Time-Reversal Asymmetry

Identifying events in financial time series – A new approach with bipower variation

Financial time series data is a cornerstone of investment strategy development, providing critical insights into market trends, asset performance, and risk assessment. This research explores the application of advanced statistical and machine learning models for analyzing financial time series data to optimize investment strategies. The study examines various techniques, including autoregressive integrated moving average (ARIMA), GARCH models for volatility forecasting, and recurrent neural networks (RNNs) for capturing temporal dependencies in financial data. By leveraging these models, the research aims to enhance the prediction of market behavior and identify profitable investment opportunities. It also investigates the integration of feature engineering and real-time data processing to improve model accuracy and adaptability. Challenges such as overfitting, non-stationarity, and the unpredictability of financial markets are addressed, along with the importance of ethical considerations in data-driven decision-making. The findings provide actionable insights into the effective use of financial time series models, offering a robust framework for data-driven investment strategy optimization.

The log‐returns of most financial assets exhibit bursts of outlying observations that are characteristic of heavy tails. As such, models formulated for financial time series must capture heavy‐tailedness. Regular variation is a natural and often used concept to describe and model heavy‐tailed phenomena. This article first provides some evidence for heavy tails in log‐returns and then describes the basics of regular variation. It turns out that the two most commonly used models for financial time series, the GARCH and heavy‐tailed stochastic volatility (SV) processes, have finite‐dimensional distributions that are regularly varying. Regular variation is also a powerful tool for deriving large sample properties of important statistics of financial time series, from maxima to sample autocorrelations of functions of the process. These techniques show that although GARCH and SV processes share many common features, there can be a substantial difference in the large sample properties of the maxima and sample autocorrelations.

Many studies tried to apply machine learning (ML) methods to forecast the financial time series during the past decade. Moreover, the emergence of deep learning has led to another researches with results that significantly outperform previous models. However, most of the deep learning researches used the raw financial time series price data which consists of open, close, high and low (OCHL) as learning features. According to statistics, Long Short Term Memory networks (LSTM) is the first choice to deal with the forecasting problems with OCHL datasets due to its feedback connection networks, resulting higher performances for price series prediction. Meanwhile, Convolutional Neural Networks (CNN) has increased its popularity since it outperforms traditional ML models in classification problems. In this paper, there are three types of future trend that are the ultimate targets to be discovered. Nevertheless, OCHL features may be too sensitive to learn the large future trend in financial time series. This study proposes a novel approach: Convolutional Neural Networks with Market Profiles (CNN-MPs) which includes (1) adapting Market Profile to covert financial time series data to grey-scale image method, (2) generating two types of learning images: stacked and sequential profile that can keep the interaction between continuous profiles, and (3) learning the structure of price activities with CNN. Market Profile is a concept that has been widely used in the financial decision-making by comparing the current price with the market fair value. In addition, the trend is well established at the accepting movement of fair value which can be confirmed from the structure of profiles. In experiments, one of the popular commodities, corn was selected to evaluate the proposed method. And the experimental results show that proposed sequential profile method obtained 17% higher accuracy and more profitability than LSTM networks and other methods. Therefore, the proposed CNN-MPs method can effectively discover the trend of corn providing those who need import corn with a reference.

In this paper, based on the characteristics of real-time and time characteristics of financial data, time series is used as an entry point to mine financial data. Using the trigonometric polynomial graph method, the visualization of financial and economic cube data and the definition of clustering distance are carried out. Combined with wavelet analysis theory to decompose the periodic, trend and random terms of financial data time series, so as to predict the development of financial data with different scale components. In addition, BIRCH method is utilized to construct CF tree through data clustering features for micro-clustering of financial data. And K-meadiods method is chosen to fill the gap of BIRCH method in the application of large datasets to realize the macro-clustering of financial and economic data, and to establish BIRCH.K-meadiods clustering method. Compared with similar models, the prediction and clustering model of financial data based on time series has an overlap rate of >99.00% between the predicted and actual values of financial data and an error in the interval of (0,300), which can assist in the in-depth mining and clustering analysis of the value of financial data with high-precision prediction, and expand the level of decision-making considerations for the internal management of the enterprise and even for the external construction.

This paper studies the portfolio optimization of mean-variance utility with state-dependent risk aversion, where the stock asset is driven by a stochastic process. The sub-game perfect Nash equilibrium strategies and the extended Hamilton-Jacobi-Bellman equations have been used to derive the system of non-linear partial differential equations. From the economic point of view, we demonstrate the numerical evaluation of the suggested solution for a special case where the risk aversion rate is proportional to the wealth value. Our results show that the asset driven by the stochastic volatility process is more general and reasonable than the process with a constant volatility.

