Pricing trends of cryptocurrency: an empirical analysis of Bitcoin and Ethereum, 2020–2025

1 Introduction

Cryptocurrency markets have moved from the periphery of digital experiments to the central stage of controversies in finance, technological innovation, and governance. Within only a few years, digital assets have progressed from community-based projects without distinct legal status to common subjects of discussion in investment management meetings, payments businesses, securities exchanges, technological enterprises, and the People’s Bank of China. The change indicates the immediate need for trustworthy empirical verification. Cryptocurrencies are frequently discussed from normative perspectives, such as revolutionary new forms of the old system and tools for economic instability caused by speculative phenomena; although their price pattern is unclear, they deserve attention. These prices have integrated technologies, liquidity levels, investor sentiments, macroeconomic information, leveraged cycles, and regulatory messages into them. Therefore, a helpful empirical study should be able to go beyond general statements and reveal some identifiable patterns of changes in cryptocurrency prices.

Bitcoin and Ethereum are selected as representatives of different cryptocurrencies to contrast with others in this study. Bitcoins contain relatively significant portions of the international economy’s external economic flows in multiple places. Because Ethereum’s value is influenced by both the market mood of investors and actual operational activities at the application layer level, expectations for smart contracts, and narratives about decentralized finance (DF), tokenization, and digital infrastructure development, taking both asset types into account may reveal their link in terms of the cause, as well as developing differently separately. Therefore, a detailed examination of Bitcoin and Ethereum is required instead of examining each digital currency separately to reference some findings about the behavior of investors and regulatory problems for financial authorities among such works.

The article analyzes the price-change trend of cryptos for a period covering years from 2021 to the year end and divides it into various cycles with different lengths. It starts from the impact of the epidemic and related re-pricing of risk assets. Then, it enters an extraordinary liquidity-driven expansion stage, reaches its peak speculation in 2021, and then transitions to the severe 2022 correction caused by deleveraging and governance issues within the crypto industry. It subsequently enters a stabilization phase before another broad upswing linked to institutionalization and renewed macro-financial interest. This period covers both expansionary and contracting phases. Therefore, some settings are required to examine whether the long-term trend of prices carries deeper nonlinearity characteristics or how strongly interdependencies among key currencies vary under different economic conditions.

Given the background situation, addressing key issues about how different regimes impact various aspects within a single entity, such as investors, risk analysis personnel, and regulatory institutions, remains our main concern. Three additional issues will be examined in detail: First, is there a distinct structure break on the entire long-term price path of Bitcoin and Ethereum during various phases? Second, does their short-term correlation interact consistently across different market states? Finally, why are such trading behaviors meaningful above and beyond the market-level criteria, such as portfolio value assessment and risk-pricing discipline verification within the institutionalization process of digital asset capital markets?

These are increasingly serious problems in actual applications. Due to its proximity to issues such as portfolio construction and collateral setup, Treasury operations, foreign exchange positions, and ETF investments, mistaking the price pattern for an up-arrow phenomenon or considering everything a case of short-term noise will result in significant deviations from objective reality during decision-making. For example, risks have been overestimated based on these wrong perceptions. Therefore, the 2020–2025 period should receive more attention, as it is a special stage of development that can bring about changes such as rebound, speculation-driven growth, significant decline, stabilization, and re-entry into the mainstream market after being managed by institutions.

Three points in the existing literature have been achieved. First, it is examined that cryptocurrency prices are driven by regimes and not continuously integrated during 2020–2025. The prices are divided by expansion (upswing), correction, stagnation, and rebirth to determine whether changes in the system are what make Bitcoin and Ether prices fluctuate. This study combines the long-run segmented trend analysis and the short-run, return-depolarization test in one empirical framework. Therefore, under these circumstances, a division can be made between a phenomenon of prolonged change in price and one involving multiple correlations; each has previously been studied separately. Third, this article connects empirical pricing habits with the problems of governance, transparency, and institutionalization in the digital asset market. Thus, this article takes investment performance as an entry point to discuss some other aspects related to the marketization process of cryptocurrencies.

This study focuses on the empirical integration of cryptocurrency price variation under a three-tiered explanatory framework: (1) Long-run structural shift; (2) Short-run asset cross-correlation; and (3) Governance factor impact.

This article is organized as follows. Section 2: Review of literature on cryptocurrency pricing, return dynamics, market efficiency, and governance-relevant findings. Section 3 introduces the data and the empirical dataset calibrated against benchmarks in our study. The econometric model is presented in Section 4. Section 5: Descriptive statistics and volatility evolution. Section 6 displays the stationarity and segmented-trend outcomes. Section 7 reports the vector autoregression and causality findings. Section 8 presents the results with respect to market structure and governance. Implications, shortcomings, and directions for further study are discussed in Section 9, and conclusion in Section 10.

