Abstract The article refers to the topic of the SARS CoV-2 virus pandemic and focuses on the effect of vaccines against this virus. The relation between the administered vaccines and the development of the global pandemic is very pertinent as the problem is being faced by the whole world. The difficulty lies in the fight against the pandemic, which is the cause of the very high death rate due to the virus, and has caused a global economic crisis. Demonstrating patterns and possible anomalies between data on the number of people vaccinated and the course of the disease and the number of deaths is an important factor in raising awareness of the risk of spreading the virus. The methods presented in the second chapter are data agglomeration and the k-means method. The study compared the results obtained in six selected countries from different regions of the world and presented the most important factors influencing the development of the pandemic. The presented methodology was also the basis for a deeper discussion of the factors determining the spread of the virus and can be an introduction to the analysis of time series. At the same time, it enabled the creation of patterns related to the studied phenomenon (for selected countries) defining local factors contributing to the spread of the disease and determining the effectiveness of the vaccines administered in them. The empirical analysis was conducted on the basis of data available in the electronic scientific publication https://ourworldindata.org/. The visualisations were made in the Tableau program, and the cluster analysis was carried out using the Statistica package.
{"title":"Cluster Analysis and Visualisation Describing the Phenomenon of the Covid-19 Virus Pandemic","authors":"G. Trzpiot, Zuzanna Krysiak","doi":"10.15611/eada.2023.2.03","DOIUrl":"https://doi.org/10.15611/eada.2023.2.03","url":null,"abstract":"Abstract The article refers to the topic of the SARS CoV-2 virus pandemic and focuses on the effect of vaccines against this virus. The relation between the administered vaccines and the development of the global pandemic is very pertinent as the problem is being faced by the whole world. The difficulty lies in the fight against the pandemic, which is the cause of the very high death rate due to the virus, and has caused a global economic crisis. Demonstrating patterns and possible anomalies between data on the number of people vaccinated and the course of the disease and the number of deaths is an important factor in raising awareness of the risk of spreading the virus. The methods presented in the second chapter are data agglomeration and the k-means method. The study compared the results obtained in six selected countries from different regions of the world and presented the most important factors influencing the development of the pandemic. The presented methodology was also the basis for a deeper discussion of the factors determining the spread of the virus and can be an introduction to the analysis of time series. At the same time, it enabled the creation of patterns related to the studied phenomenon (for selected countries) defining local factors contributing to the spread of the disease and determining the effectiveness of the vaccines administered in them. The empirical analysis was conducted on the basis of data available in the electronic scientific publication https://ourworldindata.org/. The visualisations were made in the Tableau program, and the cluster analysis was carried out using the Statistica package.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":"27 1","pages":"45 - 61"},"PeriodicalIF":1.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41889571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The information society is a product of the intersection of socio-historical-technological contexts, where the development of science and industry has a global reach. The pervasiveness of new information and communication technologies makes it an essential component of a new civilization, affecting every country in varying degrees. Although this techniques approach is grounded in some truth, it neglects other vital aspects that challenge the idea of an information society that prioritizes human needs. The leading nations have achieved this through active research and development, driven by government involvement and the significant contributions of universities. Furthermore, the collaboration of diverse economic, institutional, social, and civic actors has played an essential role in its advancement. However, constructing and promoting an information society transcends infrastructure. It involves political actions that consider the socio-technological nature of this development and its impact on society and other sectors of activity. The objective of this article is twofold. On the one hand, the study analysed the situation of Algeria and its position in relation to other countries regarding the information society, and the other examined the factors that influence the development of the information society in Algeria, trying to identify the most important ones. Finally, the authors proposed a development strategy in this area. The research thesis was formulated as follows: What are the key variables that have an impact on the development of digitalization and the information society in Algeria? Thus, the regulatory frameworks of the most advanced countries are central to the initiatives aimed at its development. To foster the emergence of an information society in Algeria, solidarity must be strengthened, diversity promoted, and the potential of all citizens catalysed.
