O objetivo deste artigo é avaliar previsões da inflação brasileira a partir do método não-paramétrico de Análise Espectral Singular (SSA). O exercício de previsão utiliza o esquema de janelas rolantes. Diferentes estratégias de combinação de previsões e procedimentos de seleção de variáveis para métodos multivariados foram contempladas. Para robustez, cinco horizontes de previsão foram utilizados. A avaliação das previsões considera diversos procedimentos e medidas estatísticas para oferecer conclusões confiáveis, incluindo razões de erro quadrático médio de previsão, teste de igualdade condicional de habilidade preditiva, diferenças de erro quadrático médio de previsão cumulativas e Model Confidence Set. Os resultados mostram que o SSA supera consistentemente os métodos competidores. Quase todas as previsões SSA superam os competidores em termos de erro quadrático médio de previsão, e em vários casos, com significância estatística. A análise da porção fora da amostra indica superioridade em performance relativa do SSA, especialmente no período de choque nos preços de energia elétrica. Adicionalmente, métodos SSA sempre foram incluídos no conjunto superior do Model Confidence Set. A falta de estudos relacionados com previsão da inflação brasileira e a relativa escassez de análises de previsões via métodos não-paramétricos ressaltam a relevância deste artigo. Não existem pesquisas na literatura de previsão de inflação brasileira aplicando SSA. Uma das estratégias de combinação de previsões aplicadas neste artigo não é comumente encontrada na literatura, na medida em que envolve combinações de diferentes especificações para cada método de previsão. Adicionalmente, restrições de parâmetros foram impostas nas previsões SSA, uma prática não reportada na literatura. / The purpose of this paper is to evaluate Brazilian inflation forecasts produced by the nonparametric method Singular Spectrum Analysis (SSA). This forecasting exercise employs rolling windows scheme. Different strategies of forecast combinations and variable selection procedures for multivariate methods were contemplated. For robustness, five forecast horizons were used. The forecast evaluation considers several statistical measures and procedures to offer reliable conclusions, including mean squared forecast error ratios, tests of equal conditional predictive ability, cumulative square forecast error difference and Model Confidence Set. The results show that SSA consistently outperforms the competitive methods. Almost all SSA forecasts outperforms the competitors in the mean squared forecast error sense, and several with statistical significance. Analysis of the out-of-sample portion indicates relative superior performance of SSA, especially over the period of electricity shock of prices. SSA methods were always included in the superior set of Model Confidence Set procedures. The lack of studies related to Brazilian inflation forecasting and the relative scarcity of nonparametric methods of forecasting analysis highlights the relevance of this paper. There is no research in Brazilian inflation literature applying SSA. One of the forecast combination strategies applied in this paper is not commonly found in the literature, as it involves combinations of different specifications for each forecast method. Additionally, parameter restrictions on SSA forecasts were imposed, a practice which is not reported in the literature.

O objetivo deste artigo é avaliar previsões da inflação brasileira a partir do método não-paramétrico de Análise Espectral Singular (SSA). O exercício de previsão utiliza o esquema de janelas rolantes. Diferentes estratégias de combinação de previsões e procedimentos de seleção de variáveis para métodos multivariados foram contempladas. Para robustez, cinco horizontes de previsão foram utilizados. A avaliação das previsões considera diversos procedimentos e medidas estatísticas para oferecer conclusões confiáveis, incluindo razões de erro quadrático médio de previsão, teste de igualdade condicional de habilidade preditiva, diferenças de erro quadrático médio de previsão cumulativas e Model Confidence Set. Os resultados mostram que o SSA supera consistentemente os métodos competidores. Quase todas as previsões SSA superam os competidores em termos de erro quadrático médio de previsão, e em vários casos, com significância estatística. A análise da porção fora da amostra indica superioridade em performance relativa do SSA, especialmente no período de choque nos preços de energia elétrica. Adicionalmente, métodos SSA sempre foram incluídos no conjunto superior do Model Confidence Set. A falta de estudos relacionados com previsão da inflação brasileira e a relativa escassez de análises de previsões via métodos não-paramétricos ressaltam a relevância deste artigo. Não existem pesquisas na literatura de previsão de inflação brasileira aplicando SSA. Uma das estratégias de combinação de previsões aplicadas neste artigo não é comumente encontrada na literatura, na medida em que envolve combinações de diferentes especificações para cada método de previsão. Adicionalmente, restrições de parâmetros foram