Volatility Of Time Series Research Articles

Prediction of fire danger index using a new machine learning based method to enhance power system resiliency against wildfires

AbstractWildfires, which can cause significant damage to power systems, are mostly inevitable and unpredictable. Fire danger indexes, such as the Forest Fire Danger Index (FFDI) and the Canadian Fire Weather Index (FWI), measure the potential wildfire danger at a given time and location. Thus, by predicting these fire danger indexes in advance, power system operators can obtain valuable insight into the potential wildfire risks and can better be prepared to tackle the wildfires. However, due to dependency on weather conditions, these indexes usually have volatile time series, which make their prediction complex. Taking these facts into account, this paper, unlike previous approaches that predict fire danger indexes based on climatological models, develops a machine learning‐based forecast process to predict these indexes using the relevant weather data and past performance. To do this, first, a volatility analysis approach is presented to analyse the volatility level of the time series data of a fire danger index. Afterwards, an effective machine learning‐based forecast methodology using a new deep feature selection model is proposed to predict fire danger indexes. The developed forecast methodology is tested on the real‐world data of FFDI and FWI and is compared with several popular alternative methods reported in the literature.

Predicting the volatility of Chinese stock indices based on realized recurrent conditional heteroskedasticity.

The realized recurrent conditional heteroscedasticity (RealRECH) model improves volatility prediction by integrating long short-term memory (LSTM), a recurrent neural network unit, into the realized generalized autoregressive conditional heteroskedasticity (RealGARCH) model. However, at present, there is no literature on the ability of the RealRECH model to fit and predict volatility in the Chinese market. In this paper, a study is conducted to test the in-sample explainability and out-of-sample prediction ability of the RealRECH model for the SSE50, CSI300, CSI500 and CSI1000 indices in the Chinese market and to determine whether it performs better than the RealGARCH model. The results of the in-sample analysis show that the RealRECH model not only provides better in-sample interpretability for all four indices but also captures the complex dynamics of time series volatility that the RealGARCH model cannot capture, such as long-term dependence and nonlinearity. The results of out-of-sample volatility prediction show that the RealRECH model better predicts the volatility of the CSI500 and CSI1000 indices but yields worse predictions for the SSE50 and CSI300 indices. Thus, the RealRECH model can be used for CSI500 and CSI1000 prediction.

Quantifying the Uncertainty of Reservoir Computing: Confidence Intervals for Time-Series Forecasting

Recently, reservoir computing (RC) has emerged as one of the most effective algorithms to model and forecast volatile and chaotic time series. In this paper, we aim to contribute to the understanding of the uncertainty associated with the predictions made by RC models and to propose a methodology to generate RC prediction intervals. As an illustration, we analyze the error distribution for the RC model when predicting the price time series of several agri-commodities. Results show that the error distributions are best modeled using a Normal Inverse Gaussian (NIG). In fact, NIG outperforms the Gaussian distribution, as the latter tends to overestimate the width of the confidence intervals. Hence, we propose a methodology where, in the first step, the RC generates a forecast for the time series and, in the second step, the confidence intervals are generated by combining the prediction and the fitted NIG distribution of the RC forecasting errors. Thus, by providing confidence intervals rather than single-point estimates, our approach offers a more comprehensive understanding of forecast uncertainty, enabling better risk assessment and more informed decision-making in business planning based on forecasted prices.

