Financial Time Series Models Research Articles

Comparative Performance of ARIMA and ARCH Models On Time Series of Monthly Libyan Brent Oil Price

Many economic and financial time series exhibit a phenomenon known as heteroscedastic, where the variance of the series changes over time. This research study focuses on financial time series modelling, with special application to modelling the price of Libyan Brent Oil. In particular, the theory of univariate nonlinear time series analysis is explored and applied to the price Libyan of Brent Oil, spanning from January 2000 to December 2010. The data was obtained from Bullent of the Platts Market Wire of Statistics. This study aims to evaluate the performance of ARIMA as a linear model and ARCH as a nonlinear modelling data. Multiple time series models were considered for fitting the data, and the best ARIMA models were selected based on the Akaike Information Criteria (AIC). ARIMA (0, 1, 1), and ARIMA (1, 1, 0) were identified as the best models. After estimating the parameters of the selected models, model checking revealed that these models were not suitable for modeling the data, as they lacked validity according to the test of squared residuals. The goodness of fit was assessed using the AIC, and based on minimum AIC values, the best fit ARCH models were found to be ARIMA (0, 1, 1) - ARCH (1). After estimating the parameters of the selected model, a series of diagnostic and forecast accuracy tests were performed. Based on this model, a twelve-month forecast of the price of Libyan Brent crude was made.

Latent level correlation modeling of multivariate discrete-valued financial time series

Latent level correlation modeling of multivariate discrete-valued financial time series

Exponential stochastic volatility model with Laplace returns and its variants

This paper explores the exponential stochastic volatility model generated by first-order exponential Markov sequences to model financial time series. The stationary exponential Markov sequences used to generate the volatility model are the linear exponential autoregressive model, minification model, new exponential autoregressive time series model, and an exponential mixture of autoregressive and minification processes. The statistical properties of the models are studied and the estimation of model parameters is carried out using the generalized method of moments. An approximate Kalman filtering method and a non-linear filtering approach are employed to diagnose the models. To verify the correctness of the estimations, simulation studies are conducted, and two real datasets are used to demonstrate how the models are applied. Furthermore, a comparison of the suggested models is performed using the measures root mean square error, mean absolute error, and Value at Risk via a backtesting procedure.

Block-diagonal idiosyncratic covariance estimation in high-dimensional factor models for financial time series

Estimation of high-dimensional covariance matrices in latent factor models is an important topic in many fields and especially in finance. Since the number of financial assets grows while the estimation window length remains of limited size, the often used sample estimator yields noisy estimates which are not even positive definite. Under the assumption of latent factor models, the covariance matrix is decomposed into a common low-rank component and a full-rank idiosyncratic component. In this paper we focus on the estimation of the idiosyncratic component, under the assumption of a grouped structure of the time series, which may arise due to specific factors such as industries, asset classes or countries. We propose a generalized methodology for estimation of the block-diagonal idiosyncratic component by clustering the residual series and applying shrinkage to the obtained blocks in order to ensure positive definiteness. We derive two different estimators based on different clustering methods and test their performance using simulation and historical data. The proposed methods are shown to provide reliable estimates and outperform other state-of-the-art estimators based on thresholding methods.

Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation

This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements.

Time series clustering based on latent volatility mixture modeling with applications in finance

Modeling financial time series data poses a significant challenge in the realm of time series analysis. The Autoregressive Conditional Heteroskedasticity (ARCH) model stands out as a potent tool for capturing time-varying volatility and heteroskedasticity in financial data. However, conventional ARCH models display sensitivity to departures from normality, leading to the development of extensions employing more flexible distributions. In this context, we propose a robust enhancement to the mixture of ARCH (MoARCH) model by integrating normal mean–variance mixture (NMVM) distributions to model component errors. The stochastic representation of the proposed model allows for a straightforward implementation of an Expectation Conditional Maximization Either (ECME) algorithm for obtaining Maximum Penalized Likelihood estimates (MPL). To thoroughly evaluate the model, we conduct four simulation studies to explore finite-sample properties, assess MPL estimators, scrutinize model robustness, and evaluate the accuracy of our proposal in fitting, clustering, and forecasting. Practical applications further highlight the effectiveness of our methodology, showcasing successful implementations across diverse real datasets.