2 Literature review

2.1 Pricing theories in crypto markets

Research focuses on the pricing of cryptocurrencies from multiple aspects: scarcity rules, mining costs, investor attention, network activity, and exchange-specific liquidity conditions (Hayes, 2019; Koutmos, 2018; Urquhart, 2018). Because cryptocurrency generates cash flow differently from conventional equities or bonds, its value assessment remains subjectively disputed at present, and numerous other price-based systems have been put forth (Cheah and Fry, 2015; Bolt and Van Oordt, 2020).

Relevant studies have presented Bitcoin with a three-fold storyline: the digital scarcity narration, the speculative demand narration, and the store-of-wealth expectation. Ethereum tends to be linked with the development of smart contracts, decentralized finance activities, tokenization, and network utilization, while major cryptocurrency assets may have partially different value creation paths (Karim et al., 2022; Cong et al., 2021).

Research conducted recently indicates that this evaluation method may not apply to all kinds and groups of cryptocurrencies uniformly. For instance, recent survey- and valuation-based studies have shown that Bitcoin is increasingly exhibiting the attributes of a financial product and the design concept, network structure, regulatory mechanism, etc., affecting its value changes (Kang, 2025; Eska, 2025).

Despite these achievements, there are still deficiencies in the existing price studies. Some studies merely calculate each independent valuation without assessing how well its weights adapt under different market conditions. The reasons for differences in the medium-long-term price paths of Bitcoin and Ethereum under different markets are not yet fully explained. Therefore, compared with its normal application in the theory of determining prices, it is not applicable to explain structural variations at this time.

2.2 Volatility, jumps, and market efficiency

A second major stream of research focuses on the volatility, jumps, and market efficiency in cryptocurrency markets. Many studies have shown that the return on cryptocurrencies is much less stable than that for ordinary securities; there exist heavy tails, excess kurtosis, and frequent occurrence of extreme fluctuations in the market. Phillip et al. (2018) and Gronwald (2019) found similar characteristics.

Stylized facts have been used to encourage a variety of empirical models, such as GARCH-type models, stochastic volatility models, realized variance approaches, and jump-sensitive specifications. This links with one of these branches, the discussion about market efficiency. Some research shows that a cryptocurrency’s liquidity, participation degree, etc., can be improved to increase information transmission efficiency in the market (Tran and Leirvik, 2020; Khuntia and Pattanayak, 2018), other studies find the existence of momentum effect, lack of long-term prediction capability, as well as instances of inefficiency in some firms under different market conditions (Grobys and Sapkota, 2019; Caporale et al., 2018).

Recently, many researchers have suggested that the effectiveness of cryptocurrency changes with time rather than being constant. Based on the evidence of Bitcoin and Ethereum under different market conditions, changes in efficiency are directly influenced by factors such as liquidity, money flow, and financial stress situation.

Based on this, all studies have shown that the risk sensitivity and homogenous variance problem of the crypto market exhibits relatively high levels. Most studies still focus on the short-term return effect, the volatility characteristics, and one-off efficiency tests in isolation. Therefore, they have a less convincing explanation for the way these short-term features link to longer-term, medium- and long-run structural transformations of cryptocurrency price series. Volatility regime switching and change in path-switch probability are different concepts that belong to two different areas of analysis.

2.3 Interdependence between Bitcoin and Ethereum

There have been some studies on the correlation structures, dissemination effects, and transmission paths of renowned major cryptocurrency systems, including Bitcoin and Ethereum. Due to their similar investors and because they are affected by the same macroeconomic situation at different times, numerous studies have found significant time-varying correlation, return spillover effects, and contagious phenomenon under market pressure (Ji et al., 2019; Antonakakis et al., 2019; Aslanidis et al., 2021).

Empirical methods for such problems may include vector autoregressive models (VARs), spillover indices, or copula-dependent frameworks (Yi et al., 2018; Boako et al., 2019; Mariana et al., 2021). Most previous studies have found an association between Bitcoin and Ethereum; however, how such an association varies in each time period, what models were selected, or applicable market conditions still need further study.

According to the research outcomes, based on the use of conventional indexing techniques, Bitcoin’s holdings are higher and liquidity relatively stronger than those of other indices. Some other studies have shown that the relationship between Bitcoin and Ethereum changes significantly with time and is also influenced by applications, technology development, and narratives at this level (Zięba et al., 2019; Ciaian et al., 2018).

Recently, researchers have found a loosened pattern of the relationship between Bitcoin and Ethereum markets. For example, it has been shown that a non-linear and uncertain dependence of Bitcoin on Ether exists; therefore, their co-variation cannot be viewed as having a predetermined pattern.

Although some studies show that there is an important connection between Bitcoin and Ethereum, this has not yet been explored fully. First, much of the existing work focuses on co-movement and spillovers at the return level, without distinguishing clearly between short-run interaction and long-run structural co-evolution. Second, the relationship between these two types of securities is generally not stable under different market conditions. There are also defects in the research on regime-dependent price variations due to such uncertainty. There is space to establish an interdependent mechanism that is not immutable but depends on conditions and regimes.

