Time-Series Analysis

Short-term Volatility Estimation for High Frequency Trades using Gaussian processes (GPs) ArXiv ID: 2311.10935 “View on arXiv” Authors: Unknown Abstract The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change unexpectedly [“1”]. Price volatility is often detrimental to the return economics, and thus, investors should factor it in whenever making investment decisions, choices, and temporal or permanent moves. It is, therefore, crucial to make necessary and regular short and long-term stock price volatility forecasts for the safety and economics of investors returns. These forecasts should be accurate and not misleading. Different models and methods, such as ARCH GARCH models, have been intuitively implemented to make such forecasts. However, such traditional means fail to capture the short-term volatility forecasts effectively. This paper, therefore, investigates and implements a combination of numeric and probabilistic models for short-term volatility and return forecasting for high-frequency trades. The essence is that one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it is not easy to set price limits in a market due to its free nature and randomness, a Censored GP was used to model the relationship between the corrected stock prices and returns. Forecasting errors were evaluated using the implied and estimated data. ...

Revisiting Cont’s Stylized Facts for Modern Stock Markets ArXiv ID: 2311.07738 “View on arXiv” Authors: Unknown Abstract In 2001, Rama Cont introduced a now-widely used set of ‘stylized facts’ to synthesize empirical studies of financial price changes (returns), resulting in 11 statistical properties common to a large set of assets and markets. These properties are viewed as constraints a model should be able to reproduce in order to accurately represent returns in a market. It has not been established whether the characteristics Cont noted in 2001 still hold for modern markets following significant regulatory shifts and technological advances. It is also not clear whether a given time series of financial returns for an asset will express all 11 stylized facts. We test both of these propositions by attempting to replicate each of Cont’s 11 stylized facts for intraday returns of the individual stocks in the Dow 30, using the same authoritative data as that used by the U.S. regulator from October 2018 - March 2019. We find conclusive evidence for eight of Cont’s original facts and no support for the remaining three. Our study represents the first test of Cont’s 11 stylized facts against a consistent set of stocks, therefore providing insight into how these stylized facts should be viewed in the context of modern stock markets. ...

Integrating feature selection and regression methods with technical indicators for predicting Apple Inc. stock prices ArXiv ID: 2310.09903 “View on arXiv” Authors: Unknown Abstract Stock price prediction is influenced by a variety of factors, including technical indicators, which makes Feature selection crucial for identifying the most relevant predictors. This study examines the impact of feature selection on stock price prediction accuracy using technical indicators. A total of 123 technical indicators and 10 regression models were evaluated using 13 years of Apple Inc. data. The primary goal is to identify the best combination of indicators and models for improved forecasting. The results show that a 3-day time window provides the highest prediction accuracy. Model performance was assessed using five error-based metrics. Among the models, Linear Regression and Ridge Regression achieved the best overall performance, each with a Mean Squared Error (MSE) of 0.00025. Applying feature selection significantly improved model accuracy. For example, the Multi-layered Perceptron Regression using Forward Selection improved by 56.47% over its baseline version. Support Vector Regression improved by 67.42%, and Linear Regression showed a 76.7% improvement when combined with Forward Selection. Ridge Regression also demonstrated a 72.82% enhancement. Additionally, Decision Tree, K-Nearest Neighbor, and Random Forest models showed varying levels of improvement when used with Backward Selection. The most effective technical indicators for stock price prediction were found to be Squeeze_pro, Percentage Price Oscillator, Thermo, Decay, Archer On-Balance Volume, Bollinger Bands, Squeeze, and Ichimoku. Overall, the study highlights that combining selected technical indicators with appropriate regression models can significantly enhance the accuracy and efficiency of stock price predictions. ...

