This study aims to investigate the information spillover among four traditional financial assets (i.e., crude oil, gold, stock, and U.S. dollar) and nine main cryptocurrencies (i.e., Bitcoin, Cardano, Dai, Ripple, Dogecoin, Ethereum, Ethereum Classic, Monero, and Tether), by constructing entropy-based information spillover network and information integration network from both static and dynamic perspectives. The empirical results show that the information spillover among these assets is time-varying, experiencing an obvious increase trend after the COVID-19. As a whole, traditional financial assets mainly play the role of net information transmitter while cryptocurrencies mainly play the role of net information recipient. Tether and Dai are the two main visual coins that can transmit net information flow to traditional assets, while gold and stock are the two main traditional assets that transmit net information flow to cryptocurrencies. Tether and U.S. dollar are the central nodes that link traditional financial assets and cryptocurrencies together.
Joana Katina, Igor Katin, ĐĐ”ŃĐ° ĐĐŸĐŒĐ°ŃĐŸĐČĐ°
This article presents a novel approach to cryptocurrency price forecasting, leveraging advanced machine-learning techniques.By comparing traditional autoregressive models with recurrent neural network approaches, the study aims to evaluate the forecasting accuracy of Autoregressive Integrated Moving Average (ARIMA), Seasonal ARIMA (SARIMA), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU) models across various cryptocurrencies, including Bitcoin, Ethereum, Dogecoin, Polygon, and Toncoin.The data for this empirical study was sourced from historical prices of these specific cryptocurrencies, as recorded on the CoinMarketCap platform, covering January 2022 to April 2024.The methodology employed involves rigorous statistical and neural network modelling where each model's parameters were meticulously optimized for the specific characteristics of each cryptocurrency's price data.Performance metrics such as Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) were used to assess the precision of each model.The main results indicate that LSTM and GRU models, leveraging deep learning techniques, generally outperformed the traditional ARIMA and SARIMA models regarding error metrics.This demonstrates a higher efficacy of neural networks in handling the non-linear complexities and volatile nature of cryptocurrency price movements.This study contributes to the ongoing discourse in financial technology by elucidating the practical implications of using advanced machine-learning techniques for economic forecasting.Importantly, it provides valuable insights that can directly inform and enhance the decision-making processes of investors and traders in digital assets.
The emergence of Bitcoin Exchange-Traded Funds (ETFs) marks a significant milestone in the evolution of cryptocurrency investment. This research paper investigates the potential impact of Bitcoin ETFs on existing cryptocurrency exchanges, focusing on liquidity dynamics and institutional investment trends. By examining the mechanisms through which ETFs may draw liquidity away from direct Bitcoin exchanges, this study aims to shed light on the evolving landscape of cryptocurrency trading. Additionally, the paper explores the potential for Bitcoin ETFs to attract increased institutional investment in the cryptocurrency market, analyzing the factors that may contribute to this trend. Through a comprehensive analysis of market data and expert insights, this research provides valuable insights into the evolving relationship between Bitcoin ETFs and traditional cryptocurrency exchanges.
This work proposes a novel methodology to help in decision making in the cryptocurrency market. Two investment strategies have been designed for Ethereum (ETH), based on predictions of the price and trend of this cryptocurrency using real data. The two Ethereum cryptocurrency prediction systems rely solely on past values of other contextual stock indices, market indicators and online trends, and ignore any technical indicators of price evolution. Real data from cryptocurrency market has been collected and processed with different feature selection methods. Applying a regression approach with Gated Recurrent Unit (GRU) and Long Short-Term Memory (LSTM) networks, prediction models for the ETH price for 1, 7 and 15 days are obtained and compared. Also, support vector machine (SVM) is applied to predict the ETH price trend by applying a classification approach. In both approaches, sentiment analysis has been included to check its effect on the prediction results. The reliability of these prediction models in the current market has been evaluated by designing two original knowledge-based investment strategies. They are tested over two different time periods with real cryptocurrency market data. The results show that it is possible to generate up to 5.16 profit factor with few operations using these models. Furthermore, adding sentiment analysis has shown to have little influence. In this way, we contribute to the advancement of our knowledge of this volatile and still young cryptocurrency market, and specifically of the evolution of Ethereum and the factors that can influence its behavior.