Statistical inference for the first-order autoregressive process with the fractional Gaussian noise

While the statistical inference of first-order autoregressive processes driven by independent and identically distributed noises has a long history, the statistical analysis for first-order autoregressive processes driven by dependent noises is more recent. This paper considers the problem of estimating all the unknown parameters in first-order autoregressive processes driven by the fractional Gaussian noise, which is a self-similar stochastic process used to model persistent or anti-persistent dependency structures in observed time series. The estimation procedure is built upon the marriage of the log-periodogram regression and the method of moments. The usual asymptotic properties, including consistency and asymptotic normality, are established under some mild conditions. Monte Carlo simulations are performed to demonstrate the feasibility and effectiveness of the proposed method. Finally, the estimation methods are applied to model some realized volatility time series, where we find that the realized volatility is rough. Moreover, the proposed model is compared with some alternative models, including the first-order autoregressive process driven by the standard Gaussian noise, the heterogeneous autoregression model with lag structure (1,5,21) (HAR(1,5,21)), the autoregressive fractionally integrated moving average model (ARFIMA(1,d,0)) and the scaled fractional Brownian motion, in forecasting the logarithmic realized volatility.

Analyzing the Selective Stock Price Index Using Fractionally Integrated and Heteroskedastic Models

Stock market indices are important tools to measure and compare stock market performance. The Selective Stock Price (SSP) index reflects fluctuations in a set value of financial instruments of Santiago de Chile’s stock exchange. Stock indices also reflect volatility linked to high uncertainty or potential investment risk. However, economic shocks are altering volatility. Evidence of long memory in SSP time series also exists, which implies long-term persistence. In this paper, we studied the volatility of SSP time series from January 2010 to September 2023 using fractionally heteroskedastic models. We considered the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) innovations—the ARFIMA-GARCH model—for SSP log returns, and the fractionally integrated GARCH, or FIGARCH model, was compared with a classical GARCH one. The results show that the ARFIMA-GARCH model performs best in terms of volatility fit and predictive quality. This model allows us to obtain a better understanding of the observed volatility and its behavior, which contributes to more effective investment risk management in the stock market. Moreover, the proposed model detects the influence volatility increments of the SSP index linked to external factors that impact the economic outlook, such as China’s economic slowdown in 2012 and the subprime crisis in 2008.

Enhancing Multi-step Brent Oil Price Forecasting with Ensemble Multi-scenario Bi-GRU Networks

Accurate crude oil price forecasting is crucial for economic stability, investment planning, and strategic decision-making across various industries. Despite numerous research efforts in applying deep learning to time-series forecasting, achieving high accuracy in multi-step predictions for volatile time-series like crude oil prices remains a significant challenge. Moreover, most existing approaches primarily focus on one-step forecasting, and the performance often varies depending on the dataset and specific case study. This paper introduces ensemble-based deep-learning models to capture Brent oil price volatility and enhance the multi-step price prediction. Our methodology employs a two-pronged approach. First, we present an empirical comparison of deep-learning models and architectures, including RNNs, CNNs, and transformers, for forecasting Brent oil prices. We also examine the impact of various external factors on forecasting accuracy. Then, we introduce a novel approach that employs ensemble GRU-based models to enhance prediction accuracy across multiple forecasting scenarios. Extensive experiments were conducted using a dataset of historical Brent prices encompassing the COVID-19 pandemic, which significantly impacted energy markets. The results demonstrate that the proposed model outperforms benchmark and established models, achieving a 9.3% reduction in MSE compared to the closest benchmark model for a 3-day forecasting horizon.

EMPIRICAL ANALYSIS OF THE CAUSAL RELATIONSHIPS OF SPILLOVERS IN THE VOLATILITY OF THE S&P-500 INDEX

The volatile nature of the relationship between the stock index and the stocks which stand for it, is revealed. The directions of volatility spillovers are studied in the context of the transformation of causal relationships. The article analyses the interrelationships and volatility spillovers between the S&P-500 index and the shares of META and GOOG (technology sector), JPM and BAC (financial sector), MRO and OXY (oil and gas sector), which are included in the index. The research methodology is based on the GARCH (1,1) model, which allows considering the development of variance over time and the dynamics of conditional volatility of time series. The identified interdependencies are focused on forecasting volatility spillover shocks from the S&P 500 to stocks and vice versa.

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.

