Sums Of Squares Algorithm Research Articles

Applications of Long-Memory and Structure Breaks for Carbon Indexes

This paper aims to investigatethe long-memory properties of four carbon indexes by utilizing the autoregressive frictionally integrated moving average–fractionally integrated general autoregressive conditional heteroskedasticity models. First, this study discovered a significant long-memory effect for two carbon indexes such as CCX and JOI, whereas others like CER and EUA possess intermediate memory in the returns. Second, the multiple structure breaks in the four carbon indexes were examined using the iterated cumulative sum of squares algorithm. Evidence shows that the sudden shifts are mainly attributed to macroeconomic factors, energy dynamics, and political policies.

Forecasting carbon price in the European carbon market: The role of structural changes

Examining and analyzing the role of breakpoints in carbon price prediction can help people better understand the carbon market's structural changes to carry out technological predictions. However, the current carbon price prediction models lack comprehensive utilization of structural breakpoints. Then, a hybrid forecasting model is proposed by combining the Bai&Perron test, Iterated Cumulative Sums of Squares algorithm (ICSS), wavelet transform, and long short-term memory neural network (LSTM). According to the results, there are fifteen breakpoints in the EU allowance (EUA) carbon price. And the breakpoints can improve the prediction accuracy of the proposed model by 10–20 %. The ICSS algorithm is superior to the Bai&Perron test in detecting the breakpoints and improving the prediction accuracy. Compared with other benchmark models, the proposed hybrid model has the best prediction accuracy. We suggest that two types of breakpoints information could be accounted for in future prediction models.

K-Space Data Reconstruction Algorithm-Based MRI Diagnosis and Influencing Factors of Knee Anterior Cruciate Ligament Injury.

This study was aimed at investigating the diagnostic value of MRI based on K-space data reconstruction algorithm for anterior cruciate ligament (ACL) injury of knee joint and the influencing factors of ligament injury. 96 patients with ACL injury of knee joint were selected, and they were randomly divided into two groups: group A (arthroscopy) and group B (MRI examination), and another 96 healthy volunteers in the same period were selected as the control group. The test results of each indicator were compared. The results showed that the signal-to-noise ratio (SNR) of SMASH algorithm was higher than that of sum of squares (SOS) algorithm. In group A, there were 66 positive and 30 negative tests, and in group B, there were 56 positive and 40 negative tests (P < 0.05). The intercondylar fossa width, the intercondylar fossa width index, and the ratio of tibial intercondylar eminence width to intercondylar fossa width in group B were lower than those in the control group (P < 0.05). Compared with the traditional SOS algorithm, SMASH algorithm can improve the image quality, reduce the impact of damage data on the final synthesis image, and improve the image SNR. In clinical work, the ratio of the width of tibial intercondylar eminence to the width of femoral intercondylar fossa can be measured by imaging data to evaluate the matching between tibial intercondylar eminence and femoral intercondylar fossa, so as to evaluate the risk of ACL rupture.

A New Hybrid VMD-ICSS-BiGRU Approach for Gold Futures Price Forecasting and Algorithmic Trading

The gold market plays a vital role in the world economy. Due to its complex and nonstationary nature, predicting the price of gold is particularly challenging. In this study, a new hybrid forecasting approach named variational mode decomposition (VMD)-iterated cumulative sums of squares (ICSS)-bidirectional gated recurrent unit (BiGRU) is proposed by integrating BiGRU deep learning model, VMD, and iterated cumulative sum of squares algorithm. The forecasting framework is able to extract the inner factors and patterns within the gold futures market movements, decompose its correlation with external markets and detect shifts within market conditions in order to accurately predict price movements in the gold futures market. The experimental results show that the hybrid forecasting approach can improve the prediction performance significantly in comparison to the benchmarks. Furthermore, we extend the proposed hybrid forecasting approach to generate trading strategies and test trading performance of the gold futures market. The testing results over an out-of-sample period of 11 years (2008–2019) indicate that the strategy generated based on the prediction of the proposed approach displays high levels of consistency in generating positive returns and outperforms several other common trading strategies under various market conditions. The approach also shows consistent better results when generalized to the spot gold market, providing practical guidance for minimizing investment risk and hedging strategies in the gold commodity market.