Cryptocurrency market has striking development and aims to build open, transparent and efficient financial market. More applications are tried to build on blockchain and using cryptocurrency in multiple scenarios, and DeFi ecosystem is set up. Many niche cryptocurrencies related to DeFi market may have wide utility and demand in the future. Therefore, more research is needed to focus these cryptocurrencies and try to establish sturdy price prediction. In this study, two cryptocurrencies, Binance Coin (BNB) and Huobi Tokens (HT), which are rooted in two crypto exchange platform are used for price prediction based on three machine learning models, i.e., Random Forest (RF), Long Short-Term Memory (LSTM) and Extreme Gradient Boosting (XGBoost). Four prediction windows are selected (1, 3, 7 and 30 days span). The results for different prediction window are compared and discussed. 1 day prediction window outperforms all prediction windows with the average MSE 0.0117. Additionally, RF and XGBoost outperform LSTM with lower MSE and more stable performance, while RF and XGBoost have average MSE 0.0157 and 0.0158 separately. The research tries to predict cryptocurrencies that based on relatively niche market and discuss the performance in comprehensive ways, aiming at providing novel insights into cryptocurrency price prediction.
Sergio Luis Nåñez Alonso, Javier Jorge-VĂĄzquez, Miguel Ăngel Echarte FernĂĄndez, David Sanz Bas
Abstract A number of financial bubbles have occurred throughout history. The objective of this study was to identify the main similarities between Bitcoin price behavior during bubble periods and a number of historical bubbles. Once this had been carried out, we aimed to determine whether the solutions adopted in the past would be effective in the present to reduce investorsâ risk in this digital asset. This study brings a new approach, as studies have previously been conducted analyzing the similarity of Bitcoin bubbles to other bubbles individually, but these were not conducted in such a broad manner, addressing different types of bubbles, and over such a broad time period. Starting from a dataset with 9967 records, a combined methodology was used. This consisted of an analysis of the standard deviations, the growth rates of the prices of the assets involved, the percentage increase in asset prices from the origin of the bubble to its peak and its fundamental value, and, finally, the bubble index. Lastly, correlation statistical analysis was performed. The results obtained from the combination of the above methods reveal the existence of certain similarities between the Bitcoin bubbles (2011, 2013, 2017, and 2021) and the tulip bubble (1634â1637) and the Mississippi bubble (1719â1720). We find that the vast majority of the measures taken to avoid past bubbles will not be effective now; this is due to the digital and decentralized nature of Bitcoin. A limitation of the study is the difficulty in making a comparison between bubbles that occurred at different historical points in time. However, the results obtained shed light and provide guidance on the actions to be taken by regulators to ensure the protection of investors in this digital asset.
This study investigates the application of the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm for detecting anomalies in Bitcoin trading data. With the growing significance of Bitcoin in the financial market, identifying irregular trading patterns is crucial for maintaining market integrity and preventing market manipulation. Utilizing a dataset from Kaggle, which includes features such as date, timestamp, open, high, low, close, volume, and number of trades, the data was aggregated from minute-by-minute to hourly intervals for more manageable analysis. The DBSCAN algorithm effectively identified a primary cluster comprising 29,612 data points and flagged 2 points as anomalies, achieving a precision of 1.0, recall of 0.0068, F1-score of 0.0135, and an AUC-ROC of 0.5034. The optimal parameters, determined through sensitivity analysis, were epsilon (Δ) = 0.1 and min_samples = 3, yielding the highest silhouette score of 0.21499. These results underscore the algorithm's ability to accurately label anomalies while highlighting the challenge of comprehensive anomaly detection. The study contributes to the field of financial anomaly detection by demonstrating the effectiveness of DBSCAN in analyzing high-dimensional, noisy datasets. It also addresses gaps in the literature regarding the application of density-based clustering methods to Bitcoin trading data. Despite its contributions, the study acknowledges limitations, such as potential data aggregation impact and the need for further validation with different datasets. Future research directions include integrating additional features like social media sentiment and exploring hybrid approaches that combine supervised and unsupervised methods.
