Upper and Lower Bound Interval Forecasting Methodology Based on Ideal Boundary and Multiple Linear Regression Models

Li, Wei; Zhou, Jianzhong; Lu, Chenyang; Feng, Kuaile; Zhang, Hairong; Meng, Changqing; Sun, Na

doi:10.1007/s11269-018-2177-0

Cited by 8 publications

(5 citation statements)

References 29 publications

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“…In the linear regression, the considered model is a linear relationship between the model parameters (Ali et al, 2020). Thus, if we have n observations of x independent variable with p dimension and want to establish a linear relationship with the dependent variable y, we can use the following linear regression model (Li et al, 2019):…”

Section: The Multiple Linear Regression Modelmentioning

confidence: 99%

Estimation of seasonal and annual river flow volume based on temperature and rainfall by multiple linear and Bayesian quantile regressions

Modabber-Azizi¹,

Salarijazi²,

Ghorbani³

2022

Időjárás

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Investigation of river flow volume in different conditions as a function of temperature and rainfall variables can be quite effective in understanding the hydrological and hydro-climatic conditions of the watershed. Multiple linear regression models were applied in estimating river flow in several studies due to their straightforwardness and appropriate interpretation of results. In this study, to overcome the limitations of the multiple linear regression model, the Bayesian quantile regression model was used to estimate the river flow volume as a function of rainfall and temperature, and the results were compared. The data and information used for the Qareh-Sou basin in northern Iran are of substantial environmental and socio-economic importance. Five data series, including spring, summer, autumn, winter, and annual series, were created and used for this study. It was found that the Bayesian quantile regression model has considerable flexibility to model the volume of flow for different quantiles, predominantly upper and lower quantiles, and can be used to model high and low flows. With increasing the values of quantiles, a limited decreasing pattern in the effect of rainfall on the volume of flow was identified, which can be due to increasing the effect of other factors in the formation of extreme flows of the river. For summer data in high quantiles, the effect of rainfall on river flow volume shows an increasing pattern. This pattern is different from the other studied series, which may be due to the low base flow in summer. The results confirm that the application of Bayesian quantile regression compared to multiple linear regression leads to much more valuable information on the impact of rainfall and temperature on river flow volume.

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Section: The Multiple Linear Regression Modelmentioning

confidence: 99%

Estimation of seasonal and annual river flow volume based on temperature and rainfall by multiple linear and Bayesian quantile regressions

Modabber-Azizi¹,

Salarijazi²,

Ghorbani³

2022

Időjárás

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“…Probability methods [ 24 , 25 ], such as ARIMA, dynamic regression model, and the autoregressive threshold model, are quite challenging to get accurate model due to the difficulty of obtaining the prior knowledge required. While learning methods, such as the linear regression forecasting model [ 26 – 28 ], can get the hidden relationship between the data through adaptive learning.…”

Section: Related Workmentioning

confidence: 99%

Modeling and Analysis of Data‐Driven Systems through Computational Neuroscience Wavelet‐Deep Optimized Model for Nonlinear Multicomponent Data Forecasting

Zhang

Bai

et al. 2021

Computational Intelligence and Neuroscience

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Complex time series data exists widely in actual systems, and its forecasting has great practical significance. Simultaneously, the classical linear model cannot obtain satisfactory performance due to nonlinearity and multicomponent characteristics. Based on the data-driven mechanism, this paper proposes a deep learning method coupled with Bayesian optimization based on wavelet decomposition to model the time series data and forecasting its trend. Firstly, the data is decomposed by wavelet transform to reduce the complexity of the time series data. The Gated Recurrent Unit (GRU) network is trained as a submodel for each decomposition component. The hyperparameters of wavelet decomposition and each submodel are optimized with Bayesian sequence model-based optimization (SMBO) to develop the modeling accuracy. Finally, the results of all submodels are added to obtain forecasting results. The PM2.5 data collected by the US Air Quality Monitoring Station is used for experiments. By comparing with other networks, it can be found that the proposed method outperforms well in the multisteps forecasting task for the complex time series.

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Section: B Lower Upper Bound Estimation Algorithmmentioning

confidence: 99%

“…Ideal absolute and relative lower and upper bounding of data can be generated to identify the prediction interval associated with it [38]. Multiple linear regression models benefiting from the least square algorithm to estimate their parameters are used in [38] to identity the prediction interval width as well as the measured value. This approach is used to find the prediction interval of the daily-sampled discharge value of the Yangtze river, the longest river in Asia, located within the Chinese territory [38].…”

Section: B Lower Upper Bound Estimation Algorithmmentioning

confidence: 99%

“…Multiple linear regression models benefiting from the least square algorithm to estimate their parameters are used in [38] to identity the prediction interval width as well as the measured value. This approach is used to find the prediction interval of the daily-sampled discharge value of the Yangtze river, the longest river in Asia, located within the Chinese territory [38]. The lower upper bound estimator (LUBE) proposed by Khosravi et.…”

Section: B Lower Upper Bound Estimation Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Prediction Interval Identification Using Interval Type-2 Fuzzy Logic Systems: Lake Water Level Prediction Using Remote Sensing Data

Khanesar

Branson

2021

IEEE Sensors J.

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This paper presents a novel approach to identify the prediction interval associated with data using interval type-2 fuzzy logic systems with support vector regression. For such a purpose, a constrained quadratic objective function is defined which is then solved using well-established quadratic programming approaches. Not only does the output of interval type-2 fuzzy logic system replicates the measured value, but also it provides the lower bound and the upper bound for measured data values. In the proposed approach, to have more valuable information, a penalty term is added in the cost functions to have full control over the width of prediction interval. This method has been successfully applied to two benchmark identification problems. It is observed that by using the control parameter in the cost function, it is possible to obtain a narrower, yet inclusive prediction interval. Furthermore, superior prediction accuracy is obtained compared to existing methods in literature. Motivated by these results, the proposed approach is used to predict time series collected using a satellite from Urmia lake water level which resulted in high accuracy and an inclusive prediction interval. The graphical abstract presented for the paper illustrates the overall data gathering as well as data analysis made to estimate the prediction interval associated with Urmia lake water level data.

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Upper and Lower Bound Interval Forecasting Methodology Based on Ideal Boundary and Multiple Linear Regression Models

Cited by 8 publications

References 29 publications

Estimation of seasonal and annual river flow volume based on temperature and rainfall by multiple linear and Bayesian quantile regressions

Estimation of seasonal and annual river flow volume based on temperature and rainfall by multiple linear and Bayesian quantile regressions

Modeling and Analysis of Data‐Driven Systems through Computational Neuroscience Wavelet‐Deep Optimized Model for Nonlinear Multicomponent Data Forecasting

Prediction Interval Identification Using Interval Type-2 Fuzzy Logic Systems: Lake Water Level Prediction Using Remote Sensing Data

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