Academic literature on the topic 'Temporal heteroscedasticity'

Abstract. Bayesian inference of microbial soil respiration models is often based on the assumptions that the residuals are independent (i.e., no temporal or spatial correlation), identically distributed (i.e., Gaussian noise), and have constant variance (i.e., homoscedastic). In the presence of model discrepancy, as no model is perfect, this study shows that these assumptions are generally invalid in soil respiration modeling such that residuals have high temporal correlation, an increasing variance with increasing magnitude of CO2 efflux, and non-Gaussian distribution. Relaxing these three assumptions stepwise results in eight data models. Data models are the basis of formulating likelihood functions of Bayesian inference. This study presents a systematic and comprehensive investigation of the impacts of data model selection on Bayesian inference and predictive performance. We use three mechanistic soil respiration models with different levels of model fidelity (i.e., model discrepancy) with respect to the number of carbon pools and the explicit representations of soil moisture controls on carbon degradation; therefore, we have different levels of model complexity with respect to the number of model parameters. The study shows that data models have substantial impacts on Bayesian inference and predictive performance of the soil respiration models such that the following points are true: (i) the level of complexity of the best model is generally justified by the cross-validation results for different data models; (ii) not accounting for heteroscedasticity and autocorrelation might not necessarily result in biased parameter estimates or predictions, but will definitely underestimate uncertainty; (iii) using a non-Gaussian data model improves the parameter estimates and the predictive performance; and (iv) accounting for autocorrelation only or joint inversion of correlation and heteroscedasticity can be problematic and requires special treatment. Although the conclusions of this study are empirical, the analysis may provide insights for selecting appropriate data models for soil respiration modeling.

Temporal variables and vertical ground reaction force have been used as measures characterizing sprinting. A recently developed wireless pressure sensor insole (sensor insole) could be useful for monitoring sprinting in terms of temporal variables and vertical ground reaction force during training sessions. The purpose of this study was to examine the concurrent validity of the sensor insole for measuring temporal and vertical force variables during sprinting. One athlete performed five 50-m sprints, and the step-to-step vertical ground reaction force and plantar pressure were simultaneously measured by a long-force platform system (reference device) and the sensor insole, respectively. The temporal and vertical ground reaction force variables were calculated using signals from both devices, and a comparison was made between values obtained with both devices for 125 steps analyzed. The percentage bias, 95% limits of agreement, and Bland–Altman plots showed low agreement with the reference device for all variables except for step frequency. For the vertical ground reaction force variables, the sensor insole underestimated the values (−18.9 to −48.3%) compared to the force platform. While support time and time to maximal vertical force from the foot strike were overestimated by the sensor insole (54.6 ± 8.0% and 94.2 ± 23.2%), flight time was underestimated (−48.2 ± 15.0%). Moreover, t-test revealed the significant difference in all variables between the sensor insole and force platform, except for step frequency. The bias for step frequency (0.4 ± 7.5%) was small. However, there was heteroscedasticity for all variables. The results from this study demonstrate that a wireless pressure sensor insole is generally not valid to measure the temporal and vertical force variables during sprinting. Thus, using the examined sensor insole for monitoring sprinting characteristics is not recommended at this time.

The existing index system for volatility forecasting only focuses on asset return series or historical volatility, and the prediction model cannot effectively describe the highly complex and nonlinear characteristics of the stock market. In this study, we construct an investor attention factor through a Baidu search index of antecedent keywords, and then combine other trading information such as the trading volume, trend indicator, quote change rate, etc., as input indicators, and finally employ the deep learning model via temporal convolutional networks (TCN) to forecast the volatility under high-frequency financial data. We found that the prediction accuracy of the TCN model with investor attention is better than those of the TCN model without investor attention, the traditional econometric model as the generalized autoregressive conditional heteroscedasticity (GARCH), the heterogeneous autoregressive model of realized volatility (HAR-RV), autoregressive fractionally integrated moving average (ARFIMA) models, and the long short-term memory (LSTM) model with investor attention. Compared with the traditional econometric models, the multi-step prediction results for the TCN model remain robust. Our findings provide a more accurate and robust method for volatility forecasting for big data and enrich the index system of volatility forecasting.