An effective similarity measure approach on specific data sets is becoming the focus in time series data mining. To solve the problem that financial time series are lacking dynamic information of trend after they are deal with dimension reduction with SAX, in this work we propose a novel similarity measure function, Composite-Distance-Function which joins point-distance advantages and trend-distance advantages together. Through the experiments of SAX with different distance function, we prove that Composite-Distance-Function is a useful function which provides new ideas to reveal the interdependence between the financial data and helps to solve the problem of time series similarity.

Mining of scalable patterns hidden in financial time series is a challenging pattern recognition task in nature. Patterns of price movements in financial time series are highly scalable and highly dimensional, making pattern recognition in time series a computational complex data mining effort. Thus, data representation plays a very crucial role in ensuring the effectiveness of time series pattern recognition algorithm. A robust data representation technique not only reduces the dimensionality of the original time series data, but also retains the critical features of the original time series. This study proposes a dynamic time interval data representation approach that adapts to the nature of price movement in financial time series. Since the interval is determined by the price movement magnitude, the proposed data representation approach is more responsive in capturing the major price movements, yet maintaining its agenda in reducing the dimensionality of the raw financial time series data.

Objectives: This research study presents a forecasting model that integrates an efficient discrete wavelet transform and a Backpropagation Neural Network (BPNN) for predicting financial time series. Methods/Statistical analysis: The presented model uses the wavelet transform at several time instances based on local smooth B-Spline wavelets of order d(BSd) to decompose the financial time series data. So, an approximation (long-term trends) component and several details (shortterm deviations) components are obtained. Since the details components act as a complementary part of the approximation component, to prepare a prediction model which applies all decomposed components is very advantageous. Therefore, all components are used as smooth input samples of the neural network to forecast the future of the financial time series. Findings: The proposed model is designed to forecast the stock prices of five different companies, and according to the obtained results, the presented model outperforms a conventional model that uses only the approximation component as a wavelet de-noising-based model. The numerical results have shown the prediction accuracy. Applications/Improvements: The proposed model can predict future stock prices better than the de-noised based model in nearly 70%cases. Keywords: B-Spline Wavelets Multiresolution, Back Propagation Neural Network, Financial Time Series, Stock Market Prediction

In this paper, we develop a new Hybrid method based on machine learning algorithms for jump detection in financial time series. Jump is an important behavior in financial time series, since it implies a change in volatility. Ones can buy the volatility instrument if ones expect the volatility will bloom up in the future. A jump detection model attempts to detect short-term market instability, since it could be jumping up or down, instead of a directional prediction. The directional prediction can be considered as a momentum or trend following, which is not the focus of this paper. A jump detection model is commonly applied in a systematic fast-moving strategy, which reallocates the assets automatically. Also, a systematic opening position protection strategy can be driven by a jump detection model. For example, for a tail risk protection strategy, a pair of long call and put option order could be placed in the same time, in order to protect the open position given a huge change in volatility. One of the key differentiations of the proposed model with the classical methods of time-series anomaly detection is that, jump threshold parameters are not required to be predefined in our proposed model. Also the model is a combination of a Long short-term memory (LSTM) neural network model and a machine learning pattern recognition model. The LSTM model is applied for time series prediction, which predicts the next data point. The historical prediction errors sequence can be used as the information source or input of the jump detection model/module. The machine learning pattern recognition model is applied for jump detection. The combined model attempts to determine whether the current data point is a jump or not. LSTM neural network is a type of Recurrent Neural Networks (RNNs). LSTM records not only the recent market, but also the historical status. A stacked RNN is trained on a dataset which is mixed with normal and anomalous data. We compare the performance of the proposed Hybrid jump detection model and different pattern classification algorithms, such as k-nearest neighbors algorithm identifier, Hampel identifier, and Lee Mykland test. The model is trained and tested using real financial market data, including 11 global stock market in both developed and emerging markets in US, China, Hong Kong, Taiwan, Japan, UK, German, and Israel. The experiment result shows that the proposed Hybrid jump detection model is effective to detect jumps in terms of accuracy, comparing to the other classical jump detection methods.

OBST-based segmentation approach to financial time series

Financial time series forecasting poses significant challenges due to the diverse risk profiles and dynamic behaviors of assets such as the S&P 500, NASDAQ, and Bitcoin, especially across different market periods. This study introduces a novel framework, waveletstochastic-chaos informed machine learning, that integrates wavelet transforms, stochastic processes, and chaos theory to improve machine learning prediction accuracy over a decade (2015–2025). The analysis is divided into four distinct periods: All Time, PreCOVID, COVID, and Post-COVID. The aim is to capture the multi-scale patterns, volatility, and complexity inherent in financial data, which will be assessed across various market conditions. The framework outperforms the baseline maximum likelihood models in most scenarios, achieving significant root mean squared errors for the scaled price predictions of S&P 500 (e.g., from 0.0348 to 0.0122 in All Time), NASDAQ (e.g., from 0.0284 to 0.0180 in All Time) and Bitcoin (e.g., from 0.0838 to 0.0288 in All Time) based on 1000 experimental trials. It excels in volatile periods like COVID and for high-risk Bitcoin, though it slightly underperforms in the stable Post-COVID recovery for S&P 500. Wavelet features are found to be critical for accuracy. Additionally, stochastic and chaos-based elements enhance performance in volatile and complex contexts, respectively, as confirmed by ablation studies. This study provides empirical evidence of predictive utility for financial time-series forecasting in assets with different dynamics and market regimes. The results indicate that multi-scale, stochastic, and complexity-based feature representations can improve forecasting performance within the examined datasets, suggesting that the framework may apply to other non-stationary time-series settings, although such extensions remain for future investigation.