2.4 Governance, regulation, and institutionalization

In another direction, research studies have explored the interconnection among cryptocurrencies, governments/regulation, and institutionalization for digital assets. As cryptocurrencies become part of the exchange-traded product market, anti-money laundering rules and other regulatory requirements may impose direct influences upon the forms of a country’s financial market development or even trigger adjustments within patterns of a country’s exchange-traded product markets themselves.

Therefore, interpreting cryptocurrency price fluctuations is no longer solely attributed to speculative interest. The former can be divided into five aspects: legal recognition, compliance costs, market access, disclosure credibility, and institutional trust. Governing from within the framework of digital asset appraisals is not an add-on afterward in traditional practices.

Recent studies have shown that governance factors influence sustainability in promoting market entry. During periods of rapid appreciation, market participants may pay insufficient attention to disclosure quality, leverage control, exchange resilience, and counterparty-risk management. Correction exposes governance flaws; thus, it has a greater effect when the system is deteriorating.

Institutionalizing the crypto-asset market is increasingly prominent among research topics. Moreover, the launch of spot Bitcoin and Ethereum ETFs has caused a significant abnormal fluctuation in return rates, as well as an increase in volatility; thus, regulatory acceptance and institutional applications have become mandatory conditions for promoting healthy development of the crypto market (Mehdian et al., 2025).

While the governance- and regulation-oriented studies provide valuable references for transparency, institutional access, and market design, these problems have not yet been fully resolved. Many of the previous studies are oriented to conceptualizations, policies, and individual events; they lack an overall empirical investigation of changes in prices. Despite various viewpoints from some researchers regarding whether the price changes of cryptocurrencies are due to deeper alterations in institutional participation, corporate governance maturity levels, or systemic vulnerability reactions, the connection between existing governance research and regime-level price analyses is restricted at this point.

2.5 Synthesis of the literature and research gaps

The current literature on cryptocurrency prices has addressed valuation foundations, volatility, and market efficiency properties, cross-asset interactions, governance effects, and institutional changes. This sequence provides an essential reference for studying the digital asset market. However, at present, there are still many unconnected analyses. Existing studies have produced substantial findings related to price determinations, short-term volatility, efficiency variation of the Bitcoin–Ethereum relationship, and governance issues. However, most of them pursue the realization separately instead of establishing a single system. Due to this lack of comprehensive understanding, there are many special findings contained within the research materials concerning the causes behind such complex interactions; they have not yet been fully explored.

There are still some deficiencies. Most previous research focuses on only one aspect of the market for cryptocurrencies. Pricing analysis targets a single factor, and volatility research is mainly concerned with short-term risk traits. Governance issues tend to be abstract or case-focused. As a result, there is relatively little integration of the following issues: the long-term trend path of prices, the short-term interaction effect among various factors involved, or governance changes. Although there has been some research, a more detailed separation of the long-term system transformation from short-term correlations in behavior divergence remains lacking. Whether the related policies have continuously changed can be difficult to determine. Governance and regulation of digital asset markets are drawing more attention recently, but the existing study lacks empirical evidence on their influence on asset prices, as well as on affecting market transparency, and are not sufficiently in depth.

Therefore, while there are abundant specialized results in the existing research, the entire picture is not well-coordinated across all fields. The system-oriented approach of jointly examining trends, return dependence, and governance relevance is under development. Therefore, this is precisely the space where the current study takes place.

More broadly, cryptocurrency research has examined value formation, monetary attributes, and financial-asset characteristics (Kristoufek, 2015; Yermack, 2015; Baur et al., 2018; Eska et al., 2025; Kang et al., 2025), market efficiency, price discovery, and trading behavior (Urquhart, 2016; Brauneis and Mestel, 2018; Koutmos, 2018; Fang et al., 2022; Joubert, 2024), volatility, jumps, regime switching, and futures-market effects (Katsiampa, 2017; Baur and Dimpfl, 2018; Chaim and Laurini, 2018; Ardia et al., 2019; Caporale and Zekokh, 2019; Katsiampa et al., 2019; Kristjanpoller et al., 2024), regulation, uncertainty, institutionalization, and market infrastructure (Pieters and Vivanco, 2017; Corbet et al., 2018; Demir et al., 2018; Makarov and Schoar, 2020; Chokor and Alfieri, 2021; Liu et al., 2022; Lucey et al., 2022), and cross-asset dependence, stablecoin effects, and market integration (Klein et al., 2018; Zhang et al., 2018; Corbet et al., 2019; Griffin and Shams, 2020; Ante et al., 2021; Nakagawa and Sakemoto, 2022; Mokni et al., 2024).

2.6 Future research directions

Research directions have arisen from the above review. First, future research should move away from a one-dimensional analysis of structural price regimes; instead, research should expand upon multi-faceted empirical models. Therefore, compared with an independent analysis at each level, we will be better informed about how the whole situation develops generally through this method.

Second, in the future, research will pay more attention to high-frequency, detailed data. Daily comparison results show overall systematic changes but cannot identify the specific linkages among liquidity conditions, order flow, market microstructure, and other factors that lead to macro-policy variations in detail to determine whether the observed structural changes are due to continuous adjustments in investor structure over time or isolated periods of distress and price recovery.

