In this paper PC-VAR estimation of vector autoregressive models (VAR) is proposed. The estimation strategy successfully lessens the curse of dimensionality affecting VAR models, when estimated using sample sizes typic...In this paper PC-VAR estimation of vector autoregressive models (VAR) is proposed. The estimation strategy successfully lessens the curse of dimensionality affecting VAR models, when estimated using sample sizes typically available in quarterly studies. The procedure involves a dynamic regression using a subset of principal components extracted from a vector time series, and the recovery of the implied unrestricted VAR parameter estimates by solving a set of linear constraints. PC-VAR and OLS estimation of unrestricted VAR models show the same asymptotic properties. Monte Carlo results strongly support PC-VAR estimation, yielding gains, in terms of both lower bias and higher efficiency, relatively to OLS estimation of high dimensional unrestricted VAR models in small samples. Guidance for the selection of the number of components to be used in empirical studies is provided.展开更多
In this paper, vector autoregressive （VAR） models have been recognized for the selected indicators of Dhaka stock exchange （DSE）. Bangladesh uses the micro economic variables, such as stock trade, invested stock c...In this paper, vector autoregressive （VAR） models have been recognized for the selected indicators of Dhaka stock exchange （DSE）. Bangladesh uses the micro economic variables, such as stock trade, invested stock capital, stock volume, current market value, and DSE general indexes which have the direct impact on DSE prices. The data were collected for the period from June 2004 to July 2013 as the basis on daily scale. But to get the maximum explorative information and reduction of volatility, the data have been transformed to the monthly scale. The outliers and extreme values of the study variables are detected through box and whisker plot. To detect the unit root property of the study variables, various unit root tests have been applied. The forecast performance of the different VAR models is compared to have the minimum residual. Moreover, the dynamics of this financial market is analyzed through Granger causality and impulse response analysis.展开更多
Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. ...Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.展开更多
It is well known that a high degree of positive dependency among the errors generally leads to 1) serious underestimation of standard errors for regression coefficients;2) prediction intervals that are excessively wid...It is well known that a high degree of positive dependency among the errors generally leads to 1) serious underestimation of standard errors for regression coefficients;2) prediction intervals that are excessively wide. This paper set out to study the performances of classical VAR and Sims-Zha Bayesian VAR models in the presence of autocorrelated errors. Autocorrelation levels of (-0.99, -0.95, -0.9, -0.85, -0.8, 0.8, 0.85, 0.9, 0.95, 0.99) were considered for short term (T = 8, 16);medium term (T = 32, 64) and long term (T = 128, 256). The results from 10,000 simulation revealed that BVAR model with loose prior is suitable for negative autocorrelations and BVAR model with tight prior is suitable for positive autocorrelations in the short term. While for medium term, the BVAR model with loose prior is suitable for the autocorrelation levels considered except in few cases. Lastly, for long term, the classical VAR is suitable for all the autocorrelation levels considered except in some cases where the BVAR models are preferred. This work therefore concludes that the performance of the classical VAR and Sims-Zha Bayesian VAR varies in terms of the autocorrelation levels and the time series lengths.展开更多
Forecasting solar irradiance is a critical task in the renewable energy sector, as it provides essential information regarding the potential energy production from solar panels. This study aims to utilize the Vector A...Forecasting solar irradiance is a critical task in the renewable energy sector, as it provides essential information regarding the potential energy production from solar panels. This study aims to utilize the Vector Autoregression (VAR) model to forecast solar irradiance levels and weather characteristics in the San Francisco Bay Area. The results demonstrate a correlation between predicted and actual solar irradiance, indicating the effectiveness of the VAR model for this task. However, the model may not be sufficient for this region due to the requirement of additional weather features to reduce disparities between predictions and actual observations. Additionally, the current lag order in the model is relatively low, limiting its ability to capture all relevant information from past observations. As a result, the model’s forecasting capability is limited to short-term horizons, with a maximum horizon of four hours.展开更多
In time series literature, many authors have found out that multicollinearity and autocorrelation usually afflict time series data. In this paper, we compare the performances of classical VAR and Sims-Zha Bayesian VAR...In time series literature, many authors have found out that multicollinearity and autocorrelation usually afflict time series data. In this paper, we compare the performances of classical VAR and Sims-Zha Bayesian VAR models with quadratic decay on bivariate time series data jointly influenced by collinearity and autocorrelation. We simulate bivariate time series data for different collinearity levels (﹣0.99, ﹣0.95, ﹣0.9, ﹣0.85, ﹣0.8, 0.8, 0.85, 0.9, 0.95, 0.99) and autocorrelation levels (﹣0.99, ﹣0.95, ﹣0.9, ﹣0.85, ﹣0.8, 0.8, 0.85, 0.9, 0.95, 0.99) for time series length of 8, 16, 32, 64, 128, 256 respectively. The results from 10,000 simulations reveal that the models performance varies with the collinearity and autocorrelation levels, and with the time series lengths. In addition, the results reveal that the BVAR4 model is a viable model for forecasting. Therefore, we recommend that the levels of collinearity and autocorrelation, and the time series length should be considered in using an appropriate model for forecasting.展开更多
In the paper, a general framework for large scale modeling of macroeconomic and financial time series is introduced. The proposed approach is characterized by simplicity of implementation, performing well independentl...In the paper, a general framework for large scale modeling of macroeconomic and financial time series is introduced. The proposed approach is characterized by simplicity of implementation, performing well independently of persistence and heteroskedasticity properties, accounting for common deterministic and stochastic factors. Monte Carlo results strongly support the proposed methodology, validating its use also for relatively small cross-sectional and temporal samples.展开更多