Retracted: Enriching the value‐at‐risk framework to ensemble empirical mode decomposition with an application to the European carbon market

AbstractUnlike common financial markets, the European carbon market is a typically heterogeneous market, characterised by multiple timescales and affected by extreme events. The traditional value‐at‐risk (VaR) with single‐timescale fails to deal with the multi‐timescale characteristics and the effects of extreme events, which can result in the VaR overestimation for carbon market risk. To measure accurately the risk on the European carbon market, we propose ensemble empirical mode decomposition (EEMD) based multiscale VaR approach. First, the EEMD algorithm is utilised to decompose the carbon price return into several intrinsic mode functions (IMFs) with different timescales and a residue, which are modelled respectively using the ARMA‐GARCH model to obtain their conditional variances at different timescales. Furthermore, the Iterated Cumulative Sums of Squares algorithm is employed to determine the windows of an extreme event, so as to identify the IMFs influenced by an extreme event and conduct an exponentially weighted moving average on their conditional variations. Finally, the VaRs of various IMFs and the residue are estimated to reconstruct the overall VaR, the validity of which is verified later. Then, we illustrate the results by considering several European carbon futures contracts. Compared with the traditional VaR framework with single timescale, the proposed multiscale VaR‐EEMD model can effectively reduce the influences of the heterogeneous environments (such as the influences of extreme events), and obtain a more accurate overall risk measure on the European carbon market. By acquiring the distributions of carbon market risks at different timescales, the proposed multiscale VaR‐EEMD estimation is capable of understanding the fluctuation characteristics more comprehensively, which can provide new perspectives for exploring the evolution law of the risks on the European carbon market.

A statistical approach for reconstructing natural streamflow series based on streamflow variation identification

Abstract Natural streamflow reconstruction is highly significant to assess long-term trends, variability, and pattern of streamflow, and is critical for addressing implications of climate change for adaptive water resources management. This study proposed a simple statistical approach named NSR-SVI (natural streamflow reconstruction based on streamflow variation identification). As a hybrid model coupling Pettitt's test method with an iterative algorithm and iterative cumulative sum of squares algorithm, it can determine the reconstructed components and implement the recombination depending only on the information of change points in observed annual streamflow records. Results showed that NSR-SVI is suitable for reconstructing natural series and can provide the stable streamflow processes under different human influences to better serve the hydrologic design of water resource engineering. Also, the proposed approach combining the cumulative streamflow curve provides an innovative way to investigate the attributions of streamflow variation, and the performance has been verified by comparing with the relevant results in nearby basin.

Sum of Squares Approach for Nonlinear H∞ Control

A proper Hamilton-Jacobi-Isaacs (HJI) inequality must be solved in a nonlinear H∞ control problem. The sum of squares (SOS) method can now be used to solve an analytically unsolvable nonlinear problem. A HJI inequality suitable for SOS approach is derived in the paper. The SOS algorithm for solving the HJI inequality is also provided. Conservativeness of the SOS method is then discussed in the paper. The conservativeness of the SOS approach is caused by the method itself, because it is really a synthesis method over the entire state space. To reduce the conservativeness, a local H∞ design on a restricted state-space region is proposed. But the SOS approach for the local H∞ design also suffers from the conservativeness problem, because the S-procedure for solving the set-containment constraint provides only a sufficient condition. The above-mentioned sources of conservativeness are peculiar for the SOS approaches. So a proper approach must be carefully selected in the design process to get a reasonable result. A design example is also given in the paper.

Measuring the risk of European carbon market: an empirical mode decomposition-based value at risk approach

Unlike common financial markets, the European carbon market is a typically heterogeneous market, characterized by multiple timescales and affected by extreme events. The traditional Value-at-Risk (VaR) with single-timescale fails to deal with the multi-timescale characteristics and the effects of extreme events, which can result in the VaR overestimation for carbon market risk. To measure accurately the risk on the European carbon market, we propose an empirical mode decomposition (EMD) based multiscale VaR approach. Firstly, the EMD algorithm is utilized to decompose the carbon price return into several intrinsic mode functions (IMFs) with different timescales and a residue, which are modeled respectively using the ARMA–EGARCH model to obtain their conditional variances at different timescales. Furthermore, the Iterated Cumulative Sums of Squares algorithm is employed to determine the windows of an extreme event, so as to identify the IMFs influenced by an extreme event and conduct an exponentially weighted moving average on their conditional variations. Finally, the VaRs of various IMFs and the residue are estimated to reconstruct the overall VaR, the validity of which is verified later. Then, we illustrate the results by considering several European carbon futures contracts. Compared with the traditional VaR framework with single timescale, the proposed multiscale VaR–EMD model can effectively reduce the influences of the heterogeneous environments (such as the influences of extreme events), and obtain a more accurate overall risk measure on the European carbon market. By acquiring the distributions of carbon market risks at different timescales, the proposed multiscale VaR–EMD estimation is capable of understanding the fluctuation characteristics more comprehensively, which can provide new perspectives for exploring the evolution law of the risks on the European carbon market.