Stock Market Price Prediction and Forecasting Using Stacked LSTM

Stock price movement is non-linear and complex. Several research works have been carried out to predict stock prices. Traditional approaches such as Linear Regression and Support Vector Regression were used but accuracy was not adequate. Researchers have tried to improve stock price prediction using ARIMA. Due to very high variations in stock prices, deep learning techniques are applied due to its proven accuracy in various analytics fields. Artificial Neural Network was deployed to predict stock prices but as stock prices are time-series based, recurrent neural network was applied to further improve prediction accuracy. Therefore, data scientists and analysts found that Deep Learning outperformed Machine Learning which is also proofed by all the collected research papers, and it is the most suitable methodologies to apply to the stock market forecasting domain. This paper explores different stacked LSTM Models for non-stationary financial time series in stock price prediction. This study is to predict stock market prices to make more acquaint and precise investment decisions. The experimental result will show that, this method can get quite accurate result, particularly effective in stock prediction. The proposed LSTM model will be designed to overcome gradient explosion, gradient vanishing, and save long-term memory. Firstly, The Model will have a comparative analysis between different LSTM models and integrating the model based on the result obtained from the analysis. The results will suggest that the developed stacked LSTM produces better predictive power and generalization. Key Words: stock market prediction, stacked LSTM, Deep Learning, Data pre-processing techniques, Data normalization, Neural Networks, Data Visualization, Training and Testing Set, Time series analysis, Predictive models, Future Forecasting.

Induced Garima Stochastic Volatility Models

In the present paper, a stochastic volatility model generated by a first-order induced Garima Markov sequence has been suggested for modeling financial time series. The statistical and probabilistic properties of the suggested model are studied, and the estimation of the model parameters is done using the generalized method of moments. Simulation studies and real data analysis aredone to demonstrate the applicability of the model. Also, the fit has been compared with an existing stochastic volatility model.

Application of ARIMA-GARCH-S model to short-term stock forecasting

The performance of the stock market in the financial domain profoundly impacts the economic well-being of many individuals. Thus, accurately predicting stock prices is an essential task. Although traditional financial time series models such as ARIMA and GARCH play a crucial role in predictions, they may fail to capture all the market dynamics. This study explores a composite model combining ARIMA, GARCH, and Stacking techniques (ARIMA-GARCH-S) to enhance the accuracy of predictions. The research data are derived from the stock closing price time series data of “Amazon” from June 29, 2020, to April 12, 2022, with 653 entries and “Caterpillar” from February 8, 2021, to October 21, 2022, with 621 entries. The model’s fitting performance is evaluated by comparing the fitting residual plots and variance graphs, while predictive performance is determined by comparing the MAPE, RMSE, and EC statistical metrics. The results indicate that the ARIMA-GARCH-S composite model has a significant predictive advantage over the ARIMA model. This finding not only offers a new avenue for model innovation but also provides financial market participants with a more precise and stable prediction tool, aiding them in making more informed investment decisions.

Power of Unit Root Tests Against Nonlinear and Noncausal Alternatives with an Application to the Brent Crude Oil Price

Abstract The increasing sophistication of economic and financial time series modelling creates a need for a test of the time dependence structure of the series which does not require a proper specification of the alternative. Indeed, the latter is unknown beforehand. Yet, the stationarity has to be established before proceeding to the estimation and testing of causal/noncausal or linear/nonlinear models as their econometric theory has been developed under the maintained assumption of stationarity. In this paper, we propose a new unit root test statistics which is both asymptotically consistent against all stationary alternatives and still keeps good power properties in finite sample. A large simulation study is performed to assess the power of our test compared to existing unit root tests built specifically for various kinds of stationary alternatives, when the true DGP is either causal or noncausal, linear or nonlinear stationary. Based on various sample sizes and degrees of persistence, it turns out that our new test performs very well in terms of power in finite sample, no matter the alternative under consideration. The proposed approach is illustrated using recent Brent crude oil price data.