In this study, impact of inflation （WPI--Wholesale Price Index）, exchange rate, and interest rate on the production of red meat in Turkey was examined using the vector autoregressive （VAR） model. The model consist...In this study, impact of inflation （WPI--Wholesale Price Index）, exchange rate, and interest rate on the production of red meat in Turkey was examined using the vector autoregressive （VAR） model. The model consisting of variables of dollar exchange rate, inflation rate, interest rate, beef, buffalo meat, mutton, and goat meat production amounts has been estimated for the period from 1981 to 2014. It has been detected that there is a tie among the dollar exchange rate, inflation rate, interest rate, and the amount of red meat production in Turkey. In order to determine the direction of this relation, Granger causality test was conducted. A one-way causal relation has been observed between： the goat meat production and dollar exchange rate; the buffalo meat production and the mutton production; and the beef production and the mutton production. To interpret VAR model, the impulse response function and variance decomposition analysis was used. As a result of variance decomposition, it has been detected that explanatory power of changes in the variance of dollar exchange rate, inflation rate, and interest rate in goat meat production amount is more than explanatory power of changes in the variances of mutton, beef, and buffalo meat variables.展开更多
Students in South African Universities come from different socio-cultural backgrounds, countries and high schools. This suggests that these students have different experiences which impact on their levels of grasping ...Students in South African Universities come from different socio-cultural backgrounds, countries and high schools. This suggests that these students have different experiences which impact on their levels of grasping information in class as they potentially use different lenses on tuition. The current practice in Universities in contributing to the academic performance of students includes the use of tutors, the use of mobile devices for first year students, use of student assistants and the use of different feedback measures. What is problematic about the current practice is that students are quitting university in high numbers. In this study, knowledge has been drawn from data through the use of machine learning algorithms. Bayesian networks, support vector machines （SVMs） and decision trees algorithms were used individually in this work to construct predictive models for the academic performance of students. The best model was constructed using SVM and it gave a prediction of 72.87% and a prediction cost of 139. The model does predict the performance of students in advance of the year-end examinations outcome. The results suggest that South African Universities must recognize the diversity in student population and thus provide students with better support and equip them with the necessary knowledge that will enable them to tap into their full potential and thus enhance their skills.展开更多
Kernel-based slow feature analysis(SFA)methods have been successfully applied in the industrial process fault detection field.However,kernel-based SFA methods have high computational complexity as dealing with nonline...Kernel-based slow feature analysis(SFA)methods have been successfully applied in the industrial process fault detection field.However,kernel-based SFA methods have high computational complexity as dealing with nonlinearity,leading to delays in detecting time-varying data features.Additionally,the uncertain kernel function and kernel parameters limit the ability of the extracted features to express process characteristics,resulting in poor fault detection performance.To alleviate the above problems,a novel randomized auto-regressive dynamic slow feature analysis(RRDSFA)method is proposed to simultaneously monitor the operating point deviations and process dynamic faults,enabling real-time monitoring of data features in industrial processes.Firstly,the proposed Random Fourier mappingbased method achieves more effective nonlinear transformation,contrasting with the current kernelbased RDSFA algorithm that may lead to significant computational complexity.Secondly,a randomized RDSFA model is developed to extract nonlinear dynamic slow features.Furthermore,a Bayesian inference-based overall fault monitoring model including all RRDSFA sub-models is developed to overcome the randomness of random Fourier mapping.Finally,the superiority and effectiveness of the proposed monitoring method are demonstrated through a numerical case and a simulation of continuous stirred tank reactor.展开更多
Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis. Traditional causality inference methods have a salient limitation that the model must be linea...Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis. Traditional causality inference methods have a salient limitation that the model must be linear and with Gaussian noise. Although additive model regression can effectively infer the nonlinear causal relationships of additive nonlinear time series, it suffers from the limitation that contemporaneous causal relationships of variables must be linear and not always valid to test conditional independence relations. This paper provides a nonparametric method that employs both mutual information and conditional mutual information to identify causal structure of a class of nonlinear time series models, which extends the additive nonlinear times series to nonlinear structural vector autoregressive models. An algorithm is developed to learn the contemporaneous and the lagged causal relationships of variables. Simulations demonstrate the effectiveness of the nroosed method.展开更多
The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, whi...The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.展开更多
文摘In this paper PC-VAR estimation of vector autoregressive models (VAR) is proposed. The estimation strategy successfully lessens the curse of dimensionality affecting VAR models, when estimated using sample sizes typically available in quarterly studies. The procedure involves a dynamic regression using a subset of principal components extracted from a vector time series, and the recovery of the implied unrestricted VAR parameter estimates by solving a set of linear constraints. PC-VAR and OLS estimation of unrestricted VAR models show the same asymptotic properties. Monte Carlo results strongly support PC-VAR estimation, yielding gains, in terms of both lower bias and higher efficiency, relatively to OLS estimation of high dimensional unrestricted VAR models in small samples. Guidance for the selection of the number of components to be used in empirical studies is provided.