A Novel and Effective Method for Quantifying the Performance of Time Series Volatility

A Novel and Effective Method for Quantifying the Performance of Time Series Volatility

So different and yet so alike: A comparative analysis of firms' connectedness in the stock and corporate bond markets

AbstractWe study firms' return and volatility connectedness in the stock and corporate bond markets. Our approach to capturing firm‐specific return and volatility time series in the corporate bond market is based on a repeat‐sales index at the firm level. Measuring the pairwise connectedness of firms, we show that the two markets share similar dynamics in the connectedness of their firms. Firms tend to cluster within their own sectors and ties between firms in the corporate bond market are proportionally weaker. Financial firms play a critical role in the propagation of shocks, but this role differs markedly in the two markets.

Developing Exp-FIGARCH Hybrid Models for Time Series Modelling

In this paper, we introduced a new hybrid model namely Exponential Autoregressive-Fractional Integrated Generalized Autoregressive Conditional Heteroscedasticity (ExpAR-FIGARCH) model and study financial data. The Daily Nigeria All Share Stock Index that exhibit nonlinear, volatility and long memory effect were analyzed in the study. The existing ExpAR-Generalized Autoregressive Conditional Heteroscedasticity (ExpAR-GARCH) model were estimated and compared with the proposed ExpAR-FIGARCHmodel. Results showed that the new hybrid model is better based on efficient parameters, serial correlation analysis and forecast measures of accuracy. Therefore, as a conclusion, the current study indicates that the ExpAR-FIGARCHmodel performed better compared to the ExpAR-GARCHhybrid model. Therefore, the ExpAR-FIGARCHmodel is a better option for modeling nonlinear, volatility and long memory characteristics of time series. Future study should focus on the application of the developed hybrid ExpAR-FIGARCHmodel using health, meteorological and economic data.

ATTnet: An explainable gated recurrent unit neural network for high frequency electricity price forecasting

The primary contribution of this study is the proposal of an explainable deep-learning neural network (ATTnet) that employs an attention mechanism to achieve accurate electricity spot price forecasting and an explainable model pipeline. The concise, single-stream network consists of a 5-head attention mechanism and gated recurrent units, which have been developed to model the temporal dependencies of the volatile market data. In addition to introducing a novel neural network architecture for volatile time series data, this study makes a substantial contribution by investigating prediction factors in two ways: temporally via the attention scores from the input sequences and globally via feature Shapely values. In real-time electricity price prediction, historical prices, temperature, hour, and zonal load are found to be the most important variables. The deep learning model was tested on real-time price profiles from eight generators within the New York Independent System Operator (NYISO) network. The proposed model achieves performance gains of 21% in MAE and 22% in MAPE over the state-of-the-art benchmark methods.

Local and global trend Bayesian exponential smoothing models

This paper describes a family of seasonal and non-seasonal time series models that can be viewed as generalisations of additive and multiplicative exponential smoothing models to model series that grow faster than linear but slower than exponential. Their development is motivated by fast-growing, volatile time series. In particular, our models have a global trend that can smoothly change from additive to multiplicative and is combined with a linear local trend. Seasonality, when used, is multiplicative in our models, and the error is always additive but heteroscedastic and can grow through a parameter sigma. We leverage state-of-the-art Bayesian fitting techniques to fit these models accurately, which are more complex and flexible than standard exponential smoothing models. When applied to the M3 competition data set, our models outperform the best algorithms in the competition and other benchmarks, thus achieving, to the best of our knowledge, the best results of per-series univariate methods on this dataset in the literature. An open-source software package of our method is available.