impostas nas previsões SSA, uma prática não reportada na literatura. / The purpose of this paper is to evaluate Brazilian inflation forecasts produced by the nonparametric method Singular Spectrum Analysis (SSA). This forecasting exercise employs rolling windows scheme. Different strategies of forecast combinations and variable selection procedures for multivariate methods were contemplated. For robustness, five forecast horizons were used. The forecast evaluation considers several statistical measures and procedures to offer reliable conclusions, including mean squared forecast error ratios, tests of equal conditional predictive ability, cumulative square forecast error difference and Model Confidence Set. The results show that SSA consistently outperforms the competitive methods. Almost all SSA forecasts outperforms the competitors in the mean squared forecast error sense, and several with statistical significance. Analysis of the out-of-sample portion indicates relative superior performance of SSA, especially over the period of electricity shock of prices. SSA methods were always included in the superior set of Model Confidence Set procedures. The lack of studies related to Brazilian inflation forecasting and the relative scarcity of nonparametric methods of forecasting analysis highlights the relevance of this paper. There is no research in Brazilian inflation literature applying SSA. One of the forecast combination strategies applied in this paper is not commonly found in the literature, as it involves combinations of different specifications for each forecast method. Additionally, parameter restrictions on SSA forecasts were imposed, a practice which is not reported in the literature.

O objetivo deste artigo é avaliar previsões da inflação brasileira a partir do método não-paramétrico de Análise Espectral Singular (SSA). O exercício de previsão utiliza o esquema de janelas rolantes. Diferentes estratégias de combinação de previsões e procedimentos de seleção de variáveis para métodos multivariados foram contempladas. Para robustez, cinco horizontes de previsão foram utilizados. A avaliação das previsões considera diversos procedimentos e medidas estatísticas para oferecer conclusões confiáveis, incluindo razões de erro quadrático médio de previsão, teste de igualdade condicional de habilidade preditiva, diferenças de erro quadrático médio de previsão cumulativas e Model Confidence Set. Os resultados mostram que o SSA supera consistentemente os métodos competidores. Quase todas as previsões SSA superam os competidores em termos de erro quadrático médio de previsão, e em vários casos, com significância estatística. A análise da porção fora da amostra indica superioridade em performance relativa do SSA, especialmente no período de choque nos preços de energia elétrica. Adicionalmente, métodos SSA sempre foram incluídos no conjunto superior do Model Confidence Set. A falta de estudos relacionados com previsão da inflação brasileira e a relativa escassez de análises de previsões via métodos não-paramétricos ressaltam a relevância deste artigo. Não existem pesquisas na literatura de previsão de inflação brasileira aplicando SSA. Uma das estratégias de combinação de previsões aplicadas neste artigo não é comumente encontrada na literatura, na medida em que envolve combinações de diferentes especificações para cada método de previsão. Adicionalmente, restrições de parâmetros foram impostas nas previsões SSA, uma prática não reportada na literatura. / The purpose of this paper is to evaluate Brazilian inflation forecasts produced by the nonparametric method Singular Spectrum Analysis (SSA). This forecasting exercise employs rolling windows scheme. Different strategies of forecast combinations and variable selection procedures for multivariate methods were contemplated. For robustness, five forecast horizons were used. The forecast evaluation considers several statistical measures and procedures to offer reliable conclusions, including mean squared forecast error ratios, tests of equal conditional predictive ability, cumulative square forecast error difference and Model Confidence Set. The results show that SSA consistently outperforms the competitive methods. Almost all SSA forecasts outperforms the competitors in the mean squared forecast error sense, and several with statistical significance. Analysis of the out-of-sample portion indicates relative superior performance of SSA, especially over the period of electricity shock of prices. SSA methods were always included in the superior set of Model Confidence Set procedures. The lack of studies related to Brazilian inflation forecasting and the relative scarcity of nonparametric methods of forecasting analysis highlights the relevance of this paper. There is no research in Brazilian inflation literature applying SSA. One of the forecast combination strategies applied in this paper is not commonly found in the literature, as it involves combinations of different specifications for each forecast method. Additionally, parameter restrictions on SSA forecasts were imposed, a practice which is not reported in the literature.

Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Researchers and investors have been attempting to predict stock market activity for years. The possible financial gain that accurate predictions would offer lit a flame of greed and drive that would inspire all kinds of researchers. However, after many of these researchers have failed, they started to hypothesize that a goal such as this is not only improbable, but impossible. Previous predictions were based on historical data of the stock market activity itself and would often incorporate different types of auxiliary data. This auxiliary data ranged as far as imagination allowed in an attempt to find some correlation and some insight into the future, that could in turn lead to the figurative pot of gold. More often than not, the auxiliary data would not prove helpful. However, with the birth of the internet, endless amounts of new sources of auxiliary data presented itself. In this thesis I propose that the near in finite amount of data available on the internet could provide us with information that would improve stock market predictions. With this goal in mind, the different sources of information available on the internet are considered. Previous studies on similar topics presented possible ways in which we can measure internet activity, which might relate to stock market activity. These studies also gave some insights on the advantages and disadvantages of using some of these sources. These considerations are investigated in this thesis. Since a lot of this work is therefore based on the prediction of a time series, it was necessary to choose a prediction algorithm. Previously used linear methods seemed too simple for prediction of stock market activity and a new non-linear method, called Singular Spectrum Analysis, is therefore considered. A detailed study of this algorithm is done to ensure that it is an appropriate prediction methodology to use. Furthermore, since we will be including auxiliary information, multivariate extensions of this algorithm are considered as well. Some of the inaccuracies and inadequacies of these current multivariate extensions are studied and an alternative multivariate technique is proposed and tested. This alternative approach addresses the inadequacies of existing methods. With the appropriate methodology chosen and the appropriate sources of auxiliary information chosen, a concluding chapter is done on whether predictions that includes auxiliary information (obtained from the internet) improve on baseline predictions that are simply based on historical stock market data. / AFRIKAANSE OPSOMMING: Navorsers en beleggers is vir jare al opsoek na maniere om aandeelpryse meer akkuraat te voorspel. Die moontlike finansiële implikasies wat akkurate vooruitskattings kan inhou het 'n vlam van geldgierigheid en dryf wakker gemaak binne navorsers regoor die wêreld. Nadat baie van hierdie navorsers onsuksesvol was, het hulle begin vermoed dat so 'n doel nie net onwaarskynlik is nie, maar onmoontlik. Vorige vooruitskattings was bloot gebaseer op historiese aandeelprys data en sou soms verskillende tipes bykomende data inkorporeer. Die tipes data wat gebruik was het gestrek so ver soos wat die verbeelding toegelaat het, in 'n poging om korrelasie en inligting oor die toekoms te kry wat na die guurlike pot goud sou lei. Navorsers het gereeld gevind dat hierdie verskillende tipes bykomende inligting nie van veel hulp was nie, maar met die geboorte van die internet het 'n oneindige hoeveelheid nuwe bronne van bykomende inligting bekombaar geraak. In hierdie tesis stel ek dus voor dat die data beskikbaar op die internet dalk vir ons kan inligting gee wat verwant is aan toekomstige aandeelpryse. Met hierdie doel in die oog, is die verskillende bronne van inligting op die internet gebestudeer. Vorige studies op verwante werk het sekere spesifieke maniere voorgestel waarop ons internet aktiwiteit kan meet. Hierdie studies het ook insig gegee oor die voordele en die nadele wat sommige bronne inhou. Hierdie oorwegings word ook in hierdie tesis bespreek. Aangesien 'n groot gedeelte van hierdie tesis dus gebasseer word op die vooruitskatting van 'n tydreeks, is dit nodig om 'n toepaslike vooruitskattings algoritme te kies. Baie navorsers het verkies om eenvoudige lineêre metodes te gebruik. Hierdie metodes het egter te eenvoudig voorgekom en 'n relatiewe nuwe nie-lineêre metode (met die naam "Singular Spectrum Analysis") is oorweeg. 