文摘In this paper, vector autoregressive （VAR） models have been recognized for the selected indicators of Dhaka stock exchange （DSE）. Bangladesh uses the micro economic variables, such as stock trade, invested stock capital, stock volume, current market value, and DSE general indexes which have the direct impact on DSE prices. The data were collected for the period from June 2004 to July 2013 as the basis on daily scale. But to get the maximum explorative information and reduction of volatility, the data have been transformed to the monthly scale. The outliers and extreme values of the study variables are detected through box and whisker plot. To detect the unit root property of the study variables, various unit root tests have been applied. The forecast performance of the different VAR models is compared to have the minimum residual. Moreover, the dynamics of this financial market is analyzed through Granger causality and impulse response analysis.
文摘Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.
文摘It is well known that a high degree of positive dependency among the errors generally leads to 1) serious underestimation of standard errors for regression coefficients;2) prediction intervals that are excessively wide. This paper set out to study the performances of classical VAR and Sims-Zha Bayesian VAR models in the presence of autocorrelated errors. Autocorrelation levels of (-0.99, -0.95, -0.9, -0.85, -0.8, 0.8, 0.85, 0.9, 0.95, 0.99) were considered for short term (T = 8, 16);medium term (T = 32, 64) and long term (T = 128, 256). The results from 10,000 simulation revealed that BVAR model with loose prior is suitable for negative autocorrelations and BVAR model with tight prior is suitable for positive autocorrelations in the short term. While for medium term, the BVAR model with loose prior is suitable for the autocorrelation levels considered except in few cases. Lastly, for long term, the classical VAR is suitable for all the autocorrelation levels considered except in some cases where the BVAR models are preferred. This work therefore concludes that the performance of the classical VAR and Sims-Zha Bayesian VAR varies in terms of the autocorrelation levels and the time series lengths.
文摘Forecasting solar irradiance is a critical task in the renewable energy sector, as it provides essential information regarding the potential energy production from solar panels. This study aims to utilize the Vector Autoregression (VAR) model to forecast solar irradiance levels and weather characteristics in the San Francisco Bay Area. The results demonstrate a correlation between predicted and actual solar irradiance, indicating the effectiveness of the VAR model for this task. However, the model may not be sufficient for this region due to the requirement of additional weather features to reduce disparities between predictions and actual observations. Additionally, the current lag order in the model is relatively low, limiting its ability to capture all relevant information from past observations. As a result, the model’s forecasting capability is limited to short-term horizons, with a maximum horizon of four hours.
文摘In time series literature, many authors have found out that multicollinearity and autocorrelation usually afflict time series data. In this paper, we compare the performances of classical VAR and Sims-Zha Bayesian VAR models with quadratic decay on bivariate time series data jointly influenced by collinearity and autocorrelation. We simulate bivariate time series data for different collinearity levels (﹣0.99, ﹣0.95, ﹣0.9, ﹣0.85, ﹣0.8, 0.8, 0.85, 0.9, 0.95, 0.99) and autocorrelation levels (﹣0.99, ﹣0.95, ﹣0.9, ﹣0.85, ﹣0.8, 0.8, 0.85, 0.9, 0.95, 0.99) for time series length of 8, 16, 32, 64, 128, 256 respectively. The results from 10,000 simulations reveal that the models performance varies with the collinearity and autocorrelation levels, and with the time series lengths. In addition, the results reveal that the BVAR4 model is a viable model for forecasting. Therefore, we recommend that the levels of collinearity and autocorrelation, and the time series length should be considered in using an appropriate model for forecasting.
