Volatility Of Financial Time Series Research Articles

Volatility Analysis of Financial Time Series Using the Multifractal Conditional Diffusion Entropy Method

In this article, we introduce the multifractal conditional diffusion entropy method for analyzing the volatility of financial time series. This method utilizes a q-order diffusion entropy based on a q-weighted time lag scale. The technique of conditional diffusion entropy proves valuable for examining bull and bear behaviors in stock markets across various time scales. Empirical findings from analyzing the Dow Jones Industrial Average (DJI) indicate that employing multi-time lag scales offers greater insight into the complex dynamics of highly fluctuating time series, often characterized by multifractal behavior. A smaller time scale like t=2 to t=256 coincides more with the state of the DJI index than larger time scales like t=256 to t=1024. We observe extreme fluctuations in the conditional diffusion entropy for DJI for a short time lag, while smoother or averaged fluctuations occur over larger time lags.

Evolution of temporal fluctuation scaling exponent in nonstationary time series using supersymmetric theory of stochastic dynamics.

Temporal fluctuation scaling (TFS) is an emergent property of complex systems that relates the variance (Ξ_{2}) and the mean (M_{1}) from an empirical data set in the form Ξ_{2}∼M_{1}^{α_{TFS}}, where the dispersion (fluctuation) of the data has been described in terms of Ξ_{2}. At present, it has been shown that this law of complex systems has different multidisciplinary applications such as characterizing the market rate based on its exponent, explaining the spatial spread of a pandemic or measuring dispersion in a counting process, among others, if it is known how the average value M_{1} of a representative quantity in a system changes. Then, using the path integral formalism and Parisi-Sourlas method, we propose an extension of path integral formalism to understand the origin of the temporal fluctuation scaling and the evolution of its exponent over time in nonstationary time series. To this end, we first show how the probability of transition between two states of a stochastic variable x(t) can be expressed once it is known its cumulant generating function. Also, we introduce a nonlinear term in a cumulant generating function of the form H^{(n)}(p,t;γ)∼p^{n} to obtain a model where the nth moment of the probability distribution evolves arbitrarily. Subsequently, in order to reproduce the temporal fluctuation scaling, a linear combination of H^{(n)}(p,t;γ) with n∈{1,2} is used. Therefore this allows describing how the mean M_{1}(t) and the variance Ξ_{2}(t) of empirical time series evolve. Thence, an analytical expression is deduced for the evolution of the temporal evolution of the temporal fluctuation scaling exponent α_{TFS}(t). Likewise, the validity of the expression found for α_{TFS}(t) is verified with a toy model based on white noise. Finally, this approach is verified in two stock indices (Dow Jones and Sao Paulo stock index) and two currencies (GBP-USD and EUR-USD) with daily data. It is found that this approach accurately captures the evolution of the mean and variance of these four financial derivatives after contrasting the results with a coefficient of determination that depends on H^{(n)}(p,t;γ). Also, it is shown that the temporal fluctuation scaling exponent is a measure of uncertainty or volatility in financial time series.

High-Frequency Volatility Modeling of Chinese Agricultural Products Market Based on Garch-Type Models

The modeling of high-frequency volatility is of utmost importance in comprehending market dynamics and the characteristics of risk. The adoption of high-frequency volatility modeling in the agricultural sector has the potential to enhance risk management for food production enterprises through the utilization of hedging strategies to mitigate the impact of food price changes. The GARCH (Generalized Autoregressive Conditional Heteroskedasticity) class of models is well-suited for the analysis and prediction of volatility in financial time series. These models effectively capture the highest level of volatility observed in the time series data. Therefore, this research utilizes one-minute trade data of the Wind Agriculture Index (886045.WI) to examine the efficacy and predictability of several GARCH class volatility models. When it comes to fitting the data within the sample, the TGARCH model demonstrates superior performance compared to both the GARCH and EGARCH models. The fluctuations in the price changes of the Wind Agriculture Index exhibit characteristics of time variability and clustering, which can be attributed to the relatively low barriers for entry and exit in the agricultural planting sector. Simultaneously, within the agricultural market, an imbalance is observed whereby the influence of positive information on price volatility surpasses that of negative information.