A framework for automated landslide dating utilizing SAR-Derived Parameters Time-Series, An Enhanced Transformer Model, and Dynamic Thresholding

Determining the timing of landslide occurrence is crucial for establishing an accurate, comprehensive and systematic landslide inventory while assessing the potential for reducing landslide risk. Unfortunately, many existing landslide inventories lack temporal information such as the precise time of landslide events. Optical and Synthetic Aperture Radar (SAR) sensors are the most commonly used remote sensing technologies for landslide detection. Unlike optical sensors, SAR sensors are not affected by cloudy conditions and provide valuable imagery regardless of sunlight availability. Therefore, SAR-derived parameters, i.e., SAR amplitude, interferometric coherence, and polarimetric features (alpha and entropy), offer a higher temporal resolution for detecting landslide occurrence times compared to optical data. Despite the advantages, there is currently no universally accepted automatic method for determining the time of landslide events using SAR data. This is due to the lack of anomaly labels and the high time-series volatility in detecting landslide occurrence times. Despite advances in deep-learning methods for anomaly detection in time-series, only a few of them can address these challenges in our case. In this paper, we propose an unsupervised multivariate transformed-based deep-learning model to automatically and efficiently estimate landslide occurrence times using multivariate SAR-derived parameters time-series analysis. The designed gated relative position can increase robustness and temporal context information, by learning global temporal trends in the time-series. Subsequently, the time-series of the anomaly score derived from the proposed Transformer model is analyzed using an adaptive thresholding strategy to dynamically and automatically mark anomalies related to the landslide occurrence. Our research focuses on collapsed landslides characterized by dramatic changes in ground surface topography, with a particular attention for the need of a prior knowledge about landslide boundaries. We assess the performance of the proposed methodology for several collapsed landslides including the July 21, 2020 Shaziba and 23 July, 2019 Shuicheng landslides in China, March 19, 2019 Takht landslide in Iran, June 15, 2018 Jalgyz-Jangak and May 25, 2018 Kugart landslides in Kyrgyzstan, July 7, 2018 Hitardalur landslide in Iceland, and January 25, 2019 Brumadinho landslide in Brazil. In comparison to commonly used neural networks like the LSTM algorithm, our proposed framework leads to a more accurate estimate for the time of landslide failure using time-series of SAR-derived parameters. Furthermore, our results suggest the great potential of SAR data to narrow the time period detected from optical data when used in conjunction with them.

The Impacts of the Interest Rate, the Exchange Rate, and the Market Index on the Stock Returns of the Brazilian Banks

Abstract This paper aims to analyze the impact of interest rate, exchange rate, and market on the returns and volatility of the stocks of banks listed on the Brazilian Stock Exchange. This analysis used two statistical models: the linear model estimated using Ordinary Least Squares and the ARCH/GARCH time series volatility models. The econometric studies considered the daily data of 15 financial institutions listed on the stock exchange during the period from January 2009 to December 2021. Regarding the market effect, the Ibovespa index for the period was considered; for the interest rate, the CDI (Certificate of Interbank Deposit) was used; and, about the exchange rate, the dollar rate was adopted as a reference. The results indicate that the distribution of stock returns is asymmetrical, with an elongated tail on the right. It was observed, based on the econometric model applied, that the daily returns of the shares are significantly influenced by the market, and the interest rate exerts the least impact on the returns. These findings are relevant to the scientific community exploring the topic and provide valuable insights for bankers, analysts, market investors, regulatory authorities, and society in the decision-making process. JEL classification numbers: C32, G00, G21. Keywords: Banking, Interest rates, Exchange rate, Bank stocks.

Rough Volatility: Fact or Artefact?

We investigate the statistical evidence for the use of ‘rough’ fractional processes with Hurst exponent H<0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H< 0.5$$\\end{document} for modeling the volatility of financial assets, using a model-free approach. We introduce a non-parametric method for estimating the roughness of a function based on discrete sample, using the concept of normalized p-th variation along a sequence of partitions. Detailed numerical experiments based on sample paths of fractional Brownian motion and other fractional processes reveal good finite sample performance of our estimator for measuring the roughness of sample paths of stochastic processes. We then apply this method to estimate the roughness of realized volatility signals based on high-frequency observations. Detailed numerical experiments based on stochastic volatility models show that, even when the instantaneous volatility has diffusive dynamics with the same roughness as Brownian motion, the realized volatility exhibits rough behaviour corresponding to a Hurst exponent significantly smaller than 0.5. Comparison of roughness estimates for realized and instantaneous volatility in fractional volatility models with different values of Hurst exponent shows that, irrespective of the roughness of the spot volatility process, realized volatility always exhibits ‘rough’ behaviour with an apparent Hurst index H^<0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widehat{H}<0.5$$\\end{document}. These results suggest that the origin of the roughness observed in realized volatility time series lies in the estimation error rather than the volatility process itself.

