predict the future direction of Bitcoin (target_direction_t7), we explored a third model: XGBoost. Known for its robustness in noisy environments like financial markets, XGBoost offers gradient boosting with regularization.

The goal is to determine whether XGBoost can outperform previous models when trained on lag-optimized variables, with advanced hyperparameter tuning via GridSearchCV.

The XGBoost model confirms the added value of optimal lag structures. The most important variables include macroeconomic (e.g., M2, VIX, GBTC) and technical indicators (SMA, RSI), all derived from historical values.

This demonstrates that even in highly volatile environments like Bitcoin, it is possible to extract meaningful predictive signals over a 7-day horizon when the feature engineering is well-structured.

The high recall and F1-score for the bullish class suggest the model is capable of detecting upward trends with reasonable reliability. While XGBoost shows clear improvements over Random Forest in this setting, it is also computationally more intensive.

Although the optimized XGBoost model delivers overall better performance than Random Forest, the results must be interpreted with caution. A closer look at the confusion matrix reveals a clear imbalance in predictive power across classes.

The model performs well in detecting bullish signals (class 1), with a high recall of 84%. However, it significantly underperforms in identifying bearish signals (class 0), reaching only 31% recall. This limitation is important, especially when the strategy aims to anticipate corrections or downturns.

This bias is not unexpected. The Bitcoin market is structurally bullish over long timeframes, which leads to a statistical overrepresentation of class 1 in the training data. As a result, the model naturally tends to favor bullish classifications, which may explain its weakness on bearish periods.

To address this asymmetry and improve real-world usability, several options can be considered:

1. Implement a probabilistic decision threshold (e.g., enter a bullish position only if p(bullish) > 0.70).
2. Combine ML classification models & manual hedge variables (for bearish movements).
3. Build a dedicated bearish model that specializes in anticipating downside risks.

In summary, XGBoost is a strong and flexible model, but its current implementation remains biased toward bullish predictions. This makes it a suitable candidate for long-biased strategies but a limited tool for short-selling or bearish detection unless reinforced with further calibration.

After validating the predictive relevance of the XGBoost model on the T+7 horizon, we aimed to move beyond pure prediction and toward a logic of real investment strategy allocation.

In other words, the objective was no longer simply to forecast the future direction of Bitcoin's price, but to apply these signals in a concrete strategic framework:

• When to enter a long position (CALL)?
• When to stay neutral (hedge)?
• When to attempt a short position?

This gave rise to the next phase of the project: the design of hybrid strategies, combining multiple models (XGBoost, Logistic Regression, Random Forest) to distinguish between bullish, neutral, and bearish phases.

These strategies rely primarily on the predicted probabilities of upward or downward movement rather than binary outputs, allowing for greater flexibility and responsiveness in decision-making. The models does not act as an oracle, it gives investments recommandations based on probabilies of succes of the underlying model to predict bullish and bearish movements. We will also build hybrid strategies based on both ML classification models and macroeconomic indicators (S&P500, Interest rate or BTC_dominance) that we will parameter manually.

Before fully focusing on the weekly horizon (T+7), we experimented with shorter-term signals using T+1 (next-day variation) and TAVG3 (average of 3-day price changes). These preliminary strategies aimed to test whether early bullish signals could be exploited profitably in highly volatile markets like Bitcoin.

The approach was straightforward: use a classification model to estimate the probability of a bullish move, and enter a CALL position only if this probability exceeded a given threshold. This probabilistic framework ensures fewer, more selective decisions, rather than a continuous exposure to market fluctuations.

Despite a promising accuracy of 58.16% on the days the model took action, the strategy performed poorly compared to a passive Buy & Hold benchmark:

• Model Strategy: +4 813.87 USD

• Buy & Hold BTC: +45 003.76 USD

The model rarely triggered trades, and its conservative stance led to insufficient exposure during bullish periods.

The 3-day average horizon reduced some of the daily noise and led to improved (but still limited) performance:

• Model Strategy: +11 377.68 USD

• Buy & Hold BTC: +89 375.09 USD

The strategy remained highly selective, issuing few signals, which limited its cumulative return despite correct directional calls.

In order to evaluate whether other models besides XGBoost could provide usable trading signals, we also tested a Random Forest-based strategy using the TAVG3 target (3-day average of ΔClose).

The strategy follows the same logic as before: take a CALL position only when the predicted probability of a bullish movement exceeds a certain threshold. In this case, a relatively low threshold of 0.38 was selected, reflecting the model’s modest average confidence.

While results are better than those obtained with Logistic Regression on the same target, the Random Forest model remains insufficiently selective. The low threshold suggests it picks up on some relevant signals, but uncertainty remains too high to support a truly robust long-term trading strategy (it doesnt take any position with higher thresholds).

To further validate our strategic focus on the T+7 horizon, we also tested an XGBoost classifier on the TAVG3 target (3-day average return). The model was trained using the same pipeline and hyperparameter tuning process as for T+7, with strict temporal separation and no data leakage.