Markov-switching threshold stochastic volatility models with regime changes

<abstract><p>This paper introduces a comprehensive class of models known as Markov-Switching Threshold Stochastic Volatility (MS-TSV) models, specifically designed to address asymmetry and the leverage effect observed in the volatility of financial time series. Extending the classical threshold stochastic volatility model, our approach expresses the parameters governing log-volatility as a function of a homogeneous Markov chain with a finite state space. The primary goal of our proposed model is to capture the dynamic behavior of volatility driven by a Markov chain, enabling the accommodation of both gradual shifts due to economic forces and sudden changes caused by abnormal events. Following the model's definition, we derive several probabilistic properties of the MS-TSV models, including strict (or second-order) stationarity, causality, ergodicity, and the computation of higher-order moments. Additionally, we provide the expression for the covariance function of the squared (or powered) process. Furthermore, we establish the limit theory for the Quasi-Maximum Likelihood Estimator (QMLE) and demonstrate the strong consistency of this estimator. Finally, a simulation study is presented to assess the performance of the proposed estimation method.</p></abstract>

Empirical analysis of stock prices based on ARIMA-GARCH

Although ARIMA time series model can grasp the dynamic law of financial time series well, it can not reflect the volatility characteristics of stock price. GARCH can reflect the volatility of financial time series well and is suitable for forecasting in financial field. Taking the closing price of Shanghai Dazhong Public Utilities (dzgy) from January 2, 2019 to December 31, 2021 and using R , ARIMA-GARCH is proposed and the predictive analysis is carried out. The results show that ARIMA-GARCH has a good effect in short-term stock prediction, and has certain reference value and practical significance.

An Empirical Study on Yield Volatility of Cryptocurrencies

With the rapid development of cryptocurrencies, the volatility characteristics of their yields have received more and more attention. At the same time, many empirical studies show that the GARCH family model is more effective in describing the volatility of financial time series. Firstly, this paper briefly introduces the research background of cryptocurrency and the research method using GARCH model. Next, the daily rate of return is calculated and descriptive statistical analysis is carried out on the collected closing price data of cryptocurrency, and on this basis, the GARCH model is constructed for empirical test to explore the volatility characteristics of its rate of return. Then the corresponding research conclusions and relevant policy recommendations are given.

A semiparametric approach to the detection of change-points in volatility dynamics of financial data

Volatility is one of the most important features of financial time series data. There are often structural changes in volatility over time, and an accurate estimation of the volatility of financial time series requires careful identification of change-points. A common approach to modeling the volatility of time series data is based on the well-known GARCH model. Although the problem of change-point estimation of volatility dynamics derived from the GARCH model has been considered in the literature, these approaches rely on parametric assumptions of the conditional error distribution, which are often violated in financial time series. This may lead to inaccuracies in change-point detection, resulting in unreliable GARCH volatility estimates. This article introduces a novel change-point detection algorithm based on a semiparametric GARCH model. The proposed method retains the structural advantages of the GARCH process while incorporating the flexibility of nonparametric conditional error distribution. The approach utilizes a penalized likelihood derived from a semiparametric GARCH model and an efficient binary segmentation algorithm. The results show that in terms of change-point estimation and detection accuracy, the semiparametric method outperforms the commonly used Quasi-MLE (QMLE) and other variations of the GARCH models in wide-ranging scenarios.