'n Deeglike studie van hierdie algoritme is gedoen om te verseker dat die metode van toepassing is op aandeelprys data. Verder, aangesien ons gebruik wou maak van bykomende inligting, is daar ook 'n studie gedoen op huidige multivariaat uitbreidings van hierdie algoritme en die probleme wat dit inhou. 'n Alternatiewe multivariaat metode is toe voorgestel en getoets wat hierdie probleme aanspreek. Met 'n gekose vooruitskattingsmetode en gekose bronne van bykomende data is 'n gevolgtrekkende hoofstuk geskryf oor of vooruitskattings, wat die bykomende internet data inkorporeer, werklik in staat is om te verbeter op die eenvoudige vooruitskattings, wat slegs gebaseer is op die historiese aandeelprys data.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: In this research work, auto-associative neural networks have been used for changepoint detection. This is a nonlinear technique that employs the use of artificial neural networks as inspired among other by Frank Rosenblatt’s linear perceptron algorithm for classification. An auto-associative neural network was used successfully to detect change-points for various types of time series data. Its performance was compared to that of singular spectrum analysis developed by Moskvina and Zhigljavsky. Fraction of Explained Variance (FEV) was also used to compare the performance of the two methods. FEV indicators are similar to the eigenvalues of the covariance matrix in principal component analysis. Two types of time series data were used for change-point detection: Gaussian data series and nonlinear reaction data series. The Gaussian data had four series with different types of change-points, namely a change in the mean value of the time series (T1), a change in the variance of the time series (T2), a change in the autocorrelation of the time series (T3), and a change in the crosscorrelation of two time series (T4). Both linear and nonlinear methods were able to detect the changes for T1, T2 and T4. None of them could detect the changes in T3. With the Gaussian data series, linear singular spectrum analysis (LSSA) performed as well as the NLSSA for the change point detection. This is because the time series was linear and the nonlinearity of the NLSSA was therefore not important. LSSA did even better than NLSSA when comparing FEV values, since it is not subject to suboptimal solutions as could sometimes be the case with autoassociative neural networks. The nonlinear data consisted of the Belousov-Zhabotinsky (BZ) reactions, autocatalytic reaction time series data and data representing a predator-prey system. With the NLSSA methods, change points could be detected accurately in all three systems, while LSSA only managed to detect the change-point on the BZ reactions and the predator-prey system. The NLSSA method also fared better than the LSSA method when comparing FEV values for the BZ reactions. The LSSA method was able to model the autocatalytic reactions fairly accurately, being able to explain 99% of the variance in the data with one component only. NLSSA with two nodes on the bottleneck attained an FEV of 87%. The performance of both NLSSA and LSSA were comparable for the predator-prey system, both systems, where both could attain FEV values of 92% with a single component. An auto-associative neural network is a good technique for change point detection in nonlinear time series data. However, it offers no advantage over linear techniques when the time series data are linear. / AFRIKAANSE OPSOMMING: In hierdie navorsing is outoassosiatiewe neurale netwerk gebruik vir veranderingspuntwaarneming. Dis is ‘n nielineêre tegniek wat neurale netwerke gebruik soos onder andere geïnspireer deur Frank Rosnblatt se lineêre perseptronalgoritme vir klassifikasie. ‘n Outoassosiatiewe neurale netwerk is suksesvol gebruik om veranderingspunte op te spoor in verskeie tipes tydreeksdata. Die prestasie van die outoassosiatiewe neurale netwerk is vergelyk met singuliere spektrale oontleding soos ontwikkel deur Moskvina en Zhigljavsky. Die fraksie van die verklaarde variansie (FEV) is ook gebruik om die prestasie van die twee metodes te vergelyk. FEV indikatore is soortgelyk aan die eiewaardes van die kovariansiematriks