Abstract We study the statistical properties of the Bitcoin return series and provide a thorough forecasting exercise. Also, we calibrate stateâofâtheâart machine learning techniques and compare the results with econometric time series models. The empirical assessment provides evidence that the application of machine learning techniques outperforms econometric benchmarks in terms of forecasting precision for both inâ and outâofâsample forecasts. We find that both deep learning architectures as well as complex layers, such as LSTM, do not increase the precision of daily forecasts. Specifically, a simple recurrent neural network describes a sensible choice for forecasting daily return series.
The bubbles and spikes in cryptocurrency prices increase considerably the risk on investments in these assets. In the traditional time series literature bubbles are viewed as nonstationary and non-estimable components of a process. In this paper, we adopt a different approach and consider the bubbles as inherent features of a strictly stationary causal-noncausal (mixed) Vector Autoregressive (VAR) process. This approach allows us to model and estimate the common bubbles and spikes in cryptocurrency prices. It also provides us linear combinations of cryptocurrencies that eliminate common bubbles analogously to the cointegrating vectors eliminating common trends in unit root processes. They are used to build cryptocurrency portfolios immune to the risk of common bubbles that ensure stable investment strategies. The mixed VAR model is estimated from the US Dollar prices of Bitcoin, Ethereum, Ripple, and Stellar over the period 2017â2019. We document the common bubbles and illustrate the behavior of bubble-free portfolios.
We present tail risk analysis of cryptocurrencies (Bitcoin, Ethereum and Litecoin), non-fungible tokens, stocks (FTSE 100 and S&P 500) and Gold from November 12, 2017 to March 31, 2022 using conditional model-based Value-at-Risk (VaR). We explored which model specification and distributional innovation could best capture the tail risk in these assets. Using the VaR and other risk metrics, we showed that there is no superior model/metric for capturing tail risk. We found that, for all the assets, non-Gaussian distributional assumptions best modelled the asymmetry and fat-tails in the distributions of the returns; though there was more homogeneity in the distributional assumptions for Gold unlike the other assets. Our research is crucial for internal risk modelling and may increase global investor confidence for those who blend conventional and unconventional assets. Also, this study can help investors make informed decisions about asset allocation and risk tolerance in the events of extreme market conditions. Understanding the tail risks in financial assets can help investors hedge and diversify against risk in their portfolios. The theoretical implications also show a trade-off between the different assets as the presence of tail risk reflect the potential of returns, yet possible losses in the presence of extreme events. Last, the findings reinforce the need for risk managers to re-focus their attention to a set of superior models rather than a single best model for risk assessment.
Abstract We aim to identify the determinants of nonâfungible tokens (NFTs) returns. The 10 most popular NFTs based on their price, trading volume, and market capitalisation are examined. Twentyâthree potential drivers of the returns of each NFT are considered. We employ a Bayesian LASSO model which takes into account stochastic volatility and leverage effect. The results indicate that NFTs returns are primarily driven by volatility and ethereum returns. We find a weak connection between NFTs returns and conventional assets, such as stock, oil, and gold markets.
Since the creation of Bitcoin in 2008, these digital currencies have not only attracted widespread attention from the public and economists, but have also triggered a rethinking of the nature of money, the store of value, and the modes of exchange. This paper explores the transformative impact of Bitcoin and digital currencies on global finance, emphasizing their emergence as a challenge to the traditional concept of money and a paradigm shift. Furthermore, the paper delves into the birth of Bitcoin, its decentralized nature and its pioneering role in the field of digital currencies, discusses the historical background, technological underpinnings, and monetary functions of digital currencies, and highlights the potential and challenges of their integration into the financial system. It aims to examine the characteristics and functions of bitcoin and digital currencies in the contemporary financial landscape, focusing on how they can challenge traditional monetary policy as an emerging financial asset, as well as their potential impact and integration challenges in the global economic system.
Ijaz Younis, Himani Gupta, Anna Min Du, Waheed Ullah Shah · 5 authors
Decentralized finance (DeFi) has become of significant interest for investors in both the financial and digital sectors. We use a time-varying parameter vector autoregression (TVP-VAR) approach to estimate the static and dynamic connections between and within DeFi, G7 banking, and equity markets. We focus on critical events such as the COVID-19 pandemic, the cryptocurrency bubble, and the Russia-Ukraine conflict. The results highlight interconnectedness and significant spillovers within and between the markets, especially during the COVID-19 pandemic. Notably, there were significant spillover effects from the G7 banking and equity markets to Japan and DeFi assets. The findings demonstrate a robust connection between DeFi platforms, G7 banking, and stock markets throughout these tumultuous periods. Policymakers, investors, and entrepreneurs are recommended to keep a close eye on changes in traditional banking and equity markets to adjust the risk of DeFi assets.