An Efficient GAN-Based Multi-classification Approach for Financial Time Series Volatility Trend Prediction

Deep learning has achieved tremendous success in various applications owing to its robust feature representations of complex high-dimensional nonlinear data. Financial time-series prediction is no exception. Hence, the volatility trend prediction in financial time series (FTS) has been an active topic for several decades. Inspired by generative adversarial networks (GAN), which have been studied extensively in image processing and have achieved excellent results, we present the ordinal regression GAN for financial volatility trends (ORGAN-FVT) method for the end-to-end multi-classification task of FTS. An improved generative model based on convolutional long short-term memory (ConvLSTM) and multilayer perceptron (MLP) is proposed to capture temporal features effectively and mine the data distribution of volatility trends (short, neutral, and long) from given FTS data. Meanwhile, ordinal regression is leveraged for the discriminator to improve the multi-classification performance, making the model more practical. Finally, we empirically compare ORGAN-FVT with several state-of-the-art approaches on three real-world stock datasets: MICROSOFT(MSFT), Tesla(TSLA), and The People’s Insurance Company of China(PAICC). ORGAN-FVT demonstrated significantly better AUC and F1 scores, at most 20.81% higher than its competitors.

On the asymmetry in the volatility of financial time series: a buffered transition approach

ABSTRACT In this paper, we propose a new threshold model to deal with the asymmetry and leverage effect in the volatility of financial time series. Our model generalizes the classical threshold stochastic volatility model. By introducing a new flexible and smooth regime-switching mechanism, we avoid the sudden jump in the log-volatility imposed by the classical model. More precisely, we propose a new threshold model that we call Buffered Threshold Stochastic Volatility (BTSV) model. After the definition of our model, we derive a sufficient condition for the strict stationarity of the model. Then, we develop a Sequential Monte Carlo method to estimate the parameters. Next, we analyse the performance of the proposed method through a simulation study. Finally, we apply our new methodology to model the Honeywell International Inc and Standard and Poor Composite 500 stock market indices. This empirical analysis shows that BTSV model is a competitive alternative for the asymmetry modelling in financial returns analysis.

The role of China's crude oil futures in world oil futures market and China's financial market

China's crude oil futures (COF) denominated in RMB were formally launched in 2018 and traded in the Shanghai International Exchange (INE), which was an important milestone in China's energy financialization. Combining TVP-VAR method and DY spillover index, this paper firstly studied the information spillover relationship between the world's major COF and crude oil spot (COS) markets before and after the launch of China's COF. It is found that China's COF mainly play the role of net information receiver in world COF/COS market, and its influence in international market and price discovery function needs to be improved. Further, this paper comprehensively considered China's financial system, taking volatility of financial time series as risk proxy to investigate the risk spillover effect. The results show that the financial attributes of China's COF have become prominent. The dynamic analysis shows that since the launch of China's COF, the degree of its net spillover to other markets has generally been on the decrease, assuming a net risk transmitter role. On this basis, this paper puts forward policy recommendations to promote the development of China's COF.

A Hybrid Model Combining a Gated Recurrent Unit Network Based on Variational Mode Decomposition with Error Correction for Stock Price Prediction

Due to the nonlinearity and high volatility of financial time series, hybrid forecasting systems combining linear and nonlinear models can provide more precise performance than a single model. Therefore, this study proposes a hybrid stock price forecasting model with error correction based on secondary decomposition. The modules of data decomposition, a prediction module and an error correction module constitute the overall framework of the model proposed in this paper. First, variational mode decomposition (VMD) decomposes the original stock closing price data and the initial prediction error sequence. Second, a gated recurrent unit (GRU) neural network model is selected to predict the original subseries. Finally, a new hybrid model consisting of the VMD method combined with an autoregressive integrated moving average (ARIMA) model is established to correct the error subseries. The proposed model is verified through four financial time series. The results show that (a) The combination of the VMD method and GRU network has a better prediction effect than a single model. (b) The combination of the VMD method and ARIMA method can effectively amend the error sequence and improve the prediction accuracy. (c) Error correction to the hybrid model has a great effect on improving the prediction performance of the model. The empirical results have illustrated that the proposed model indeed displays a good performance in forecasting stock market fluctuations compared with other baseline methods.