Enriching the VaR framework to EEMD with an application to the European carbon market

AbstractUnlike common financial markets, the European carbon market is a typically heterogeneous market, characterized by multiple timescales, and affected by extreme events. The traditional value‐at‐risk (VaR) with single‐timescale fails to deal with the multi‐timescale characteristics and the effects of extreme events, which can result in the VaR overestimation for carbon market risk. To measure accurately the risk on the European carbon market, we propose an ensemble empirical mode decomposition (EEMD)‐based multiscale VaR approach. First, the EEMD algorithm is utilized to decompose the carbon price return into several intrinsic mode functions (IMFs) with different timescales and a residue, which are modelled, respectively, using the ARMA‐Generalized Autoregressive Conditional Heteroscedasticity model to obtain their conditional variances at different timescales. Furthermore, the Iterated Cumulative Sums of Squares algorithm is employed to determine the windows of an extreme event, so as to identify the IMFs influenced by an extreme event and conduct an exponentially weighted moving average on their conditional variations. Finally, the VaRs of various IMFs and the residue are estimated to reconstruct the overall VaR, the validity of which is verified later. Then, we illustrate the results by considering several European carbon futures contracts. Compared with the traditional VaR framework with single timescale, the proposed multiscale VaR‐EEMD model can effectively reduce the influences of the heterogeneous environments (such as the influences of extreme events) and obtain a more accurate overall risk measure on the European carbon market. By acquiring the distributions of carbon market risks at different timescales, the proposed multiscale VaR‐EEMD estimation is capable of understanding the fluctuation characteristics more comprehensively, which can provide new perspectives for exploring the evolution law of the risks on the European carbon market.

Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

ABSTRACTIn this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.

Applying sum‐of‐squares decomposition technique to power system robust control problem

For the first time, we apply the sum‐of‐squares (SOS) decomposition technique for robust control of power systems. We propose an SOS L2 robust control scheme aiming at a power system characterized by exogenous disturbances. A set of states‐related inequalities are utilized to guarantee L2 gain disturbance attenuation performance of the system. It involves semidefinite programming relaxations based on the SOS decomposition technique, which is employed to solve the inequalities that bring about robust control of the system. This method is superior to other traditional approaches. It is able to construct a robust controller that guarantees L2 gain disturbance attenuation performance of the system featuring exogenous disturbance by the SOS algorithm without solving Hamilton–Jacobi inequalities or using the recursive design of back‐stepping. Then, the proposed approach is applied to derive a robust excitation controller for multimachine power systems. Moreover, a three‐machine power system model is employed to test the robust excitation controller, which finally verifies its effectiveness and superiority. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

Long memory and scaling behavior study of bulk freight rate volatility with structural breaks

ABSTRACTDue to the effect of credit crunch and slowdown in marine transportation, analysis of freight rate volatility characters under structural breaks is of great importance after year 2008. In this paper, the presence of structural break points in bulk freight rate index time series is investigated through the Iterated Cumulative Sum of Squares algorithm. Furthermore, long memory features of different vessel sizes, Supramax, Panamax and Capesize bulk carriers are also accomplished, and emperical results show that the daily returns of Baltic Supramax Index inclined to have stronger long-range correlation. Multifractal detrended fluctuation analysis (MF-DFA) method is applied with the influence of seasonality taken into consideration and the origin of multifractality is revealed. For policy-makers and investors with different trading horizons, structural break is an important indicator of different long memory characters of freight rate index time series in different time ranges. Hence, structural breaks in MF-DFA results are picked out and conclusions of long memory feature are achieved.