Manoel Fernando Alonso Gadi, MiguelâĂngel Sicilia
Abstract The objective of this paper is to describe Cryptocurrency Linguo (CryptoLin), a novel corpus containing 2683 cryptocurrency-related news articles covering more than a three-year period. CryptoLin was human-annotated with discrete values representing negative, neutral, and positive news respectively. Eighty-three people participated in the annotation process; each news title was randomly assigned and blindly annotated by three human annotators, one in each different cohort, followed by a consensus mechanism using simple voting. The selection of the annotators was intentionally made using three cohorts with students from a very diverse set of nationalities and educational backgrounds to minimize bias as much as possible. In case one of the annotators was in total disagreement with the other two (e.g., one negative vs two positive or one positive vs two negative), we considered this minority report and defaulted the labeling to neutral. Fleissâs Kappa, Krippendorffâs Alpha, and Gwetâs AC1 inter-rater reliability coefficients demonstrate CryptoLinâs acceptable quality of inter-annotator agreement. The dataset also includes a text span with the three manual label annotations for further auditing of the annotation mechanism. To further assess the quality of the labeling and the usefulness of CryptoLin dataset, it incorporates four pretrained Sentiment Analysis models: Vader, Textblob, Flair, and FinBERT. Vader and FinBERT demonstrate reasonable performance in the CryptoLin dataset, indicating that the data was not annotated randomly and is therefore useful for further research1. FinBERT (negative) presents the best performance, indicating an advantage of being trained with financial news. Both the CryptoLin dataset and the Jupyter Notebook with the analysis, for reproducibility, are available at the projectâs Github. Overall, CryptoLin aims to complement the current knowledge by providing a novel and publicly available Gadi and Ăngel Sicilia (Cryptolin dataset and python jupyter notebooks reproducibility codes, 2022) cryptocurrency sentiment corpus and fostering research on the topic of cryptocurrency sentiment analysis and potential applications in behavioral science. This can be useful for businesses and policymakers who want to understand how cryptocurrencies are being used and how they might be regulated. Finally, the rules for selecting and assigning annotators make CryptoLin unique and interesting for new research in annotator selection, assignment, and biases.
This research proposes a novel arbitrage approach in multivariate pair trading, termed the Optimal Trading Technique (OTT). We present a method for selectively forming a "bucket" of fiat currencies anchored to cryptocurrency for monitoring and exploiting trading opportunities simultaneously. To address quantitative conflicts from multiple trading signals, a novel bi-objective convex optimization formulation is designed to balance investor preferences between profitability and risk tolerance. We understand that cryptocurrencies carry significant financial risks. Therefore this process includes tunable parameters such as volatility penalties and action thresholds. In experiments conducted in the cryptocurrency market from 2020 to 2022, which encompassed a vigorous bull run followed by a bear run, the OTT achieved an annualized profit of 15.49%. Additionally, supplementary experiments detailed in the appendix extend the applicability of OTT to other major cryptocurrencies in the post-COVID period, validating the model's robustness and effectiveness in various market conditions. The arbitrage operation offers a new perspective on trading, without requiring external shorting or holding the intermediate during the arbitrage period. As a note of caution, this study acknowledges the high-risk nature of cryptocurrency investments, which can be subject to significant volatility and potential loss.
The current investigation delves into the valuation trends of prominent Non-Fungible Token (NFT) collections, entities at the forefront of the digital economy that are redefining concepts of asset ownership and artistic appreciation. The academic import of this study is anchored in the emergent nature of NFTs and their paradigmatic shift from traditional economic models. This research aims to decipher the market value fluctuations of top NFT collections through a comprehensive time-series analysis, the application of the ARIMA model. Methodologically, the study adheres to established time-series analytical procedures, with a focus on identifying and interpreting patterns and trends within the market data. The approach synthesizes a broad spectrum of economic and cultural variables that potentially exert influence over the NFT marketplace. Results gleaned from the analysis yield insights into the price movements of NFTs, offering a juxtaposition of predicted and actual market data to deepen the understanding of this unique market sector. The implications of this research extend beyond academic interest, offering a vital resource for stakeholders within the digital economy. The discerned patterns and dynamics of NFTs, as revealed through the study, contribute to a granular understanding of digital assets, providing a scaffold for future research endeavors and practical guidance for participants in the digital art and ownership space.