A new frontier for studying within-person variability: Bayesian multivariate generalized autoregressive conditional heteroskedasticity models.

Research on individual variation has received increased attention. The bulk of the models discussed in psychological research so far, focus mainly on the temporal development of the mean structure. We expand the view on within-person residual variability and present a new model parameterization derived from classic multivariate GARCH models used to predict and forecast volatility in financial time-series. We propose a new pdBEKK and a modified dynamic conditional correlation (DCC) model that accommodate external time-varying predictors for the within-person variance. The main goal of this work is to evaluate the potential usefulness of MGARCH models for research in within-person variability. MGARCH models partition the within-person variance into, at least, 3 components: An overall constant and unconditional baseline variance, a process that introduces variance conditional on previous innovations, or random shocks, and a process that governs the carry-over effects of previous conditional variance, similar to an AR model. These models allow for variance spillover effects from one time-series to another. We illustrate the pdBEKK- and the DCC-MGARCH on two individuals who have rated their daily positive and negative affect over 100 consecutive days. The full models comprised a multivariate ARMA(1,1) model for the means and included physical activity as moderator of the overall baseline variance. Overall, the pdBEKK seems to result in a more straightforward psychological interpretation, but the DCC is generally easier to estimate and can accommodate more simultaneous time-series. Both models require rather large amounts of datapoints to detect nonzero parameters. We provide an R-package bmgarch that facilitates the estimation of these types of models. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Volatility Analysis in International Indices

Modeling and the estimation of volatility in financial time series are important research subjects for which ARCH family models are recommended. These models are widely used to analyze volatility and manage risk in financial assets. In this study, share indices from the BRIC countries, Europe and the United States were analyzed to determine volatility in international indices. Current data was used to examine the period 1982-2021. Within this framework, the existence of asymmetric information, the leverage effect and the permanence of shocks were examined. Estimation results show the existence of asymmetric information. Bad news affects the system more than good news. The leverage effect is also experienced. Estimation results show that the shocks affecting the system are permanent. At the last stage, static foresight estimations were conducted on the explanatory power of the estimation results. Static foresight estimations present strong and weak evidence together. All parameters are statistically significant.

The exponentiated half logistic skew-t distribution with GARCH-type volatility models

Most financial time series have non-normal features such as heavy tails, excess kurtosis and skewness. Financial asset returns volatility is also a significant measure in financial decisions, option pricing, risk management, and portfolio selection, so it is important to create vigorous driven conditional innovation density for GARCH-type volatility models for investigating volatility in financial time series. In this research, a new exponentiated half logistic skew-t (EHLST) innovation distribution for fitting generalized autoregressive conditional heteroskedasticity (GARCH)-type models is proposed. Structural properties of the proposed distribution such as density and distribution functions, quantile function and raw moments were derived. The maximum likelihood estimation criterion discussed is to estimate the parameters of the proposed distribution via a simulation study and real-life dataset. Application on Bitcoin digital-currency price index log-returns was carried-out to inspect the performance of the GARCH-type models with EHLST innovation density relative to five innovation densities in volatility modeling. The research results showed that the GARCH-EHLST model was selected as the best for the BTC log-returns conditional variance. More so, three forecasts performance measures were used to compare the out-of-sample performance of the models, and the GARCH-EHLST model outperformed the other models in terms of superior volatility predictive capability.

Reducing Overestimating and Underestimating Volatility via the Augmented Blending-ARCH Model

SVR-GARCH model tends to “backward eavesdrop” when forecasting the financial time series volatility in which case it tends to simply produce the prediction by deviating the previous volatility. Though the SVR-GARCH model has achieved good performance in terms of various performance measurements, trading opportunities, peak or trough behaviors in the time series are all hampered by underestimating or overestimating the volatility. We propose a blending ARCH (BARCH) and an augmented BARCH (aBARCH) model to overcome this kind of problem and make the prediction towards better peak or trough behaviors.The method is illustrated using real data sets including SH300 and S&P500. The empirical results obtained suggest that the augmented and blending models improve the volatility forecasting ability.