The impact evaluation of exogenous policies over time is of great importance in several areas. Unfortunately, an adequate time-series analysis has not always been taken into account in the literature, mainly in health problems. When regression models are used in the known interrupted time-series approach, the required error assumptions are in general neglected. Specifically, usual linear segmented regression (lmseg) models are not adequate when the errors have nonconstant variance and serial correlation. To instigate the correct use of intervention analysis, we present a simple approach extending a linear model with log-linear variance (lmvar) to estimate linear trend changes under heteroscedastic errors (lmsegvar). When the errors are autocorrelated, the Cochrane-Orcutt (CO) modification is implemented to correct the estimated parameters. As an application, we estimate the impact in temporal trend of the Brazilian Rede Mãe Paranaense (RMP) program in gestational syphilis occurrences in the state of Parana, Brazil. The comparison of the proposed linear segmented model (lmsegvar+CO) modeling both the average and variance, with the usual segmented linear model (lmseg), where just the average is modeled, shows the importance of taking heteroscedasticity and autocorrelation into account.

This study was conducted to evaluate the variability, trends, volatility, and transition patterns of rainfall in drought-prone northwest Bangladesh. Daily rainfall recorded at five stations for the period 1959–2018 were used for this purpose. Non-parametric tests of variability changes, a modified Mann–Kendall trend test, innovative trend analysis (ITA), a generalized autoregressive conditional heteroscedasticity (GARCH)–jump model, and a Markov chain (MC) were used to assess the variability changes, trends, volatility, and transitions in rainfall to understand the possibility of the persistence of droughts and their predictability. The results showed an overall decrease of variability in annual and seasonal rainfall, but an increase in mean pre-monsoon rainfall and a decrease in mean monsoon rainfall. This caused a decrease in pre-monsoon droughts, but few changes in monsoon droughts. The ITA and rainfall anomaly analysis revealed high temporal variability and, thus, rapid shifts in rainfall regimes, which were also supported by the volatility dynamics and time-varying jumps from the GARCH–jump model and the rapid changes in drought index from the MC analysis. Therefore, the lack of drought in recent years cannot be considered as an indicator of declining droughts in the region.

Background Markerless systems to capture body motion require no markers to be attached to the body, thereby improving clinical feasibility and testing time. However, the lack of markers might affect the accuracy of measurements. Objective This study aimed to determine the absolute reliability and concurrent validity of the Kinect system with MotionMetrix software for spatiotemporal variables during running at a comfortable velocity, by comparing data between the combination system and two widely used systems—OptoGait and high-speed video analysis at 1000 Hz. Methods In total, 25 runners followed a running protocol on a treadmill at a speed of 12 km/h. The Kinect+MotionMetrix combination measured spatiotemporal parameters during running (ie, contact time, flight time, step frequency, and step length), which were compared to those obtained from two reference systems. Results Regardless of the system, flight time had the highest coefficients of variation (OptoGait: 16.4%; video analysis: 17.3%; Kinect+MotionMetrix: 23.2%). The rest of the coefficients of variation reported were lower than 8.1%. Correlation analysis showed very high correlations (r>0.8; P<.001) and almost perfect associations (intraclass correlation coefficient>0.81) between systems for all the spatiotemporal parameters except contact time, which had lower values. Bland-Altman plots revealed smaller systematic biases and random errors for step frequency and step length and larger systematic biases and random errors for temporal parameters with the Kinect+MotionMetrix system as compared to OptoGait (difference: contact time +3.0%, flight time −7.9%) and high-speed video analysis at 1000 Hz (difference: contact time +4.2%, flight time −11.3%). Accordingly, heteroscedasticity was found between systems for temporal parameters (r2>0.1). Conclusions The results indicate that the Kinect+MotionMetrix combination slightly overestimates contact time and strongly underestimates flight time as compared to the OptoGait system and high-speed video analysis at 1000 Hz. However, it is a valid tool for measuring step frequency and step length when compared to reference systems. Future studies should determine the reliability of this system for determining temporal parameters.