Examining the structural changes of European carbon futures price 2005–2012

The aim of this research was to examine the structural changes of European carbon futures price under the European Union Emissions Trading Scheme during 2005–2012. More specifically, by relying on the daily EU allowance futures contract, we investigate the structural changes of the European carbon futures price. Structural breakpoints are detected based on the iterative cumulative sums of squares algorithm and event study models. The results show that since 2005, there have been three major breakpoints of the European carbon futures price, stemming from the two extreme events of the 2008 global financial crisis and the 2011 European debt crisis. This study contributes to understanding the pricing mechanism of the EU ETS and effectively forecasting carbon prices.

Testing for variance changes in autoregressive models with unknown order

The problem of change point in autoregressive process is studied in this article. We propose a Bayesian information criterion-iterated cumulative sums of squares algorithm to detect the variance changes in an autoregressive series with unknown order. Simulation results and two examples are presented, where it is shown to have good performances when the sample size is relatively small.

MODELLING SOUTH AFRICAN CURRENCY CRISES AS STRUCTURAL CHANGES IN THE VOLATILITY OF THE RAND

AbstractThis study tests the theory that currency crises are associated with sudden large changes in the structure of foreign exchange market volatility. Due to increases in market uncertainty, crisis periods exhibit abnormally high levels of volatility. By studying short‐term changes in volatility dynamics, it is possible to identify the start and end dates of crisis periods with a high degree of precision. We use the iterative cumulative sum of squares algorithm to detect multiple shifts in the volatility of rand returns between January 1994 and March 2009. Dummy variables controlling for the detected shifts in variance are incorporated in a generalised autoregressive conditional heteroscedasticity modelling framework. The analysis indicates that previously identified crisis periods in the rand coincide with significant structural changes in market volatility.

The impact of sudden changes on the persistence of volatility: evidence from the BRIC countries

This article analyses sudden changes of volatility in the stock markets of the BRIC countries (Brazil, Russia, India and China) using the iterated cumulative sums of squares algorithm for the period 1990 to 2007 and examines their impacts on the persistence of volatility. The results show that when endogenously determined sudden shifts in variance are taken into account in the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, the estimated persistence in return volatility is reduced significantly in every return series. These results suggest that the findings of previous studies could have overestimated the degree of the persistence of volatility existing in the financial time series. These results have important policy implications for the financial market participants and policy makers.

The Contingent Asymmetric Volatility, Structural Change Detect, Long Run Equilibrium - Accession Vicious Cross-Strait Macroeconomic Relationship and Sector Effects

We gauge the dynamics of macroeconomic and industry sector interactions between Mainland China and Taiwan in Greater China multivariate GARCH systems. Many studies have investigated the relations among the mainland Chinese, Hong Kong and Taiwan, some analysed the notion of cointegration among GCEA share markets (Cheung et al., 2003, Groenewold et al., 2004), others focused on economic integration (Wang and Schuh, 2000). Our paper contributes to the existing research on de facto or de jure integration among GCEA in deriving determinacy properties and version for these areas, especially from the point of vicious Cross-Strait macroeconomic relationship and sector effects. Since opening up to the outside world and transiting from a centrally planned to an increasingly market-based economy, Chinese economy is approaching to a so-called 'socialist market economy'. Which is different from the traditional centrally planned economy as well as the modern capitalist economy, to some extent, the patterns of structural change in the Chinese economy is difficult to detect. We apply sophisticated modeling techniques combined with an algorithm（iterated cumulative sums of squares algorithm, ICSS）to detect the economy and industrial sector structural changes under the increasingly opening of the Chinese economy. As the Mainland has gone through a period associated with a gradual opening of the economy, the dynamic interrelationships among Hong Kong, Taiwan and Mainland China has received considerable attention, especially during the period of regional or world financial crisis. By the way, we use a time-varying asymmetry conditional covariance multivariate GARCH systems combined with an algorithm (ICSS) which detects structural change during 1997 East Asian financial crisis and the nineteen terrorists on September 11, 2001, allowing for the asymmetric covariance effect due to simultaneously innovations between Mainland China, Taiwan and Mainland China, Hong Kong during the specific structural period. Owing to the different economic systems among the GCEA, VS (Volatility-switching) model generalizes the GJR model, provides a more flexible framework than any other ad hoc econometric model to scrutinize the disparate but identical market microstructure among these markets. Besides, this article provides an alternative explanation of dynamic interactions by application asymmetries conditional mean (ARAS) model to perform the Granger causality test. The causality relationship among GCEA, based on macroeconomic and industry sectors react to past positive and negative autoregressive process within and across broader would imply deindustrialization effect of Taiwan and the influence of increasing and persistent expansion in the Chinese economy over the last decade. The transmission of capital market and the embedded industrial structure thought-out primary, secondary and tertiary industries within the GCEA is examined for the period from 1996 through 2006. Long run equilibrium relationship among the Chinese Economic Zone is proved in this research. Our empirical result reveals two-way causality between Shenzhen A-stock markets and Taiwan stock markets. Different from previous studies investigating GCEA focus on the interaction of B-shares (instead of A-shares )with the other markets, A-shares are denominated in local currency which would not be affected by the variation of exchange rate as B-shares. A-share market seems to be driven by fundamental components. From the industry's clustering point of view, Taiwan's industries may follow a flying-geese style move to mainland China gathering on Shenzhen. Our evidence proves asymmetric covariance during the period nineteen terrorists between mainland China and Taiwan, the dummy variable of asymmetric covariance effect appear statistically significant thought-out primary, secondary and tertiary industries sectors. However, the inference of 1997 Asian financial crisis is limited.