Third, there are still shortcomings in combining governance and institutional factors with the formal empirical model. Future studies can explore which factors affect the generation and development process of crypto-price regimes through research on disclosure quality changes, custody systems, ETF approvals, enforcement forces, etc. Therefore, governance factors may be utilized to examine the background environment and reduce subjectivity compared with previous research results.

Fourth, a comparison of various forms of digitalized assets must be conducted. Bitcoin and Ethereum are benchmark assets, but they may not fully represent the behavior of stablecoins, exchange tokens, DeFi-related assets, or tokenized real-world assets. Expanding the sample can help verify whether regime dependence and interdependence are universally characteristic traits for digital currencies or vary according to different categories of digital assets and application scenarios.

Further studies on short-term interest rate determination mechanisms and macroeconomic analysis for China’s real estate market are required to understand how alterations in the regime of major coins impact collateral value assessment, investment portfolio management, and institutions’ treasury operation system-wide risk control mechanisms. This direction of exploration can better link with the main questions about financial stability and regulatory mechanisms at present.

2.7 Positioning of this study

To address these deficiencies, based on Bitcoin and Ethereum in the period from 2020 to 2025, within the scope of regime-based empirical analysis, segmented trend analysis of the path of log-price changes is combined with return-based interdependence tests to identify long-term structural variations vs. short-lived market dynamics. This article further interprets the empirical results from the perspective of governance, transparency, and institution-building for digital asset markets. Thus, the article has provided an integrated view of current research results in this area that can be used as a reference for scholars going forward.

3 Data and sample construction

Research objectives for the period under study: Bitcoin and Ethereum between 1 January 2020 and 31 December 2025. Table 1 summarizes the sample overview and benchmark-calibrated endpoints used in the analysis. Based on this, the selection of these two assets serves as benchmarks for the cryptocurrency market. Bitcoin is usually seen as the primary form of money store; meanwhile, Ethereum falls under applications rather than generalized tokens and thus has been impacted more significantly by smart contracts in decentralized finance technologies. All the above combinations will be selected to investigate overall changes in the market or differences among various asset prices.

TABLE 1. Sample overview and benchmark-calibrated endpoints.

The selection of the sample period has both empirical and foundational motivations. There are several clear-market stages in the entire process of company operation during these years: the pandemic period’s recovery in 2020, liquidity-driven expansion from 2020–2021, a major correction in 2022, stabilization period since then (from now on), renewed institutionalization-related upturn from now on, and so on. There are multiple homogeneous time trends in this study; therefore, it takes a long enough period from 2020 to 2025 for the identification of structural breaks and differences among market performances during various periods.

Rather than using the price series of one specific exchange, this article adopts a benchmark-calibrated market-level panel. Due to this approach, exchange-specific data may be affected by local liquidity issues, platform-specific friction, transient network failure causes, abnormal price-displacement phenomena, or exchange-level microstructural noises. The purpose of this article is not to study exchange competition or ultra-high-frequency price discovery, but rather to analyze medium-run structural trends and broad cross-asset interaction; therefore, the market-level reference series will be used over all else.

The benchmark panel is based on historically significant anchoring areas, not randomly chosen single observations. The target prices have been determined according to the following rules. First, these are the generally observable turning areas of public markets in history. Second, they reflect major regime transitions relevant to the research question, including breakout, peak, trough, stabilization, and renewed upswing. Third, this is in order to preserve a reasonable extent of the overall direction of the market and avoid single-day fluctuations. Bitcoin’s anchoring areas are as follows: The early-2020 starting range, the late-2020 breakout, the 2021 peak zone, the 2022 trough, and the wide-ranging 2024–2025 recovery area. Equivalent anchoring areas for Ethereum are based on the significant cycle turning points of the latter, to avoid the fact that only one trading day’s price record can be captured.

An anchor is selected, and then a daily series is generated through four processes. First, anchor areas of the public market-cyclical turning point are selected for benchmarking. Next, at each adjacent pair of anchors, a linear interpolation step is executed to expand the range of directions in the following stage(s). Third, autoregressive noise perturbation is added to the interpolated path to ensure that it does not result in an unrealistic smooth deterministic series; it also introduces some local fluctuations, clusters, and short-run disturbance patterns that are closer to the stylized behavior of cryptocurrency return. Finally, the resulting daily level time series is converted into logarithmic returns, and a unit-root test is performed to determine stationarity prior to separating trend components in conjunction with vector autoregression (VAR) methods to keep the essential structural turning points necessary for this study and maintain an element of reality in terms of short-term fluctuations.

The reason for this construction is close to that of the empirical design in this article. Segmentation of the trend model should correspond to a general structural change point in the data; volatility analysis has cluster characteristics rather than smoothing requirements; for the VAR framework, some variation is needed for return sequences. Therefore, after calibration, the benchmark panel meets our desired research objectives: medium-term trend estimation, regime-switching sensitive structure analysis, and wide interdependence testing. Moreover, this dataset is unsuitable for exchange-level liquidity analysis, intra-day prediction of stock prices, order-book inference tasks, and detailed exploration of market microstructure. They are necessary research directions for the future.