Modelos GARCH tendo a normal e a t-Student como distribuições condicionais são amplamente utilizados para modelagem da volatilidade de dados financeiros. No entanto, tais distribuições podem não ser apropriadas para algumas séries com caudas pesadas e comportamento leptocúrtico. As chamadas distribuições estáveis podem ser mais adequadas para sua modelagem, como já explorado na literatura. Por outro lado, os modelos GAS (Generalized Autoregressive Score), com desenvolvimento recente, tratam-se de modelos dinâmicos que possuem em sua estrutura a função score (derivada do logaritmo da verossimilhança). Tal abordagem oferece uma direção natural para a evolução dos parâmetros da distribuição dos dados. Neste trabalho, é proposto um novo modelo GAS em conjunção com distribuições estáveis simétricas para a modelagem da volatilidade - de fato, é uma generalização do GARCH, pois, para uma particular escolha de distribuição estável e de estrutura do modelo, tem-se o clássico modelo GARCH gaussiano. Como em geral a função densidade das distribuições estáveis não possui forma analítica fechada, é apresentado seu procedimento de cálculo, bem como de suas derivadas, para o completo desenvolvimento do método de estimação dos parâmetros. Também são analisadas as condições de estacionariedade e a estrutura de dependência do modelo. Estudos de simulação são conduzidos, bem como uma aplicação a dados reais, para comparação entre modelos usuais, que utilizam distribuições normal e t-Student, e o modelo proposto, demonstrando a eficácia deste.
GARCH models with normal and t-Student conditional distributions are widely used for volatility modeling in financial data. However, such distributions may not be suitable for some heavy-tailed and leptokurtic series. The stable distributions may be more adequate to fit such characteristics, as already exploited in the literature. On the other hand, the recently developed GAS (Generalized Autoregressive Score) models are dynamic models in which the updating mechanism of the time-varying parameters is based on the score function (first derivative of the log-likelihood function). This provides the natural direction for updating the parameters, based on the complete density. We propose a new GAS model with symmetric stable distribution for volatility modeling. The model can be interpreted as a generalization of the GARCH models, since the classic gaussian GARCH model is derived from it by using particular choices of the stable distribution and the model structure. There are no closed analytical expressions for general stable densities in most cases, hence its numeric computation and derivatives are detailed for the sake of complete development of the estimation process. The stationarity conditions and the dependence structure of the model are analysed. Simulation studies, as well as an application to real data, are presented for comparisons between the usual models and the proposed model, illustrating the effectiveness of the latter.

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O objetivo deste estudo é propor a implementação de um modelo estatístico para cálculo da volatilidade, não difundido na literatura brasileira, o modelo de escala local (LSM), apresentando suas vantagens e desvantagens em relação aos modelos habitualmente utilizados para mensuração de risco. Para estimação dos parâmetros serão usadas as cotações diárias do Ibovespa, no período de janeiro de 2009 a dezembro de 2014, e para a aferição da acurácia empírica dos modelos serão realizados testes fora da amostra, comparando os VaR obtidos para o período de janeiro a dezembro de 2014. Foram introduzidas variáveis explicativas na tentativa de aprimorar os modelos e optou-se pelo correspondente americano do Ibovespa, o índice Dow Jones, por ter apresentado propriedades como: alta correlação, causalidade no sentido de Granger, e razão de log-verossimilhança significativa. Uma das inovações do modelo de escala local é não utilizar diretamente a variância, mas sim a sua recíproca, chamada de 'precisão' da série, que segue uma espécie de passeio aleatório multiplicativo. O LSM captou todos os fatos estilizados das séries financeiras, e os resultados foram favoráveis a sua utilização, logo, o modelo torna-se uma alternativa de especificação eficiente e parcimoniosa para estimar e prever volatilidade, na medida em que possui apenas um parâmetro a ser estimado, o que representa uma mudança de paradigma em relação aos modelos de heterocedasticidade condicional.
The objective of this study is to propose the implementation of a statistical model to calculate the volatility not widespread in Brazilian literature, LSM, with its advantages and disadvantages compared to the models commonly used for risk measurement. To estimate the parameters will be used daily prices of Ibovespa in the period from January 2009 to December 2014, and to measure the empirical accuracy of the models out of sample tests will be performed, comparing the VaR obtained for the period from January to December 2014. Explanatory variables were introduced in an attempt to improve the models, and we chose to its corresponding American Ibovespa, the Dow Jones index, for presenting characteristics such as high correlation, causality in the Granger sense, and reason for significant log-likelihood. One of the local scale model innovation is not directly use the variance, but its reciprocal, called 'precision' series, which follows a kind of multiplicative random walk. LSM captured all financial series of stylized facts, and the results were favorable to use, so the model becomes an efficient and economical alternative specification for estimating and predicting volatility, to the extent that only one parameter has to be estimated, which represents a paradigm shift in the models of conditional heteroscedasticity.