Associating stock prices with web financial information time series based on support vector regression

Chaos and nonlinear theory has significant impact on the analysis of economic and financial time series. Nonlinearity plays an important role in explaining the empirical features of asymmetric business cycles, clustered volatility, and regime switching in finance data. In this Chapter, we will focus the popular local polynomial prediction method and its applications to chaotic time series prediction and financial volatility estimation. Volatility and conditional covariance estimation is important in many aspects of modern finance theory. We introduce a nonparametric volatility model, called local ARCH, and propose a weighted least square method for goodness of fit. The statistical theory is based on a martingale regression framework developed in Lu (1999a,b), which includes a wide variety of nonlinear time series models, such as nonlinear autoregression, ARCH, and nonlinear vector autoregressive models. The daily AOL stock data is used as an example to illustrate the developed techniques. First, we apply the nonlinear regression procedure to model the spread-volume relationship—We find a nice power-law relationship in all appropriate periods after discovering that the spurious nonlinearity in the overall data is due to nonstationarity. We also find a vastly changing structure in GARCH models fitted to different parts of the return rate series based on closing prices. We apply the developed local ARCH theory to a stationary subseries of the return series, and find some encouraging results.

Essays in Macroeconomics and Finance Kyle Jurado This dissertation contains three essays in macroeconomics and finance. Chapter 1 estimates the relative importance of agents receiving advance information or having distorted beliefs about future fundamentals in explaining a set of macroeconomic and financial data. Chapter 2 proposes a new measure of time-varying aggregate uncertainty, which is based on information from a large panel of macroeconomic and financial time series. Chapter 3 explores how imposing risk constraints on financial intermediaries in a continuous-time heterogeneous-agent economy can affect equilibrium allocations and asset price dynamics. Fluctuations in the beliefs of economic agents can be driven by current fundamentals, advance information about future fundamentals, or distortions resulting from informational or psychological limitations. Chapter 1 presents a dynamic stochastic general equilibrium (DSGE) model that jointly considers all three possibilities and estimates their relative importance for explaining macroeconomic and financial data. In the model, agents’ beliefs are based on a subjective probability measure that can be stochastically distorted relative to the objective measure. By directly parameterizing the Radon-Nikodým process linking these two measures, it is possible to solve the model under the subjective measure and change back to the objective measure for estimation. To help the model jointly explain macroeconomic and financial data, it features recursive preferences alongside a number of more standard business-cycle frictions. To facilitate estimation, a solution method is presented that allows risk premia to affect the model’s linear-approximate dynamics. To discipline the estimates, direct data on subjective forecasts is included in the set of observable variables. Results indicate that both advance information and distorted beliefs are important. On average about two-thirds of the fluctuations in endogenous variables can be attributed to these two sources. While they are equally important for explaining output and employment, advance information is most important for explaining inflation and investment, and distorted beliefs are most important for explaining stock returns and consumption. Chapter 2 exploits a data rich environment to provide direct econometric estimates of time-varying macroeconomic uncertainty. The estimates display significant independent variations from popular uncertainty proxies, suggesting that much of the variation in the proxies is not driven by uncertainty. Quantitatively important uncertainty episodes appear far more infrequently than indicated by popular uncertainty proxies, but when they do occur, they are larger, more persistent, and more correlated with real activity. The estimates provide a benchmark to evaluate theories for which uncertainty shocks play a role in business cycles. Finally, Chapter 3 studies the general equilibrium effects of introducing a Value-at-Risk (VaR) constraint into a dynamic continuous-time economy with homogeneous preferences, inefficient endogenous volatility, fire sales, and economically valuable financial intermediation. The main finding is that through its impact on the stationary distribution of wealth in the economy, a VaR constraint can reduce the average level of endogenous volatility and lower the probability of entering a crisis regime. It does so by forcing agents to sell off their risky asset holdings earlier than they otherwise would, while they still have a large equity buffer to absorb losses. This chapter is the first study to explore the effects of a VaR constraint in a model that does not feature any heterogeneity in preferences or beliefs, and in which endogenous volatility and crises are socially inefficient.