文摘In the paper, a general framework for large scale modeling of macroeconomic and financial time series is introduced. The proposed approach is characterized by simplicity of implementation, performing well independently of persistence and heteroskedasticity properties, accounting for common deterministic and stochastic factors. Monte Carlo results strongly support the proposed methodology, validating its use also for relatively small cross-sectional and temporal samples.
文摘In this study, impact of inflation （WPI--Wholesale Price Index）, exchange rate, and interest rate on the production of red meat in Turkey was examined using the vector autoregressive （VAR） model. The model consisting of variables of dollar exchange rate, inflation rate, interest rate, beef, buffalo meat, mutton, and goat meat production amounts has been estimated for the period from 1981 to 2014. It has been detected that there is a tie among the dollar exchange rate, inflation rate, interest rate, and the amount of red meat production in Turkey. In order to determine the direction of this relation, Granger causality test was conducted. A one-way causal relation has been observed between： the goat meat production and dollar exchange rate; the buffalo meat production and the mutton production; and the beef production and the mutton production. To interpret VAR model, the impulse response function and variance decomposition analysis was used. As a result of variance decomposition, it has been detected that explanatory power of changes in the variance of dollar exchange rate, inflation rate, and interest rate in goat meat production amount is more than explanatory power of changes in the variances of mutton, beef, and buffalo meat variables.
文摘Students in South African Universities come from different socio-cultural backgrounds, countries and high schools. This suggests that these students have different experiences which impact on their levels of grasping information in class as they potentially use different lenses on tuition. The current practice in Universities in contributing to the academic performance of students includes the use of tutors, the use of mobile devices for first year students, use of student assistants and the use of different feedback measures. What is problematic about the current practice is that students are quitting university in high numbers. In this study, knowledge has been drawn from data through the use of machine learning algorithms. Bayesian networks, support vector machines （SVMs） and decision trees algorithms were used individually in this work to construct predictive models for the academic performance of students. The best model was constructed using SVM and it gave a prediction of 72.87% and a prediction cost of 139. The model does predict the performance of students in advance of the year-end examinations outcome. The results suggest that South African Universities must recognize the diversity in student population and thus provide students with better support and equip them with the necessary knowledge that will enable them to tap into their full potential and thus enhance their skills.
基金supported by the Program of National Natural Science Foundation of China(U23A20329,62163036)Youth Academic and Technical Leaders Reserve Talent Training project(202105AC160094)Industrial Innovation Talent Special Project of Xingdian Talent Support Program(XDYC-CYCX-2022-0010).
文摘Kernel-based slow feature analysis(SFA)methods have been successfully applied in the industrial process fault detection field.However,kernel-based SFA methods have high computational complexity as dealing with nonlinearity,leading to delays in detecting time-varying data features.Additionally,the uncertain kernel function and kernel parameters limit the ability of the extracted features to express process characteristics,resulting in poor fault detection performance.To alleviate the above problems,a novel randomized auto-regressive dynamic slow feature analysis(RRDSFA)method is proposed to simultaneously monitor the operating point deviations and process dynamic faults,enabling real-time monitoring of data features in industrial processes.Firstly,the proposed Random Fourier mappingbased method achieves more effective nonlinear transformation,contrasting with the current kernelbased RDSFA algorithm that may lead to significant computational complexity.Secondly,a randomized RDSFA model is developed to extract nonlinear dynamic slow features.Furthermore,a Bayesian inference-based overall fault monitoring model including all RRDSFA sub-models is developed to overcome the randomness of random Fourier mapping.Finally,the superiority and effectiveness of the proposed monitoring method are demonstrated through a numerical case and a simulation of continuous stirred tank reactor.
基金supported by the National Natural Science Foundation of China under Grant Nos.60972150 and 10926197
文摘Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis. Traditional causality inference methods have a salient limitation that the model must be linear and with Gaussian noise. Although additive model regression can effectively infer the nonlinear causal relationships of additive nonlinear time series, it suffers from the limitation that contemporaneous causal relationships of variables must be linear and not always valid to test conditional independence relations. This paper provides a nonparametric method that employs both mutual information and conditional mutual information to identify causal structure of a class of nonlinear time series models, which extends the additive nonlinear times series to nonlinear structural vector autoregressive models. An algorithm is developed to learn the contemporaneous and the lagged causal relationships of variables. Simulations demonstrate the effectiveness of the nroosed method.
基金supported by National Natural Science Foundation of China (No.12271206)Natural Science Foundation of Jilin Province (No.20210101143JC)Science and Technology Research Planning Project of Jilin Provincial Department of Education (No.JJKH20231122KJ)。
文摘The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.