Predicting Financial Market Trends using Time Series Analysis and Natural Language Processing ArXiv ID: 2309.00136 “View on arXiv” Authors: Unknown Abstract Forecasting financial market trends through time series analysis and natural language processing poses a complex and demanding undertaking, owing to the numerous variables that can influence stock prices. These variables encompass a spectrum of economic and political occurrences, as well as prevailing public attitudes. Recent research has indicated that the expression of public sentiments on social media platforms such as Twitter may have a noteworthy impact on the determination of stock prices. The objective of this study was to assess the viability of Twitter sentiments as a tool for predicting stock prices of major corporations such as Tesla, Apple. Our study has revealed a robust association between the emotions conveyed in tweets and fluctuations in stock prices. Our findings indicate that positivity, negativity, and subjectivity are the primary determinants of fluctuations in stock prices. The data was analyzed utilizing the Long-Short Term Memory neural network (LSTM) model, which is currently recognized as the leading methodology for predicting stock prices by incorporating Twitter sentiments and historical stock prices data. The models utilized in our study demonstrated a high degree of reliability and yielded precise outcomes for the designated corporations. In summary, this research emphasizes the significance of incorporating public opinions into the prediction of stock prices. The application of Time Series Analysis and Natural Language Processing methodologies can yield significant scientific findings regarding financial market patterns, thereby facilitating informed decision-making among investors. The results of our study indicate that the utilization of Twitter sentiments can serve as a potent instrument for forecasting stock prices, and ought to be factored in when formulating investment strategies. ...

Spatial and Spatiotemporal Volatility Models: A Review ArXiv ID: 2308.13061 “View on arXiv” Authors: Unknown Abstract Spatial and spatiotemporal volatility models are a class of models designed to capture spatial dependence in the volatility of spatial and spatiotemporal data. Spatial dependence in the volatility may arise due to spatial spillovers among locations; that is, if two locations are in close proximity, they can exhibit similar volatilities. In this paper, we aim to provide a comprehensive review of the recent literature on spatial and spatiotemporal volatility models. We first briefly review time series volatility models and their multivariate extensions to motivate their spatial and spatiotemporal counterparts. We then review various spatial and spatiotemporal volatility specifications proposed in the literature along with their underlying motivations and estimation strategies. Through this analysis, we effectively compare all models and provide practical recommendations for their appropriate usage. We highlight possible extensions and conclude by outlining directions for future research. ...

Retail Demand Forecasting: A Comparative Study for Multivariate Time Series ArXiv ID: 2308.11939 “View on arXiv” Authors: Unknown Abstract Accurate demand forecasting in the retail industry is a critical determinant of financial performance and supply chain efficiency. As global markets become increasingly interconnected, businesses are turning towards advanced prediction models to gain a competitive edge. However, existing literature mostly focuses on historical sales data and ignores the vital influence of macroeconomic conditions on consumer spending behavior. In this study, we bridge this gap by enriching time series data of customer demand with macroeconomic variables, such as the Consumer Price Index (CPI), Index of Consumer Sentiment (ICS), and unemployment rates. Leveraging this comprehensive dataset, we develop and compare various regression and machine learning models to predict retail demand accurately. ...

Reconstructing cryptocurrency processes via Markov chains ArXiv ID: 2308.07626 “View on arXiv” Authors: Unknown Abstract The growing attention on cryptocurrencies has led to increasing research on digital stock markets. Approaches and tools usually applied to characterize standard stocks have been applied to the digital ones. Among these tools is the identification of processes of market fluctuations. Being interesting stochastic processes, the usual statistical methods are appropriate tools for their reconstruction. There, besides chance, the description of a behavioural component shall be present whenever a deterministic pattern is ever found. Markov approaches are at the leading edge of this endeavour. In this paper, Markov chains of orders one to eight are considered as a way to forecast the dynamics of three major cryptocurrencies. It is accomplished using an empirical basis of intra-day returns. Besides forecasting, we investigate the existence of eventual long-memory components in each of those stochastic processes. Results show that predictions obtained from using the empirical probabilities are better than random choices. ...