{"title":"Digitalization and the Information Society in Algeria: Digital Transformation Actors and Key Variables","authors":"Maria Bouberka, S. Fadel, Hassan Derrar","doi":"10.15611/eada.2023.2.02","DOIUrl":"https://doi.org/10.15611/eada.2023.2.02","url":null,"abstract":"Abstract The information society is a product of the intersection of socio-historical-technological contexts, where the development of science and industry has a global reach. The pervasiveness of new information and communication technologies makes it an essential component of a new civilization, affecting every country in varying degrees. Although this techniques approach is grounded in some truth, it neglects other vital aspects that challenge the idea of an information society that prioritizes human needs. The leading nations have achieved this through active research and development, driven by government involvement and the significant contributions of universities. Furthermore, the collaboration of diverse economic, institutional, social, and civic actors has played an essential role in its advancement. However, constructing and promoting an information society transcends infrastructure. It involves political actions that consider the socio-technological nature of this development and its impact on society and other sectors of activity. The objective of this article is twofold. On the one hand, the study analysed the situation of Algeria and its position in relation to other countries regarding the information society, and the other examined the factors that influence the development of the information society in Algeria, trying to identify the most important ones. Finally, the authors proposed a development strategy in this area. The research thesis was formulated as follows: What are the key variables that have an impact on the development of digitalization and the information society in Algeria? Thus, the regulatory frameworks of the most advanced countries are central to the initiatives aimed at its development. To foster the emergence of an information society in Algeria, solidarity must be strengthened, diversity promoted, and the potential of all citizens catalysed.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":"27 1","pages":"21 - 44"},"PeriodicalIF":1.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41377297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-18DOI: 10.3390/econometrics11020013
Chengyu Li, Luyi W. Shen, G. Qian
Time-series data, which exhibit a low signal-to-noise ratio, non-stationarity, and non-linearity, are commonly seen in high-frequency stock trading, where the objective is to increase the likelihood of profit by taking advantage of tiny discrepancies in prices and trading on them quickly and in huge quantities. For this purpose, it is essential to apply a trading method that is capable of fast and accurate prediction from such time-series data. In this paper, we developed an online time series forecasting method for high-frequency trading (HFT) by integrating three neural network deep learning models, i.e., long short-term memory (LSTM), gated recurrent unit (GRU), and transformer; and we abbreviate the new method to online LGT or O-LGT. The key innovation underlying our method is its efficient storage management, which enables super-fast computing. Specifically, when computing the forecast for the immediate future, we only use the output calculated from the previous trading data (rather than the previous trading data themselves) together with the current trading data. Thus, the computing only involves updating the current data into the process. We evaluated the performance of O-LGT by analyzing high-frequency limit order book (LOB) data from the Chinese market. It shows that, in most cases, our model achieves a similar speed with a much higher accuracy than the conventional fast supervised learning models for HFT. However, with a slight sacrifice in accuracy, O-LGT is approximately 12 to 64 times faster than the existing high-accuracy neural network models for LOB data from the Chinese market.
{"title":"Online Hybrid Neural Network for Stock Price Prediction: A Case Study of High-Frequency Stock Trading in the Chinese Market","authors":"Chengyu Li, Luyi W. Shen, G. Qian","doi":"10.3390/econometrics11020013","DOIUrl":"https://doi.org/10.3390/econometrics11020013","url":null,"abstract":"Time-series data, which exhibit a low signal-to-noise ratio, non-stationarity, and non-linearity, are commonly seen in high-frequency stock trading, where the objective is to increase the likelihood of profit by taking advantage of tiny discrepancies in prices and trading on them quickly and in huge quantities. For this purpose, it is essential to apply a trading method that is capable of fast and accurate prediction from such time-series data. In this paper, we developed an online time series forecasting method for high-frequency trading (HFT) by integrating three neural network deep learning models, i.e., long short-term memory (LSTM), gated recurrent unit (GRU), and transformer; and we abbreviate the new method to online LGT or O-LGT. The key innovation underlying our method is its efficient storage management, which enables super-fast computing. Specifically, when computing the forecast for the immediate future, we only use the output calculated from the previous trading data (rather than the previous trading data themselves) together with the current trading data. Thus, the computing only involves updating the current data into the process. We evaluated the performance of O-LGT by analyzing high-frequency limit order book (LOB) data from the Chinese market. It shows that, in most cases, our model achieves a similar speed with a much higher accuracy than the conventional fast supervised learning models for HFT. However, with a slight sacrifice in accuracy, O-LGT is approximately 12 to 64 times faster than the existing high-accuracy neural network models for LOB data from the Chinese market.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48511547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-20DOI: 10.3390/econometrics11020011
D. Bauer
When using vector autoregressive (VAR) models for approximating time series, a key step is the selection of the lag length. Often this is performed using information criteria, even if a theoretical justification is lacking in some cases. For stationary processes, the asymptotic properties of the corresponding estimators are well documented in great generality in the book Hannan and Deistler (1988). If the data-generating process is not a finite-order VAR, the selected lag length typically tends to infinity as a function of the sample size. For invertible vector autoregressive moving average (VARMA) processes, this typically happens roughly proportional to logT. The same approach for lag length selection is also followed in practice for more general processes, for example, unit root processes. In the I(1) case, the literature suggests that the behavior is analogous to the stationary case. For I(2) processes, no such results are currently known. This note closes this gap, concluding that information-criteria-based lag length selection for I(2) processes indeed shows similar properties to in the stationary case.