in hoofkomponentontleding. Twee tipes tydreeksdata is gebruik vir veranderingspuntopsporing: Gaussiaanse tydreekse en nielineêre reaksiedatareekse. Die Gaussiaanse data het vier reekse gehad met verskillende veranderingspunte, naamlik ‘n verandering in die gemiddelde van die tydreeksdata (T1), ‘n verandering in die variansie van die tydreeksdata (T2), ‘n verandering in die outokorrelasie van die tydreeksdata (T3), en ‘n verandering in die kruiskorrelasie van twee tydreekse (T4). Beide lineêre en nielineêre metodes kon die veranderinge in T1, T2 en T4 opspoor. Nie een het egter daarin geslaag om die verandering in T3 op te spoor nie. Met die Gaussiaanse tydreeks het lineêre singuliere spektrumanalise (LSSA) net so goed gevaar soos die outoassosiatiewe neurale netwerk of nielineêre singuliere spektrumanalise (NLSSA), aangesien die tydreekse lineêr was en die vermoë van die NLSSA metode om nielineêre gedrag te identifiseer dus nie belangrik was nie. Inteendeel, die LSSA metode het ‘n groter FEV waarde getoon as die NLSSA metode, omdat LSSA ook nie blootgestel is aan suboptimale oplossings, soos wat soms die geval kan wees met die afrigting van die outoassosiatiewe neural netwerk nie. Die nielineêre data het bestaan uit die Belousov-Zhabotinsky (BZ) reaksiedata, ‘n outokatalitiese reaksietydreeksdata en data wat ‘n roofdier-prooistelsel verteenwoordig het. Met die NLSSA metode kon veranderingspunte betroubaar opgespoor word in al drie tydreekse, terwyl die LSSA metode net die veranderingspuntin die BZ reaksie en die roofdier-prooistelsel kon opspoor. Die NLSSA metode het ook beter gevaaar as die LSSA metode wanneer die FEV waardes vir die BZ reaksies vergelyk word. Die LSSA metode kon die outokatalitiese reaksies redelik akkuraat modelleer, en kon met slegs een komponent 99% van die variansie in die data verklaar. Die NLSSA metode, met twee nodes in sy bottelneklaag, kon ‘n FEV waarde van slegs 87% behaal. Die prestasie van beide metodes was vergelykbaar vir die roofdier-prooidata, met beide wat FEV waardes van 92% kon behaal met hulle een komponent. ‘n Outoassosiatiewe neural netwerk is ‘n goeie metode vir die opspoor van veranderingspunte in nielineêre tydreeksdata. Dit hou egter geen voordeel in wanneer die data lineêr is nie.

Electromyogram (EMG) is an established tool to study operation of neuromuscular systems. In analysing EMG signals, accurate detection of the movement-related events in the signal is frequently necessary. I explored the application of change-point detection algorithm proposed by Moskvina et. al., 2003 to EMG event detection, and evaluated the technique’s performance comparing it to two common threshold-based event detection methods and to the visual estimates of the EMG events performed by trained practitioners in the field. The algorithm was implemented in MATLAB and applied to EMG segments recorded from wrist and trunk muscles. The quality and frequency of successful detection were assessed for all methods, using the average visual estimate as the baseline, against which techniques were evaluated. The application showed that the change-point detection can successfully locate multiple changes in the EMG signal, but the maximum value of the detection statistic did not always identify the muscle activation onset.

No description available.

Electromyogram (EMG) is an established tool to study operation of neuromuscular systems. In analysing EMG signals, accurate detection of the movement-related events in the signal is frequently necessary. I explored the application of change-point detection algorithm proposed by Moskvina et. al., 2003 to EMG event detection, and evaluated the technique’s performance comparing it to two common threshold-based event detection methods and to the visual estimates of the EMG events performed by trained practitioners in the field. The algorithm was implemented in MATLAB and applied to EMG segments recorded from wrist and trunk muscles. The quality and frequency of successful detection were assessed for all methods, using the average visual estimate as the baseline, against which techniques were evaluated. The application showed that the change-point detection can successfully locate multiple changes in the EMG signal, but the maximum value of the detection statistic did not always identify the muscle activation onset.