This study examines the impact of zero fees on market quality. This issue is examined using a natural experiment in Bitcoin provided by the Binance exchange, which eliminated makerâtaker trading fees for market participants in July 2022. I find that although zero fees increase investorsâ willingness to trade, thereby prima facie increasing liquidity, their elimination encourages market makers to widen the bidâask spread and provide a shallower market depth, which in turn reduces liquidity. Liquidity providers realize gains at the expense of liquidity takers, suggesting the emergence of new potential forms of unethical financial market conduct. Notably, despite the removal of trading fees, total transaction costs increased for customers. These outcomes, coupled with the boost in exchange market share, raise concerns about price integrity and investorsâ protection in the highly unregulated crypto environment, in turn implying that the elimination of makerâtaker fees is harmful to the market.
Ahmed Bossman, Mariya Gubareva, Samuel Kwaku Agyei, Xuan Vinh Vo
Abstract We provide empirical evidence supporting the economic reasoning behind the impossibility of diversification benefits and the hedge attributes of cryptocurrencies remaining in force during the downside trends observed in bearish financial markets. We employ a spillover connectedness model driven by time-varying parameter vector autoregressions on daily data covering January 2018 to November 2022 to analyze spillover transmissions between conventional and digital markets, focusing on the role of stablecoin issuances. We study the stock, bond, cryptocurrency, and stablecoin markets and find very high connectedness, which varies over time in response to up/down trends in financial markets. The results show that during financial turmoil, cryptocurrencies amplify downside risks rather than serve as diversifiers. In addition to risky assets from conventional financial markets, cryptocurrencies champion the transmission of spillovers to digital and conventional markets. In contrast, changes in stablecoin issuances produce few shocks because of their pegged prices, but they facilitate investorsâ switch from volatile cryptos to more stable digital instruments; that is, we observe a phenomenon designated by us as the âflight-to-cryptosafety.â We draw insightful conclusions, provoking new thinking regarding portfolio hedge strategies that could potentially benefit investors when searching for less volatile investment performance.
Nehal N. AlMadany, Omar Hujran, Ghazi AlâNaymat, Aktham Maghyereh
The emergence of cryptocurrencies has generated enthusiasm and concern in the modern global economy. However, their high volatility, erratic price fluctuations, and tendency to exhibit price bubbles have made investors cautious about investing in them. Consequently, it is essential to develop methods and models to forecast cryptocurrency returns to benefit investors, traders, and the scientific community. Despite the considerable volume of research on Bitcoin price forecasting, other cryptocurrencies have received little attention in academic literature. Additionally, the current body of literature on predicting cryptocurrency prices or returns emphasizes the use of in-sample methodologies. However, this method is susceptible to overfitting. To address these gaps in the literature, this study employs autoregressive moving average (ARMA), generalized autoregressive conditional heteroskedasticity (GARCH), exponential generalized autoregressive conditional heteroskedasticity (EGARCH), and long short-term memory (LSTM) deep learning neural networks to forecast returns for the ten most actively traded digital currencies: Bitcoin, Ethereum, Ripple, Chainlink, Litecoin, Cardano, Ethereum Classic, Bitcoin Cash, Tether, and Binance Coin. To assess the accuracy of the two models, this study utilizes an out-of-sample method with data gathered sequentially from November 9, 2017, to September 18, 2022. The results indicate that all models exhibit high accuracy, as evidenced by their low root mean square error (RMSE), mean absolute error (MAE), and mean squared error (MSE) values. Meanwhile, the hybrid EGARCH-LSTM or GARCH-LSTM models demonstrate slightly better accuracy compared with the other models. The findings are valuable for investors, traders, and researchers involved in cryptocurrency forecasting.