{"title":"Information-Criterion-Based Lag Length Selection in Vector Autoregressive Approximations for I(2) Processes","authors":"D. Bauer","doi":"10.3390/econometrics11020011","DOIUrl":"https://doi.org/10.3390/econometrics11020011","url":null,"abstract":"When using vector autoregressive (VAR) models for approximating time series, a key step is the selection of the lag length. Often this is performed using information criteria, even if a theoretical justification is lacking in some cases. For stationary processes, the asymptotic properties of the corresponding estimators are well documented in great generality in the book Hannan and Deistler (1988). If the data-generating process is not a finite-order VAR, the selected lag length typically tends to infinity as a function of the sample size. For invertible vector autoregressive moving average (VARMA) processes, this typically happens roughly proportional to logT. The same approach for lag length selection is also followed in practice for more general processes, for example, unit root processes. In the I(1) case, the literature suggests that the behavior is analogous to the stationary case. For I(2) processes, no such results are currently known. This note closes this gap, concluding that information-criteria-based lag length selection for I(2) processes indeed shows similar properties to in the stationary case.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44213583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.3390/econometrics11020010
Paul Haimerl, Tobias Hartl
The COVID-19 pandemic is characterized by a recurring sequence of peaks and troughs. This article proposes a regime-switching unobserved components (UC) approach to model the trend of COVID-19 infections as a function of this ebb and flow pattern. Estimated regime probabilities indicate the prevalence of either an infection up- or down-turning regime for every day of the observational period. This method provides an intuitive real-time analysis of the state of the pandemic as well as a tool for identifying structural changes ex post. We find that when applied to U.S. data, the model closely tracks regime changes caused by viral mutations, policy interventions, and public behavior.
{"title":"Modeling COVID-19 Infection Rates by Regime-Switching Unobserved Components Models","authors":"Paul Haimerl, Tobias Hartl","doi":"10.3390/econometrics11020010","DOIUrl":"https://doi.org/10.3390/econometrics11020010","url":null,"abstract":"The COVID-19 pandemic is characterized by a recurring sequence of peaks and troughs. This article proposes a regime-switching unobserved components (UC) approach to model the trend of COVID-19 infections as a function of this ebb and flow pattern. Estimated regime probabilities indicate the prevalence of either an infection up- or down-turning regime for every day of the observational period. This method provides an intuitive real-time analysis of the state of the pandemic as well as a tool for identifying structural changes ex post. We find that when applied to U.S. data, the model closely tracks regime changes caused by viral mutations, policy interventions, and public behavior.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42104536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-09DOI: 10.3390/econometrics11010009
Gianluca Cubadda, Alain Hecq, Elisa Voisin
This paper proposes concepts and methods to investigate whether the bubble patterns observed in individual time series are common among them. Having established the conditions under which common bubbles are present within the class of mixed causal–noncausal vector autoregressive models, we suggest statistical tools to detect the common locally explosive dynamics in a Student t-distribution maximum likelihood framework. The performances of both likelihood ratio tests and information criteria were investigated in a Monte Carlo study. Finally, we evaluated the practical value of our approach via an empirical application on three commodity prices.