Novel insights into the modeling financial time-series through machine learning methods: Evidence from the cryptocurrency market

Novel insights into the modeling financial time-series through machine learning methods: Evidence from the cryptocurrency market

A comparative study of error distributions in the GARCH model through a Monte Carlo simulation approach

Financial time series data are known to exhibit volatility clustering, which implies that the volatility of financial returns tends to persist over time. This phenomenon has significant implications for risk management and financial decision-making. To capture this volatility clustering effect, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is widely used. Through a Monte Carlo simulation experiment, the performance GARCH-type model with five different error distribution specifications were compared. The study found that the Skewed Generalized Error Distribution (SGED) was the most efficient and consistent distribution for modelling financial time series. The SGED outperformed the Normal, Student's t, GED, and skewed Student's t distributions in terms of goodness-of-fit, MSE, MAE and different sample sizes. The study suggests that the SGED may be more suitable for modelling financial time series with a GARCH-type specification in general contexts.

Theoretical Foundations and Implications of Neural Ordinary Differential Equations (Nodes) For Real-Time Portfolio Optimization

This paper embarks on a comprehensive exploration of the theoretical landscape surrounding the integration of Neural Ordinary Differential Equations (NODEs) into the domain of real-time portfolio optimization. The study commences by establishing the background and motivation for this research, shedding light on the challenges encountered in real-time portfolio management and the potential transformative role NODEs can play in addressing these challenges. The theoretical framework unfolds in a structured manner, encompassing critical facets of portfolio optimization theory. It delves into classical portfolio optimization methodologies, including the mean- variance framework and continuous-time stochastic control techniques. This solid theoretical foundation provides the basis for understanding the nuances of optimizing portfolio weights, expected returns, and risk measures. The heart of the research lies in the integration of NODEs, an innovative fusion of deep learning and differential equations, into the fabric of portfolio optimization. NODEs, with their adaptability and ability to model continuous- time dynamics, emerge as a potent tool for real-time portfolio rebalancing and decision-making. The study provides an in-depth overview of NODEs, elucidating their architecture and their application in modeling financial time series data. This theoretical journey leads to the exploration of practical implications. The study highlights the potential benefits of incorporating NODEs into portfolio management, including improved risk management, enhanced returns, and the capacity for adaptive asset allocation strategies. However, it also addresses the limitations and challenges associated with this integration, such as data quality issues and computational requirements. In conclusion, this research presents a theoretical framework that bridges the gap between deep learning and continuous-time financial models, offering a promising avenue for real-time portfolio optimization. The insights derived from this study serve as a foundation for future research and practical applications in navigating the intricate landscape of financial markets.

금융 시계열 예측 신경망에서의 과적합 완화를 위한 임의 증강 기법

Overfitting is one of the major challenges encountered when using neural network models for financial time series forecasting tasks. The nature of financial time series data, often sparser than in other fields, tends to exacerbate the symptoms of overfitting. In this study, we propose a method to alleviate overfitting in neural network-based time series forecasting tasks through a novel data augmentation algorithm. The neural network structure employed in this research is a Long Short-Term Memory (LSTM) recurrent network. The proposed method gradually reduces the learning rate during the training process, whilst randomly augmenting the training data. To validate the performance of the proposed algorithm, we divided the VIX Index, into four sections and performed cross-validation. When compared to a standard LSTM network without the application of our algorithm, we confirmed that the Root Mean Square Error (RMSE) was reduced by 23%, 34%, 32%, and 34% in each cross-validation section respectively.