Response reconstruction is used to obtain accurate replication of vehicle structural responses of field recorded measurements in a laboratory environment, a crucial step in the process of Accelerated Destructive Testing (ADT). Response Reconstruction is cast as an inverse problem whereby the desired input is inferred using the measured outputs of a system. ADT typically involves large shock loadings resulting in a nonlinear response of the structure. A promising linear regression technique known as Spanning Basis Transformation Regression (SBTR) in con- junction with non-overlapping windows casts the low dimensional nonlinear problem as a high dimensional linear problem. However, it is determined that the original implementation of SBTR struggles to invert a broader class of sensor configurations. A new windowing method called AntiDiagonal Averaging (ADA) is developed to overcome the shortcomings of the SBTR im- plementation. ADA introduces overlaps within the predicted time signal windows and averages them. The newly proposed method is tested on a numerical quarter car model and is shown to successfully invert a broader range of sensor configurations as well as being capable of describing nonlinearities in the system. / Dissertation (MEng)--University of Pretoria, 2021. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

[pt] Em função da predominância das fontes hidráulicas no sistema elétrico brasileiro, há uma grande incerteza na oferta futura de energia. Para lidar com a incerteza hidrológica, a política ótima de operação do sistema elétrico brasileiro é fruto de um sofisticado modelo de otimização estocástica no qual são considerados um amplo conjunto de séries sintéticas (cenários) de Energia Natural Afluente (ENA). Tradicionalmente, as séries sintéticas de ENA têm sido geradas por modelos periódicos autorregressivos PAR(p). Recentemente, o advento da energia eólica e o crescimento da sua participação no sistema elétrico brasileiro apontam para a necessidade de métodos capazes de gerar séries sintéticas de velocidade do vento. Assim, nesta tese propõe-se uma metodologia para geração de séries sintéticas baseada no uso combinado da modelagem PAR(p) e da análise espectral singular. A metodologia proposta é geral e pode ser usada na geração de séries sintéticas da ENA e da velocidade de vento. A análise espectral singular ou Singular Spectrum Analysis (SSA) é uma metodologia recente em séries temporais. Através de SSA pode-se extrair tendências ou sazonalidades bem como suavizar a série através da remoção de componentes ruidosas. SSA vem sendo aplicado com sucesso em diversas áreas do conhecimento como em Hidrologia e Economia. A Multi-channel Singular Spectrum Analysis (MSSA) é uma extensão natural do SSA quando aplicada a múltiplas séries simultaneamente. A metodologia proposta foi aplicada às séries de ENA dos quatro subsistemas elétricos (Nordeste, Norte, Sudeste/Centro-Oeste e Sul) e comparada ao modelo PAR(p) já existente. Adicionalmente, a metodologia proposta foi aplicada na geração de séries sintéticas de velocidade do vento em duas localidades situadas no Nordeste brasileiro. Os bons resultados alcançados indicam que a metodologia proposta pode ser utilizada na geração de séries sintéticas de ENA e de energia eólica consideradas nos modelos de otimização estocástica que auxiliam o planejamento da operação energética do sistema elétrico brasileiro. / [en] Due to the predominance of hydraulic sources in the Brazilian electrical system, there is a large uncertainty in future energy supply. To deal with hydrologic uncertainty, the optimal operation policy of the Brazilian electric system is the result of a sophisticated stochastic optimization where are considered a large set of synthetic series (scenarios) of Affluent Natural Energy (ENA). Traditionally, synthetic ENA series have been generated by periodic autoregressive models PAR (p). Recently, the advent of wind energy and its growth of participation in Brazilian electrical system indicate to the need for methods to generate synthetic series of wind speed. Thus, this thesis proposes a methodology for generating synthetic series based on the combined use of PAR (p) models and the Singular Spectrum Analysis (SSA). The proposed methodology is general and can be used to generate synthetic series of ENA and wind speed. SSA is a recent methodology in time series. Through SSA it can extract trends or seasonality and smoothing by removing the series of noisy components. SSA has been successfully applied in various fields of knowledge as in Hydrology and Economics. Multi-channel Singular Spectrum Analysis (MSSA) is a natural extension of the SSA when applied to multiple series simultaneously. The proposed methodology was applied to the ENA series of four electric subsystems (Northeast, North, Southeast / Midwest and South) and compared to the PAR (p) existing model. Additionally, the proposed methodology was applied to the generation of synthetic series of wind speed at two sites located in the Brazilian Northeast. The good results achieved demonstrate that the proposed methodology can be used to generate synthetic series of ENA and wind energy considered in stochastic optimization models that assist planning the operation of the Brazilian electric energy system.