{"title":"Detecting Common Bubbles in Multivariate Mixed Causal–Noncausal Models","authors":"Gianluca Cubadda, Alain Hecq, Elisa Voisin","doi":"10.3390/econometrics11010009","DOIUrl":"https://doi.org/10.3390/econometrics11010009","url":null,"abstract":"This paper proposes concepts and methods to investigate whether the bubble patterns observed in individual time series are common among them. Having established the conditions under which common bubbles are present within the class of mixed causal–noncausal vector autoregressive models, we suggest statistical tools to detect the common locally explosive dynamics in a Student t-distribution maximum likelihood framework. The performances of both likelihood ratio tests and information criteria were investigated in a Monte Carlo study. Finally, we evaluated the practical value of our approach via an empirical application on three commodity prices.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136178880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this research study, the authors obtained the preliminary evaluation of the impact detection of vaccinations against COVID-19 in the EU-27. The empirical basis of the study was the daily number of COVID-19 cases, vaccinations, hospitalisations, and deaths in the EU countries from March 2020 to March 2022. Rules of association were used to identify non-obvious associations between vaccinations against COVID-19 and cases of illness, hospitalisations, and deaths from COVID-19. The obtained results were used to cluster the EU countries by the level of vaccinations against COVID-19, cases of COVID-19, deaths from COVID, and COVID-19 hospitalisations for the EU member states. The K-means clustering method was used for cluster analysis. Hidden dependencies of the number of COVID-19 cases, the number of COVID-19 hospitalisations, and the number of COVID-19 deaths due to the number of vaccinations against COVID-19 by EU countries were revealed. It was established with a high probability that vaccination significantly affects the level of morbidity. For the first time, association rules were obtained, which are preliminary estimates of the relationship between the dynamics of vaccinations against COVID-19 and the dynamics of COVID-19 cases, COVID-19 hospitalisations, and deaths from COVID-19 in the EU. The results can be used to make beneficial decisions, for example, to regulate vaccination policies in individual EU countries, and predict the future consequences of the COVID-19 pandemic.
{"title":"The Application of Association Rules to Detect the Effects of Vaccinations against Covid-19 in the EU-27. Preliminary Estimates","authors":"K. Berezka, Olha Kovalchuk","doi":"10.15611/eada.2023.1.01","DOIUrl":"https://doi.org/10.15611/eada.2023.1.01","url":null,"abstract":"Abstract In this research study, the authors obtained the preliminary evaluation of the impact detection of vaccinations against COVID-19 in the EU-27. The empirical basis of the study was the daily number of COVID-19 cases, vaccinations, hospitalisations, and deaths in the EU countries from March 2020 to March 2022. Rules of association were used to identify non-obvious associations between vaccinations against COVID-19 and cases of illness, hospitalisations, and deaths from COVID-19. The obtained results were used to cluster the EU countries by the level of vaccinations against COVID-19, cases of COVID-19, deaths from COVID, and COVID-19 hospitalisations for the EU member states. The K-means clustering method was used for cluster analysis. Hidden dependencies of the number of COVID-19 cases, the number of COVID-19 hospitalisations, and the number of COVID-19 deaths due to the number of vaccinations against COVID-19 by EU countries were revealed. It was established with a high probability that vaccination significantly affects the level of morbidity. For the first time, association rules were obtained, which are preliminary estimates of the relationship between the dynamics of vaccinations against COVID-19 and the dynamics of COVID-19 cases, COVID-19 hospitalisations, and deaths from COVID-19 in the EU. The results can be used to make beneficial decisions, for example, to regulate vaccination policies in individual EU countries, and predict the future consequences of the COVID-19 pandemic.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":"27 1","pages":"1 - 16"},"PeriodicalIF":1.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43373985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper attempted using the prospect theory to explain overbidding in first price auctions. The standard outlook in the literature on auctions is that bidders overbid, but the probability weighting functions are nonlinear as in the prospect theory, so they not only tend to underweight the probabilities of winning the auction but also overweight, so that there are overbidders and underbidders. This paper proves that to some extent, non-linear weighting functions do explain overbidding the risk-neutral Nash equilibrium valuation (RNNE). Furthermore, coherent risk measures, such as certainty equivalent and translation invariance, were used to show loss aversion among bidders, and in line with the prospect theory, convexity was also confirmed with sub-additivity, monotonicity and with positive homogeneity.