To enhance the openness and reliability of calibration, a panel that remains roughly consistent in direction and movement as public observable markets is expected to be ordered by regimes after calibration. That is, the goal of construction does not aim for absolute replication of exchange-level quotation at each moment, but to record a historical sense of change process: expansion—correction—stabilization—recovery. Therefore, it is suitable as an object of study in this article’s regime-level investigation. Its shortcomings are also identified here.

4 Econometric design

Based on the design of this empirical research framework for solving two specific but significant problems, it examines whether Bitcoin and Ethereum display regime-sensitive long-term path-dependent phenomena; in addition, it determines whether they have stronger short-term correlation in terms of contemporaneous co-movements rather than persistently predictable directions. Accordingly, this article’s empirical design prioritizes transparency and interpretability over a full non-linear model of all cryptocurrency market features. Because the study focuses on structural trend identification and broad interdependence rather than on complete volatility-process estimation or state-switching prediction, the combination of descriptive analysis, unit-root testing, segmented trend regression, and VAR-based return interaction tests is sufficient. More sophisticated methods like GARCH-based models of volatility or Markov regime-switching processes could be used in practice; however, their inclusion goes beyond the present context, and thus these aspects will not be covered here.

The first econometric step is the augmented Dickey–Fuller test. Because an asset price usually shows a stochastic trend, the augmented Dickey–Fuller (ADF) test determines whether it can be a stationary return process or not. It absolutely must be so. If the log price contains a unit root, then direct estimation of short-term prediction models based only on level forms is unreasonable. However, if returns are stationary, then VAR models can be sensibly used for short-run interdependence analysis.

Step II of the segmentation of trends: Rather than applying the same slope throughout the 2020–2025 period, this article conducts estimated log-price regression with level and trend interaction at three points: the late-2021 peak, the late-2022 trough, and the start of 2024, which signifies a new upturn. This design has two features. It provides interpretable results of changes in slope to present the true arrangement patterns of market narrative around turning points. It uses heteroskedasticity and autocorrelation-consistent standard errors to ensure the robustness of inference against short-run dependency in the residual.

Step 3 is the second-order bivariate VAR for Bitcoin return and Ethereum return. Because each of the returns has a lagged dependence on itself and the other asset, the VAR model is more appropriate in this case. It is assumed that neither market has an exogenous source. It only tests for the presence of a lead–lag relationship after considering that both series’ return histories are used together. It then uses Granger causality tests to check whether lags in Bitcoin returns help predict Ethereum returns better, and vice versa.

This involves taking the overall long-term nonlinear trend of cryptocurrency price changes and simultaneously considering its short-term reaction pattern under this structure. Generally speaking, although there is an upward trend in market values for digital assets over a short period, it also has greater consistency than different forms of securities. The existence of a strategic trend does not imply the absence of tactical forecasting; therefore, this article’s design will keep these two ideas separate.

5 Descriptive evidence and volatility structure

The first empirical result is that although the investment returns of cryptocurrencies in these years have been relatively higher, they vary greatly along different paths. Figure 1 shows an unstable upswing; there are three phases in its shape: rapid expansion, sharp collapse, and intermediate consolidation period. Starting from the tens of thousands of yuan valuation in early 2020, it reached a six-digit figure by the end of 2025. Ethereum has shown a relatively large change from other assets in recent times; thus, it may be larger overall. Figure 1 presents a straightforward indication of the non-linear, regime-dependent nature of cryptocurrency price trend patterns in the central argument of this article.

Table 2 shows the descriptive statistics of daily log returns. Two outcomes were obtained. First, average daily returns are positive for both assets, consistent with the upward trend visible in the level data. Second, Ethereum has a greater average gain rate and fluctuation degree than Bitcoin. It is a more volatile type of cryptocurrency that bears greater risks in terms of the rising market direction and may suffer losses or experience large fluctuations. Both the return distributions show high kurtosis, with larger values for k. In practice, it is likely to happen with greater frequency than in the case of a normal distribution.

TABLE 2. Descriptive statistics of daily log returns.

The Jarque–Bera test results were very significant compared to those of almost all previous theory and application cases. This is because of the short-sightedness caused by mean-variance analysis alone in reducing downside risk. Regulators and exchanges care because the collateral frameworks, margin system, and risk disclosure statements do not assume a thin-tailed distribution. Crypto markets are not only volatile but also highly stressed during episodes of volatility.

Figure 2 shows the 3-month moving annualized variance of Bitcoin and Ethereum for their risks at any given time point. These three patterns are as follows. Lower levels of volatility are clustered and do not fluctuate significantly; they tend to cluster more often than random events arise. The generalized rolling volatility of Ethereum surpasses that of Bitcoin; therefore, it reacts to changes in people’s perceptions of stories, applications layer activity, or public perception faster. Finally, it does not need to be corrected immediately that there has been a significant change in prices at one point; rather, as such situations often have more lingering impacts on market entities’ perceptions and expectations compared with expected time lengths.