A New Dagum-Cauchy{Exponential} Distribution

This study proposed a four-parameter continuous distribution, called the Dagum-Cauchy{Exponential} Distribution (DCED) for modelling financial time series returns using the generalized family of Cauchy distribution by Alzaatreh et al. [1]. Some structural properties of this new distribution such as quantile function, reliability measures and hazard function, and order statistics are obtained. The method of maximum likelihood estimation was proposed in estimating its parameters. Finally, the distribution was used to model some financial datasets adequately.

Long Memory and Volatility Models in Forecasting Exchange Rate of Nigerian Naira to United State Dollar

Financial time series such as stock prices, inflation rates, interest rates, and exchange rates are known to exhibit upward and downward trend and often possesses long memory and volatility behavior. These behaviors are crucial in the analysis, modeling and forecasting of time series data. Unfortunately, many analysts don’t take into consideration the consequences of long memory and volatility while modeling financial time series data. Therefore, this paper intends to examine the effect of long memory and volatility in forecasting Exchange Rate of Nigerian Naira-United State Dollar. The data used for this study is obtained from Central Bank of Nigeria’s website for the period of January 2002 to Feb 2020. Observations from time series and Autocorrelation function (ACF) plot shows that the data was not stationary. This was confirmed by the Augmented Dickey Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) unit root tests on the datasets. Fractional differencing was used to transform the series and ARFIMA(1,d,1) and ARFIMA(1,d,2) models were selected using AIC criterion. However, the residuals of these models were found to be serially correlated and heteroscedastic. These problems led to combining ARFIMA with GARCH model in order to adequately study long memory and volatility simultaneously. Therefore ARFIMA models were combined with GARCH(1,1) to form ARFIMA(1,d,1)-GARCH(1,1) and ARFIMA(1,d,2)- GARCH(1,1). The results of the forecast performance indicate that the best model is ARFIMA(1,d,2)– GARCH(1,1).

Financial Time Series Modelling Using Fractal Interpolation Functions

Time series of financial data are both frequent and important in everyday practice. Numerous applications are based, for example, on time series of asset prices or market indices. In this article, the application of fractal interpolation functions in modelling financial time series is examined. Our motivation stems from the fact that financial time series often present fluctuations or abrupt changes which the fractal interpolants can inherently model. The results indicate that the use of fractal interpolation in financial applications is promising.

Towards an efficient machine learning model for financial time series forecasting

Towards an efficient machine learning model for financial time series forecasting

Econometric Modelling of Financial Time Series

This paper examines the relationship between assets, capital, liabilities and liquidity in South Africa using the Johansen cointegration analysis and the GARCH model using times data for the period 02/2005 to 06/2018. The results obtained from the study suggests that the time series are integrated of order one, I(1). The findings from the Johansen cointegration test indicated that the variables have a long run cointegrating relationship. Furthermore, the results from the GARCH model revealed that the estimated model has statistically significant coefficients at 5% significance level. Additionally, results revealed that assets have a positive relationship with capital, liabilities and liquidity. This implies that a percentage increase in assets will result to a percentage increase in capital, liabilities and liquidity. The results also revealed that shocks decay quickly in the future and that the conditional variance is explosive. The diagnostic tests revealed that the estimated models show the characteristics of a well specified model. The recommendations for future studies were formulated. Keywords: ARCH model; Cointegration; Financial time series; GARCH model; VECM; Volatility

Unsupervised expectation-maximization algorithm initialization for mixture models: A complex network-driven approach for modeling financial time series

An efficient initialization of the Expectation-Maximization algorithm to estimate mixture models via maximum likelihood is proposed. A fully unsupervised network-based initialization technique is provided by mapping time series to complex networks using as adjacency matrix the Markov Transition Field associated to the time series. In this way, the optimal number of mixture model components and the vector of initial parameters can be directly obtained. An experiment conducted on financial times series with very different characteristics shows that our approach produces significantly better results if compared to conventional methods of initialization, such as K-means and Random, thus demonstrating the effectiveness of the proposed method.