Despite identical training conditions, the performance on TAVG3 proved significantly weaker, particularly in detecting bullish phases — which are critical to activating CALL positions.

These results reinforced our decision to discard TAVG3 as a core predictive target and focus entirely on t+7. The t+7 model offers higher predictive stability, better discrimination between bullish and bearish phases, and a stronger signal-to-noise ratio.

While further testing on T+1 and TAVG3 could have been pursued using alternative models or tuning, we made a conscious decision to concentrate on the most promising setup: XGBoost on the t+7 directionnal target. It consistently outperformed all other models and targets in terms of accuracy, recall, and real-world strategy potential.

This strategic focus allowed us to build hybrid allocation frameworks based on robust, data-driven signals, rather than diluting efforts across weaker predictive horizons.

In this section, we lay the groundwork for building a hybrid strategy that combines probabilistic signals from Machine Learning models with manually defined macro and technical indicators. These manually defined signals help reinforce or temper the baseline decisions made by the XGBoost model on the T+7 horizon.

Among these, RSI is the most frequently used filter to deactivate or reverse a position. Combined with a rising interest rate signal, it can directly lead to a SHORT position, especially when multiple bearish signals overlap.

The following visualizations illustrate the key macro and technical indicators manually used in our hybrid strategy. Each chart displays the thresholds and activation zones for bullish (CALL) or bearish (HEDGE/SHORT) signals.

As part of our hybrid strategy framework combining Machine Learning with handcrafted macro filters, we tested two versions of the final allocation logic. While both strategies rely on probabilistic signals from the XGBoost model trained on T+7, they differ in the manual signals added.

Version V3 is a simpler implementation, focusing only on XGBoost, BTC Dominance Spread, GBTC Boost, and SP500 Spread overrides. Version V4 builds on this by incorporating two additional mechanisms:

1. Interest Rate Hedge: if macro tightening is detected, the model hedges positions for 60 days.
2. RSI Short: if RSI falls below 30 for 3 days, a 15-day short is triggered (only if no long position is active).

Despite their structural differences, both strategies end up deploying the same number of bullish trades. However, the presence of the RSI-based short in V4 slightly improves the Sharpe ratio without increasing drawdown. The additional filters offer marginal yet meaningful improvements in terms of selectivity and robustness.

The fact that both V3 and V4 yield strong cumulative returns highlights the robustness of the hybrid logic. These results will serve as reference points to evaluate future implementations based on ensemble models (e.g., stacking).

The use of manually tuned macro and technical filters, while effective in improving performance, introduces significant risks of overfitting and forward-looking bias. Several thresholds were defined or adjusted after observing test results, meaning the strategy leverages information that would not be available in a real-world setting. This compromises the objectivity and reproducibility of the approach.

Moreover, the role of the XGBoost model is increasingly diminished as manual rules dominate the decision-making process. In practice, the strategy becomes fully manual, with the ML model acting more as a background reference than a core engine. This raises questions about generalizability and the true added value of Machine Learning in the final implementation.

Both hybrid strategies performed well, especially in capturing bullish trends at the T+7 horizon. However, their manual design remains fragile in terms of scalability. The ultimate goal is to replicate these results using automated ensemble frameworks, such as a stacking approach:

1. XGBoost → Detect bullish phases (CALL)
2. Random Forest or Logistic Regression → Detect bearish setups (SHORT / HEDGE)

This would ensure model robustness while eliminating overfitting risks linked to handcrafted rules.

This final section closes our Bitcoin prediction study with the most advanced model: a fully probabilistic strategy combining XGBoost for bullish signals and two independent bearish models: Random Forest and Logistic Regression. The goal is to recreate a multi-signal bearish logic (short or hedge), but without manual rules — only through ML models.

Given the strong bullish trend of Bitcoin in 2024, activating bearish signals without hurting global performance is challenging. This setup aims to protect against upward-biased overfitting while maintaining coherent signal-driven exposure.

Bearish signals are activated based on manually fixed thresholds, but chosen after analyzing predicted probabilities on the test set (making this a post-hoc calibration). The thresholds are:

1. XGboost: 0.55
2. Random Forest: 0.5457 (95th percentile)
3. Logistic Regression: 0.44

This introduces a bias, as the thresholds are tuned on the same data used for performance evaluation.

1. V9.2 achieves the highest return and Sharpe ratio of the entire study.
2. Post-hoc threshold calibration introduces a validation bias.
3. Short signals now override CALLs — no more hedging in V9.2, but overlapping positions allowed.
4. ML stacking handles bearish signals purely via probabilities, eliminating manual logic.

This version marks the end of our model testing phase. We’ve transitioned from manual rules to a fully automated ML-based framework. The final model (V9.2) combines predictive efficiency with operational simplicity.

Short signals no longer block CALLs, allowing for a more flexible structure that behaves like an aggressive directional hedge. In a bullish market, this is both rational and practical.