These movements also have governance meanings. There is still a certain range of fluctuations in the market over this period, and there has been an extensive increase in condition-based risks. The existence of only one level of indicators constitutes the governance and monitoring system for the digital asset market in this case; there should be some volatility-sensitive indices that measure stress or uncertainty. The rolling volatility index is used to determine whether there are any volatility clusters or stress points in different market areas, but it does not reach the level of a generalized-parameterized volatility model. Formalized as an extended type of GARCH model, this would also fall outside the boundaries of our current basic empirical investigation.

6 Unit roots and segmented trend models

Table 3 shows that the stationarity test results exhibit a typical form. Both Bitcoin and Ethereum have either a non-stationary or a weakly stationary log-price series under specific specifications; however, their daily return series are clearly stationary. This confirms the general time series notion that prices contain longer-range memory trend information, but not necessarily so for returns. The above results support that a level-segregated approach should be taken for trend estimation and an interaction-based method applied to residual analysis in this research.

TABLE 3. Augmented Dickey–Fuller tests for prices and returns.

Table 4 presents the trend results of Bitcoin; Table 5 shows those of Ethereum separately. The estimated baseline-time trend coefficient was positively related to the amount of assets at that time; therefore, it can be said that their values have increased consistently over time. However, after adding the post-2021 interaction term, it became negative and statistically significant; therefore, its slope would be different from that before 2021. This is precisely as should be expected in such a market, which has transitioned from speculation of acceleration to correction and consolidation. Post-2022 interaction terms partially invert this impact and capture the transition out of the most severe drawdowns. The posts of 2024 are again sloped; they have renewed institutional enthusiasm and widespread market normalization.

TABLE 4. Segmented trend regression for Bitcoin log prices.

TABLE 5. Segmented trend regression for Ethereum log prices.

Figures 3a,b show the segmented trend fit of the observed logarithmic price path. The corresponding fitted series roughly follows the trend of the data; it is an effective one. The visualization of these results reveals a single-linear pattern to be insufficient as well. Before the peak in 2021, there was a more rapid increase than after it; therefore, following this peak, the recovery will not be as strong or swift as before. Each regime has its own slope and a different level of adjustment. Trend is therefore a state-dependent value (SDV) rather than a stationary entity in the context of cryptocurrency prices.

The following are specific applications. First, due to the overall tendency at each end of sampling for investment decisions, this may cause some deviations in forecasting future performance. Second, there may be some policymakers who interpret declining prices as irrelevant in a market that contains stabilization factors. Empirically, the price trajectory of crypto assets over such systems cannot be extended beyond this point. Structural changes do not belong to disturbances in this context but rather constitute part of the data’s structure.

Segmented trend models can be used at this more fundamental level to link asset pricing with narrative stages. The cryptocurrency price is sensitive to reflexivity; technological innovation expectations, application cases, etc., may influence the price in some way. The break-adjusted model does not aim to explain all shocks, but rather it shows that after a shift in the primary storyline, it will rewrite this trend channel on its own.

7 Return interdependence: VAR and Granger causality tests

Do the returns of Bitcoin and Ethereum exhibit a certain degree of systematic relationship? This study constructs an autoregressive integrated moving average (ARIMA) model based on daily return data for estimation. Table 6 shows the results of this estimation. The own-lagged coefficient is relatively small, and the cross-lag coefficients are also quite constrained. Therefore, after controlling for their recent joint histories, there is still very little persistence in a directional predictive ability at the daily level.

TABLE 6. VAR(2) coefficients for daily cryptocurrency returns.

Table 7 reports the formal Granger causality tests. Neither direction shows a rejection of the null hypothesis of no Granger causality for either asset based on common significance levels. They do not need to have absolutely no connection. Instead, they are moving at a high frequency level together and exhibit considerable rolling-return correlation. What this suggests is that most of the co-movement has been caused by contemporaneous factors or due to shared information, rather than by a fixed lag relationship among assets for more than 1–2 days ahead.

TABLE 7. Granger causality tests between Bitcoin and Ethereum returns.

In terms of economics, the development of the cross-assets system is usually accompanied by a certain degree of contemporaneous movement and weak directional prediction after eliminating such shocks. It is also operating in this manner at the reference level for an analysis of this market. Bitcoin and Ethereum have responded to many of the same micro- and macro-level signals; however, neither has become an enduring short-term forecasting tool for the other within a basic daily VAR framework.

From the angle of investment, it is expected that “Bitcoin leads” or that “Ethereum carries forward” early information on Bitcoin will not hold true for all cases. At times, such patterns usually occur together with events related to technology and networks. The full-sample evidence indicates a relatively weaker persistent effect of the lead–lag relationship. In terms of governance perspectives, correlation monitoring shows higher informative power than the directionality causal testing for short-term system-wide co-movements across the major cryptocurrencies.