Abstract This study aims to identify the factors that robustly contribute to Bitcoin liquidity, employing a rich range of potential determinants that represent unique characteristics of the cryptocurrency industry, investor attention, macroeconomic fundamentals, and global stress and uncertainty. To construct liquidity metrics, we compile 60-min high-frequency data on the low, high, opening, and closing exchange rates of Bitcoin against the US dollar. Our empirical investigation is based on the extreme bounds analysis (EBA), which can resolve model uncertainty issues. The results of Leamerâs version of the EBA suggest that the realized volatility of Bitcoin is the sole variable relevant to explaining liquidity. With the Sala-i-Martinâs variant of EBA, however, four more variables, (viz. Bitcoinâs negative returns, trading volume, hash rates, and Google search volume) are also labeled as robust determinants. Accordingly, our evidence confirms that Bitcoin-specific factors and developments, rather than global macroeconomic and financial variables, matter for explaining its liquidity. The findings are largely insensitive to our proxy of liquidity and to the estimation method used.
Abstract In the FinTech era, we contribute to the literature by studying the pricing of Bitcoin options, which is timely and important given that both Nasdaq and the CME Group have started to launch a variety of Bitcoin derivatives. We find pricing errors in the presence of market smiles in Bitcoin options, especially for short-maturity ones. Long-maturity options display more of a âsmirkâ than a smile. Additionally, the ARJI-EGARCH model provides a better overall fit for the pricing of Bitcoin options than the other ARJI-GARCH type models. We also demonstrate that the ARJI-GARCH model can provide more precise pricing of Bitcoin and its options than the SVCJ model in term of the goodness-of-fit in forecasting. Allowing for jumps is crucial for modeling Bitcoin options as we find evidence of time-varying jumps. Our empirical results demonstrate that the realized jump variation can describe the volatility behavior and capture the jump risk dynamics in Bitcoin and its options.
Background: In recent years, investors' interest in cryptocurrencies has increased due to their notable price volatility and rapid price increases. These investors view cryptocurrencies as suitable financial assets for portfolio rebalancing strategies. Purpose: The main objective of this study is to examine the multifractality of the cryptocurrencies Bitcoin (BTC), Lisk (LSK), Quantum (QUA), Litecoin (LTC), Ripple (XRP), Augur (REP), Darkcoin (DASH), EOS, IOTA (MIOTA). Methods: The Detrended Fluctuation Analysis (DFA) econophysics model supports the methodology. Results: The results suggest that during the 2020 pandemic period, the digital currencies LSK, QUA, MIOTA, XRP, REP, BTC, ETH, LTC and DASH showed very significant persistence, indicating that price formation is not random. However, validating that cryptocurrency prices are predictable based on historical time series was impossible. On the other hand, the digital currency EOS proved to be in equilibrium; in other words, price formation follows the random walk pattern, suggesting that prices are not autocorrelated over time. During the 2022 geopolitical conflict, long-term memory patterns shifted significantly towards short-term memories, i.e. anti-persistence. The digital currencies ETH, MIOTA, EOS, LTC, REP, LSK and DASH showed anti-persistence slopes, indicating that prices were less influenced by past events and more by recent events. On the other hand, the cryptocurrencies BTC (0.50), QUA (0.50), and XRP (0.50) demonstrate that prices contain a significant random component and that the residuals are independent and identically distributed (i.i.d.), supporting the idea that white noise might be present. Conclusion: From a risk management perspective, these findings are highly relevant to investors, traders and market participants.
Abstract Research on cryptocurrency exchanges, consisting of both centralized exchanges (CEXs) and decentralized exchanges (DEXs), has seen a significant increase in contributions in recent years, driven by growing interest in the conceptual design of cryptocurrency markets. Through a comprehensive review of literature published between January 2019 and September 2023, I identify and analyze different dimensions of the ongoing CEX vs. DEX debate. While DEXs emphasize decentralization, user control, and resistance to censorship, CEXs offer higher liquidity, advanced trading features, and a more established track record. Regulatory challenges, such as Know Your Customer (KYC) and Anti-Money Laundering (AML) compliance, also feature prominently in the literature and influence the choice of exchange for both traders and policymakers. In addition, I observe a growing interest in the design of pricing functions for CEXs and DEXs, particularly in the area of automated market makers (AMMs). Finally, based on my findings, I outline future research opportunities in this context and derive research gaps as well as recommended actions for practitioners.