Modeling volatility changes in the 10-year Treasury

This paper examines the daily volatility of changes in the 10-year Treasury note utilizing the iterated cumulative sums of squares algorithm [C. Inclan, G. Tiao, Use of cumulative sums of squares for retrospective detection of changes of variance, J. Am. Stat. Assoc. 89 (1994) 913–923]. The ICSS algorithm can detect regime shifts in the volatility of the interest rate changes. A general model allows for endogenously determined changes in variance while the more restrictive model forces the variance to follow the same process throughout the sample period. A comparison of the out-of-sample volatility forecasting performance of two competing models is made using asymmetric error measures. The asymmetric error statistics penalize models for under- or over-predicting volatility. The results shed light on the importance of ignoring volatility regime shifts when performing out-of-sample forecasts. The findings are important to financial market participants who require accurate forecasts of future volatility in order to implement and evaluate asset performance.

Indexing variability: A case study with climate change impacts on ecosystems

We developed a methodology to index statistical changes in the variance of ecological measures over time. While ecological indicators are used to assess ecosystem health, vulnerability, risk and damage to ecosystems, their primary focus has been on changes to the mean of the ecological state or process. Little work has been done on incorporating variability into ecological indices. The methodology developed here is based on the Modified Levene's test of variance and a moving block where an initial time period (block) of ecosystem behavior is compared to the moving block. This allows for the detection of not only shifts in variance but also the magnitude of the shift on a continuous basis. Our results compared well with the benchmarked results from the Centered Cumulative Sum of Squares Algorithm (CUSUM) for detection of variance changes in fixed time series. The output from this methodology is a continuous stream of parameters (significant variance shift, magnitude of the shift, and the direction of the variance shift) suitable for indexing variance or integrating into an index measuring ecosystem change. Results suggest that the block interval widths should be at least 50 and that a smoothing factor of five be used to avoid false positives. We used modeled vegetation carbon output to analyze the utility of the methodology, illustrating that different model assumptions and CO2 regimes affect the variability of the ecological response. The degree of risk resource managers may want to explore can be altered by choices in the block length, the length of the string used to smooth variance shifts, the assumption that the initial period has constant variance and the alpha levels used to determine statistical significance.

Modeling Volatility Changes in the 10-Year Treasury Note Yield

This paper examines the daily volatility of changes in yield on the 10-year Treasury note utilizing the iterated cumulative sums of squares algorithm (Inclan and Tiao, 1994). The ICSS algorithm can detect regime shifts in the volatility of the interest rate changes. A general model allows for endogenously determined changes in variance while the more restrictive model forces the variance to follow the same process throughout the sample period. A comparison of the out-of-sample volatility forecasting performance of two competing models is made using asymmetric error measures. The asymmetric error statistics penalize models for under- or over-predicting volatility. The results shed light on the importance of ignoring volatility regime shifts when performing out-of-sample forecasts. The findings are important to financial market participants who require accurate forecasts of future volatility in order to implement and evaluate asset performance.