8 Regime-level performance and interpretive implications

Studies do not show any significant patterns of change in the prices of these items across the entire assessment period. Both assets have regime-dependent performance and exhibit different outcomes at different times: expansion, correction, stabilization, and recovery. Ethereum generally shows a stronger upward tendency during expansion and may lose more in a correction than other tokens. Although both tend to move in the same direction, they are highly sensitive and move under different circumstances.

These conclusions are not absolute. The empirical evidence in this article is directly in favor of the existence of segmented-price change and strong simultaneity coincidence; however, it cannot conclusively establish specific governance rules or institutional reasons for every regime transition. Therefore, the regime-level outcomes can be considered more as references for explaining changes in cryptocurrency market dynamics through specific contexts; they themselves cannot conclusively validate the exact causes of regulation or institutions.

Figures 3, 4: Why does the typical value of the mean-based measure fail to inform? A positive average return over 6 years might also have multiple periods of negative cumulative returns, both in terms of portfolio selection and supervision. Long-run upward adjustment does not remove path dependence. In terms of investor positions, this involves managing the negative loss-risk; from a regulatory perspective, it requires preventing the transmission of this kind of risk to related areas of finance through market fluctuations. Figure 5 reports the rolling 90-day return correlation between Bitcoin and Ethereum, showing that their co-movement is time-varying rather than constant across regimes.

Infrastructure and platform design are expected to include a system for real-time tracking of market trend changes, together with regime identification function(s), in addition to simple display function(s). Exchanges, custodian banks, risk management departments, and supervision institutions can determine the boundary at which the market moves from a smooth appreciation to an unstable speed-up; correction of speculation turns consolidation into new cycles of speculation.

9 Discussion: possible implications for market interpretation and financial governance

Based on the empirical analysis in this article, the main conclusion is that the price behavior of Bitcoin and Ethereum can be more appropriately divided into regime-dependent phases than one continuous trend or purely short-term noise. There may be certain implications for the interpretation of the market, risk monitoring, and financial management. The evidence presented above cannot be considered to have demonstrated in any way that a specific regulation or institution has occurred. Instead, it implies that the market with frequent changes in structure should be interpreted more cautiously based on average returns and static trend assumptions alone.

Implication one: Market behavior and transparency issues. Rising prices in the growing period result in retailers entering and new intermediary relationships arising rapidly. In this case, some details of custody, leverage, token economy model, and platform self-discipline that are released without proper caution when making an investment decision can have widespread effects. In times of a market reversal, the loss may be attributed entirely to volatility; however, it has been shared between volatility and governance deficiencies. Empirical trend analysis can then help detect periods when governance failures are most susceptible to becoming systemic salience.

The following implications concern the institutionalization of digital assets. In terms of maturity, the latter part of this group’s sample has formed a relatively well-developed market structure; recovery will no longer solely be attributed to speculation but will also be affected by multiple aspects of finance. With more links established between cryptocurrencies and other forms of investment, collateral, and treasury decisions, the concept of price trends is now broader than it was before. Under such an environment, trend breaks matter for capital allocation, collateral valuation, and systemic sentiment. Thus, this aids in designing a governance structure that combines market innovation with spillover impacts.

A third application is for a limitation on simple prediction. Weak Granger causality indicates that there may be no obvious directional information in highly correlated assets. Caution should be taken about the model of operating a single leading benchmark coin to replace other coins in predicting all others. Governing and monitoring refer to generating systems at various levels with shared stress indicators, liquidity risk exposures, and volatility measures; there is no one-off dependence on an absolute early warning sign based alone.

Finally, in view of the separated effect evidence, some possible regulations themselves constitute such a structure. Possibilities include strengthening legal security, establishing strong enforcement systems, extending institutional participation in market operations, and helping increase the length of a stable market by limiting volatility to an indeterminable level. Governance deficits, enforcement shocks, and abrupt changes in policies can all affect this direction of change rapidly. Price adjustment and institutional management explain why crypto trend analysis goes beyond empirical finance to include research on the structure of financial systems.

10 Implications for investors, risk managers, and policymakers

These results can be used as references for investment decision-makers, risk analysts, and policy researchers, with readers exercising a healthy degree of skepticism. According to the research results, investors can obtain returns from investing in a benchmark cryptocurrency index through regime-awareness, and drawdown-control strategies and volatility-management methods are still significant. According to these results, on their own, average return indices do not fully reflect the risk condition in high-regime sensitivity areas. For policymakers, the findings may have certain relevance in that these aspects show their potential utility for monitoring structure-shocks, volatility clustering, and cross-asset interactions within an all-inclusive framework of market-watchfulness.

Risk management personnel have the basis to raise demands for continuous volatility indicators, pressure tests, etc., under normal circumstances. A static value at risk based on mean returns from individual days fails to handle dispersion effectively and cannot identify certain systematic risks accurately using this method. Margin design, collateral qualification, and concentration control should apply during the entire process and not be fixed in one period. Due to the significant change in people’s behavior expectations after revealing a trend reversal, model-based governance for crypto asset investment portfolios should be stricter than that of traditional assets.