Prediction of volatility and seasonality vegetation by using the GARCH and Holt-Winters models.

Seasonality and volatility of vegetation in the ecosystem are associated with climatic sensitivity, which can have severe consequences for the environment as well as on the social and economic well-being of the nation. Monitoring and forecasting vegetation growth patterns in ecosystems significantly rely on remotely sensed vegetation indices, such as Normalized Difference Vegetation Index (NDVI). A novel integration of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and the Holt-Winters (H-W) models was used to simulate the seasonality and volatility of the three different agro-climatic zones in Jharkhand, India: the central north-eastern, eastern, and south-eastern agro-climatic zones. MODIS Terra Vegetation Indices NDVI data MOD13Q1, from 2001 to 2021, was used to create NDVI time series volatility and seasonality modeled by the GARCH and the H-W models, respectively. GARCH-based Exponential GARCH (EGARCH) [1,1] and Standard GARCH (SGARCH) [1,1] models were used to check the volatility of vegetation growth in three different agro-climatic zones of Jharkhand. The SGARCH [1,1] and EGARCH [1,1] models for the western agro-climatic zone experienced the best indicator as it has maximum likelihood and minimal Schwarz-Bayesian criterion and Akaike information criterion. The seasonality results showed that the additive H-W model showed better results in the eastern agro-climatic zone with the optimized values of MAE (16.49), MAPE (0.49), NSE (0.86), RMSE (0.49), and R2 (0.82) followed by the south-eastern and central north-eastern agro-climatic zones. By utilizing the H-W and GARCH models, the finding demonstrates that vegetation orientation and monitoring seasonality can be predicted using NDVI.

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.

ОЦЕНКА ЭКОНОМИЧЕСКОЙ УСТОЙЧИВОСТИ ОРГАНИЗАЦИЙ СЕЛЬСКОГО ХОЗЯЙСТВА

Studying the issues of sustainability and efficiency of enterprises is becoming increasingly important in the light of the emergence of periodic crises in the development of our country's economic systems, the consequences of which are difficult to predict. An increase in the stability of business entities can be achieved by introducing methods for assessing the volatility of time series of various indicators of an enterprise's activity. This approach will allow you to quickly identify critical areas that the organization's management should pay special attention to. The concept of volatility is often used to analyze stock and currency markets in order to study the risks associated with fluctuations in the value of assets. However, there are very few studies on the application of volatility in other areas, such as the sustainability and efficiency of agricultural enterprises, which may indicate insufficient study of this aspect. We suggest using volatility as an indicator to assess the economic sustainability and effectiveness of an organization. It is proposed to use the methodological apparatus for assessing the volatility of time series as an assessment of the sustainability of performance indicators of agricultural organizations, where the standard deviation for the time series of the indicator under study will be taken as a measure of deviation. The article discusses various types of volatility of financial time series: historical, expected and historical expected volatility. The formulas of their calculation and features are considered. An example of calculating volatility for time series of cash flows of an agricultural organization is given. The variability of cash flows can serve as an indicator of the economic stability of an agricultural organization under the influence of the external environment. This paper discusses a variety of techniques for measuring the volatility of time series. One of the proposed approaches involves the use of this method to assess the sustainability of cash flows of agricultural enterprises. The variability of cash flows can be considered as an indicator of the stability of an organization under the influence of the external environment.