{"title":"The Prospect Theory and First Price Auctions: an Explanation of Overbidding","authors":"Dushko Josheski, M. Apostolov","doi":"10.15611/eada.2023.1.03","DOIUrl":"https://doi.org/10.15611/eada.2023.1.03","url":null,"abstract":"Abstract This paper attempted using the prospect theory to explain overbidding in first price auctions. The standard outlook in the literature on auctions is that bidders overbid, but the probability weighting functions are nonlinear as in the prospect theory, so they not only tend to underweight the probabilities of winning the auction but also overweight, so that there are overbidders and underbidders. This paper proves that to some extent, non-linear weighting functions do explain overbidding the risk-neutral Nash equilibrium valuation (RNNE). Furthermore, coherent risk measures, such as certainty equivalent and translation invariance, were used to show loss aversion among bidders, and in line with the prospect theory, convexity was also confirmed with sub-additivity, monotonicity and with positive homogeneity.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":"27 1","pages":"33 - 74"},"PeriodicalIF":1.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42003324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this research was to study a nonparametric estimator of the density and mode function of a scalar response variable given a functional variable, when the observations are i.i.d. This proposed estimator is given by combining Missing At Random (MAR) with the local linear approach. Finally, a comparison study based on simulated data is also provided to illustrate the finite sample performances and the usefulness of the local linear approach with MAR to the presence of even a small proportion of outliers in the data.
摘要本文研究了给定函数变量的标量响应变量的密度和模态函数的非参数估计。该估计是将随机缺失(Missing At Random, MAR)方法与局部线性方法相结合得到的。最后，还提供了基于模拟数据的比较研究，以说明有限样本的性能以及局部线性方法与MAR的有用性，即使数据中存在很小比例的异常值。
{"title":"The Estimating of the Conditional Density with Application to the Mode Function in Scalar-On-Function Regression Structure: Local Linear Approach with Missing at Random","authors":"Wahiba Bouabsa","doi":"10.15611/eada.2023.1.02","DOIUrl":"https://doi.org/10.15611/eada.2023.1.02","url":null,"abstract":"Abstract The aim of this research was to study a nonparametric estimator of the density and mode function of a scalar response variable given a functional variable, when the observations are i.i.d. This proposed estimator is given by combining Missing At Random (MAR) with the local linear approach. Finally, a comparison study based on simulated data is also provided to illustrate the finite sample performances and the usefulness of the local linear approach with MAR to the presence of even a small proportion of outliers in the data.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":"27 1","pages":"17 - 32"},"PeriodicalIF":1.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46522692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-26DOI: 10.3390/econometrics11020014
T. Szabados
The aim of this paper to give a multidimensional version of the classical one-dimensional case of smooth spectral density. A spectral density with smooth eigenvalues and H∞ eigenvectors gives an explicit method to factorize the spectral density and compute the Wold representation of a weakly stationary time series. A formula, similar to the Kolmogorov–Szego formula, is given for the covariance matrix of the innovations. These results are important to give the best linear predictions of the time series. The results are applicable when the rank of the process is smaller than the dimension of the process, which occurs frequently in many current applications, including econometrics.
{"title":"Factorization of a Spectral Density with Smooth Eigenvalues of a Multidimensional Stationary Time Series","authors":"T. Szabados","doi":"10.3390/econometrics11020014","DOIUrl":"https://doi.org/10.3390/econometrics11020014","url":null,"abstract":"The aim of this paper to give a multidimensional version of the classical one-dimensional case of smooth spectral density. A spectral density with smooth eigenvalues and H∞ eigenvectors gives an explicit method to factorize the spectral density and compute the Wold representation of a weakly stationary time series. A formula, similar to the Kolmogorov–Szego formula, is given for the covariance matrix of the innovations. These results are important to give the best linear predictions of the time series. The results are applicable when the rank of the process is smaller than the dimension of the process, which occurs frequently in many current applications, including econometrics.","PeriodicalId":11499,"journal":{"name":"Econometrics","volume":"1 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41497795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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