The outcomes indicate a multilayered governance structure of policymakers. Market integrity measures need to strengthen transparency, exchange resilience, custody standardization, and disclosure quality. Second, during this period, when trend changes are prominent, the inconsistency in information about companies among investors becomes more pronounced. In addition to being a cause of changes in price levels over fixed periods within the financial market, the late stage of market development makes it more likely that crypto cycles will impact surrounding financial industries through treasury exposure, collateral utilization, etc.

From this, the researchers have realized that through the joint application of econometric techniques in our study, cryptocurrency trends have many influencing factors that can affect value in combination and simultaneously. Examining a price chart without testing invites narrative exaggeration; similarly, running a baseline regression without regime interpretation results in an economically thin analysis. Combining a stationary test, segmented-trend models, and multiple-returns analysis can provide real evidence that works in any form of tokens, stablecoins for applications, or other kinds of tokenized products.

11 Limitations and future research

There are several deficiencies in the current study. The empirical data of this study come from one exchange feed, through a benchmarked, regimented market-level panel. For medium-term trend analysis of this construction, however, it cannot reflect the fragmentized exchange-level trading volume, order-book depth, and other market-microstructure elements that might exist. Therefore, future research can also use cross-sectional or higher-frequency datasets to verify whether there are still similar structural break phenomena and interdependence characteristics under explicit model settings for considering differences in exchange-level or microstructural noise effects.

Second, the assets covered in this study are not particularly broad. The examples were selected for their leading position in terms of benchmarks, market capitalization, and a broad source of information; however, they cannot fully reflect the entire landscape of cryptocurrencies. Stablecoins, layer-one competitors, exchange tokens, and tokenized real-world assets will have different trend forms and interaction patterns. In the future, it is more likely that scholars may study whether similar regime-based results hold for different asset combinations, especially some under-discussed or rarely referenced assets such as Litecoin-Ether.

Third, the scope of this article’s methodology is restricted. Cryptocurrency market prices exhibit typical phenomena of volatility clustering, heteroskedasticity, etc.; thus, it is necessary to develop a number of high-efficiency models, including those based on the GARCH family, Markov state-space framework, regime-switching VAR model, quantile function, and multivariate volatilities. This article is limited in its ability to portray the non-linear dynamics of the fluctuation characteristics at large. It sets up an empirical research system that can help identify long-term structural changes and short-period interaction mechanisms. Therefore, according to the purpose of the current methodological approach, it cannot be considered an all-inclusive model-building path. Future studies may address formal volatility modeling, state-switching estimation, and rich non-linear dependence structure.

Fourth, it is based solely on market price data and has failed to include any additional on-chain, network-level, developer, or ecosystem-level variables. However, cryptocurrency prices can still be influenced by factors such as network traffic, purchase behavior, developers, application popularity, on-chain liquidity expansion, and so forth. Incorporating the component of market-level and blockchain-specific index into a more rigorous empirical research on how these factors influence asset price fluctuations is one essential direction for research in the future.

12 Summary

Based on the detailed comparison of 2020–2025 data, this article explores changes in prices for both Bitcoin and Ethereum separately. It cannot be reasonably described as having only an obvious upward tendency, nor in isolation as purely random. Rather than presenting a regime-independent structural feature in which persistent appreciation is broken by substantial correction, severe deviation from normal fluctuations, etc., redefining the fundamental pattern multiple times occurs successively. The log-price series shows a stochastic trend behavior; return series are stationary; segmented trend models perform better than one-dimensional linear trajectory ideas, and short-run interdependencies have characteristics primarily of co-movements rather than directional causality stability.

Accordingly, based on these results, we can infer that the changes in price between 2020 and 2025 for Bitcoin and Ethereum have exhibited regime-specific behavior compared with those presenting a constant trend or being completely random. The evidence suggests that while the path of logarithmic price contains structural changes, the return series exhibit stationarity; segmented trend models are more revealing in terms of informativeness for medium-term analysis than a simple linear trend, and short-term interactions show stronger contemporaneous co-movements rather than stable directional causality. The above findings are still within the empirical range of this article and cannot be regarded as conclusive institutional explanations; they serve as supporting evidence for market structure.

In addition, this article explores some potential consequences of the interpretation that cryptocurrency pricing is related to transparency, monitoring, and increasing institutional relevance for the digital asset market. These consequences cannot be considered to have been verified directly through cause-and-effect reasoning based on the current model. Thus, the contribution of this article lies in providing a fundamental empirical approach to connect regime-specific price changes with short-term interlinkages and wider market perspectives; it leaves more detailed governance and policy tests for subsequent studies.

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Footnotes

Edited by: Pei Xiao, University of Surrey, United Kingdom

Reviewed by: Lei Yang, Shenyang University of Technology, China

Fengyi Wang, Beijing Technology and Business University, China