Regularity in forex returns during financial distress: Evidence from India ArXiv ID: 2308.04181 “View on arXiv” Authors: Unknown Abstract This paper uses the concepts of entropy to study the regularity/irregularity of the returns from the Indian Foreign exchange (forex) markets. The Approximate Entropy and Sample Entropy statistics which measure the level of repeatability in the data are used to quantify the randomness in the forex returns from the time period 2006 to 2021. The main objective of the research is to see how the randomness of the foreign exchange returns evolve over the given time period particularly during periods of high financial instability or turbulence in the global financial market. With this objective we look at 2 major financial upheavals, the subprime crisis also known as the Global Financial Crisis (GFC) during 2006-2007 and the recent Covid-19 pandemic during 2020-2021. Our empirical results overwhelmingly confirm our working hypothesis that regularity in the returns of the major Indian foreign exchange rates increases during times of financial crisis. This is evidenced by a decrease in the values of the sample entropy and approximate entropy before and after/during the financial crisis period for the majority of the exchange rates. Our empirical results also show that Sample Entropy is a better measure of regularity than Approximate Entropy for the Indian forex rates which is in agreement with the theoretical predictions. ...

Quantitative statistical analysis of order-splitting behaviour of individual trading accounts in the Japanese stock market over nine years ArXiv ID: 2308.01112 “View on arXiv” Authors: Unknown Abstract In this research, we focus on the order-splitting behavior. The order splitting is a trading strategy to execute their large potential metaorder into small pieces to reduce transaction cost. This strategic behavior is believed to be important because it is a promising candidate for the microscopic origin of the long-range correlation (LRC) in the persistent order flow. Indeed, in 2005, Lillo, Mike, and Farmer (LMF) introduced a microscopic model of the order-splitting traders to predict the asymptotic behavior of the LRC from the microscopic dynamics, even quantitatively. The plausibility of this scenario has been qualitatively investigated by Toth et al. 2015. However, no solid support has been presented yet on the quantitative prediction by the LMF model in the lack of large microscopic datasets. In this report, we have provided the first quantitative statistical analysis of the order-splitting behavior at the level of each trading account. We analyse a large dataset of the Tokyo stock exchange (TSE) market over nine years, including the account data of traders (called virtual servers). The virtual server is a unit of trading accounts in the TSE market, and we can effectively define the trader IDs by an appropriate preprocessing. We apply a strategy clustering to individual traders to identify the order-splitting traders and the random traders. For most of the stocks, we find that the metaorder length distribution obeys power laws with exponent $α$, such that $P(L)\propto L^{"-α-1"}$ with the metaorder length $L$. By analysing the sign correlation $C(τ)\propto τ^{"-γ"}$, we directly confirmed the LMF prediction $γ\approx α-1$. Furthermore, we discuss how to estimate the total number of the splitting traders only from public data via the ACF prefactor formula in the LMF model. Our work provides the first quantitative evidence of the LMF model. ...

A causal interactions indicator between two time series using extreme variations in the first eigenvalue of lagged correlation matrices ArXiv ID: 2307.04953 “View on arXiv” Authors: Unknown Abstract This paper presents a method to identify causal interactions between two time series. The largest eigenvalue follows a Tracy-Widom distribution, derived from a Coulomb gas model. This defines causal interactions as the pushing and pulling of the gas, measurable by the variability of the largest eigenvalue’s explanatory power. The hypothesis that this setup applies to time series interactions was validated, with causality inferred from time lags. The standard deviation of the largest eigenvalue’s explanatory power in lagged correlation matrices indicated the probability of causal interaction between time series. Contrasting with traditional methods that rely on forecasting or window-based parametric controls, this approach offers a novel definition of causality based on dynamic monitoring of tail events. Experimental validation with controlled trials and historical data shows that this method outperforms Granger’s causality test in detecting structural changes in time series. Applications to stock returns and financial market data show the indicator’s predictive capabilities regarding average stock return and realized volatility. Further validation with brokerage data confirms its effectiveness in inferring causal relationships in liquidity flows, highlighting its potential for market and liquidity risk management. ...