Bounded area as a measure of volatility for financial time series

This article presents a new way to measure the volatility of financial time series, which is shown to be on a par with arc length for such endeavors. An application involving the clustering of 30 prominent stocks is presented as well.

Reducing Overestimating and Underestimating Volatility via the Augmented Blending-ARCH Model

SVR-GARCH model tends to "backward eavesdrop" when forecasting the financial time series volatility in which case it tends to simply produce the prediction by deviating the previous volatility. Though the SVR-GARCH model has achieved good performance in terms of various performance measurements, trading opportunities, peak or trough behaviors in the time series are all hampered by underestimating or overestimating the volatility. We propose a blending ARCH (BARCH) and an augmented BARCH (aBARCH) model to overcome this kind of problem and make the prediction towards better peak or trough behaviors. The method is illustrated using real data sets including SH300 and S&P500. The empirical results obtained suggest that the augmented and blending models improve the volatility forecasting ability.

Modeling time‐varying higher‐order conditional moments: A survey

AbstractSince the introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model, the literature on modeling the time‐varying second‐order conditional moment has become increasingly popular in the last four decades. Its popularity is partly due to its success in capturing volatility in financial time series, which is useful for modeling and predicting risk for financial assets. A natural extension of this is to model time variation in higher‐order conditional moments, such as the third and fourth moments, which are related to skewness and kurtosis (tail risk). This leads to an emerging literature on time‐varying higher‐order conditional moments in the last two decades. This paper outlines recent developments in modeling time‐varying higher‐order conditional moments in the economics and finance literature.Using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) framework as a foundation, this paper provides an overview of the two most common approaches for modeling time‐varying higher‐order conditional moments: autoregressive conditional density (ARCD) and autoregressive conditional moment (ARCM). The discussion covers both the theoretical and empirical aspects of the literature. This includes the identification of the associated skewness–kurtosis domain by using the solutions to the classical moment problems, the structural and statistical properties of the models used to model the higher‐order conditional moments and the computational challenges in estimating these models. We also advocate the use of a maximum entropy density (MED) as an alternative method, which circumvents some of the issues prevalent in these common approaches.

The volatility in financial time series based on granule complex network

The volatility is one of the essential characteristics of financial time series, which is vital for the knowledge acquisition from financial data. However, since the high noise and nonsteady features, the volatility identification of financial time series is still a challenging problem. In this paper, from a perspective of granule complex network, a novel approach is proposed to study this problem. First, numeric time series is structured into fuzzy information granules (FIGs), where the segments of time series in each granule would own similar volatility features. Second, by using the transfer relations among granules, granule complex network is to be constructed, which intuitively describes the transfer processes among the different volatility patterns. Third, a novel community detection algorithm is applied to divide the granule complex networks, where granules with frequent mutual transfers would belong to the same granule community. Finally, Markov chain model is carried out to analyze the higher level of transfer processes among different granule communities, which would further describe the larger-scale transitions of volatility in overall financial time series. An empirical study of the proposed system is applied in the Shanghai stock index market, where volatility patterns of financial data can be effectively acquired and the corresponding transfer processes can be analyzed by means of the granule communities.

Volatility of cryptocurrencies

Many models have been developed to model, estimate and forecast financial time series volatility, amongst which are the most popular autoregressive conditional heteroscedasticity (ARCH) model introduced by Engle (1982) and generalized autoregressive conditional heteroscedasticity (GARCH) model introduced by Bollerslev (1986). The aim of this paper is to determine which type of ARCH/GARCH models can fit the best following cryptocurrencies: Ethereum, Neo, Ripple, Litecoin, Dash, Zcash and Dogecoin. It is found that the EGARCH model is the best fitted model for Ethereum, Zcash and Neo, PARCH model is the best fitted model for Ripple, while for Litecoin, Dash and Dogecoin it depends on the selected distribution and information criterion.