Fast Piecewise Polynomial Fitting of Time-Series Data for Streaming Computing

Gao, Jianhua; Ji, Weixing; Zhang, Lulu; Shao, Senhao; Wang, Yizhuo; Shi, Feng

doi:10.1109/access.2020.2976494

Cited by 19 publications

(15 citation statements)

References 42 publications

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“…Let

y_{n}

be the set of observation and

x_{n}

be the lag of count, where n is the number is observations. The relationship between

x

and

y

is expressed as

y^{r_{((), x)}} ((), r < n)

y^{r_{((), x_{i})}} goodbreak= a_{0} goodbreak+ a_{i} x_{i} goodbreak+ a_{2} x_{i}^{2} goodbreak+ \dots goodbreak+ a_{r - 1} x_{i}^{r - 1} goodbreak+ a_{r} x_{i}^{r},

where

i = 1, \dots, n

( n = number of observations points) and

a_{0}, a_{1}, \dots, a_{r}

are regression coefficients determined by the lease square error fitting method (Gao et al, 2020; Liu & Wang, 2014). The value

e_{pi} = ∣ y_{i} - y_{(x_{i})}^{r} ∣

denotes the residual between the fitted value

y_{(x_{i})}^{r}

and the original observation

y_{i}

.…”

Section: Methodsmentioning

confidence: 99%

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ANN–polynomial–Fourier series modeling and Monte Carlo forecasting of tourism data

Danbatta

Varol

2022

Journal of Forecasting

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Modeling and forecasting of tourism data have received attention in the past decades. Turkey is one of the countries that benefit significantly from the tourism industry. Several time-series models have been recommended to best describe tourist arrivals to Turkey. However, in the 21st century, the world experiences great uncertainty in most possible event outcomes. These uncertainties are very difficult to account for. We proposed a hybrid artificial neural network (ANN)-polynomial-Fourier method to model the number of foreign visitors to Turkey from January 2004 to December 2020. The proposed model performance before and during the COVID-19 pandemic is evaluated separately. We evaluate the model performance by comparing with results from Danbatta and Varol (2021, https://doi.org/10.1142/S179396232141004X), Fourier series, and ARIMA models. To account for prediction uncertainties, we ran 300 Monte Carlo simulations within ±2σ from the model regression curve. According to the result outcomes, the proposed ANN-polynomial-Fourier has proven worthy to be considered a candidate model for the Turkish tourism data. The multistep ahead forecast suggests a 10.22% increase in the monthly foreign visitors' arrivals to Turkey in the year 2021.

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“…Let

y_{n}

be the set of observation and

x_{n}

be the lag of count, where n is the number is observations. The relationship between

x

and

y

is expressed as

y^{r_{((), x)}} ((), r < n)

y^{r_{((), x_{i})}} goodbreak= a_{0} goodbreak+ a_{i} x_{i} goodbreak+ a_{2} x_{i}^{2} goodbreak+ \dots goodbreak+ a_{r - 1} x_{i}^{r - 1} goodbreak+ a_{r} x_{i}^{r},

where

i = 1, \dots, n

( n = number of observations points) and

a_{0}, a_{1}, \dots, a_{r}

are regression coefficients determined by the lease square error fitting method (Gao et al, 2020; Liu & Wang, 2014). The value

e_{pi} = ∣ y_{i} - y_{(x_{i})}^{r} ∣

denotes the residual between the fitted value

y_{(x_{i})}^{r}

and the original observation

y_{i}

.…”

Section: Methodsmentioning

confidence: 99%

“…where i ¼ 1, …, n (n = number of observations points) and a 0 , a 1 , …, a r are regression coefficients determined by the lease square error fitting method (Gao et al, 2020;Liu & Wang, 2014). The value e pi ¼j y i À y r…”

Section: Polynomial Fitmentioning

confidence: 99%

ANN–polynomial–Fourier series modeling and Monte Carlo forecasting of tourism data

Danbatta

Varol

2022

Journal of Forecasting

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“…Considering that the trend component of user electricity consumption is relatively stable, polynomial curve fitting method [18] can be used for its forecasting. The following polynomial function is constructed to represent the functional relationship between the trend component Q t,tr and period t, and expressed as…”

Section: Monthly Load Forecasting For Different Componentsmentioning

confidence: 99%

Monthly load forecasting for China’s delegate power purchase mechanism considering customer churn

Huang¹,

Wen²,

Wen³

et al. 2023

International Conference on Computer, Artificial Intelligence, and Control Engineering (CAICE 2023)

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The delegate power purchase mechanism in China’s electricity retail reform requires power grid companies to make accurate user load forecasting and reasonable market decisions, and the result will affect the user’s electricity price. Under this background, a monthly load forecasting method is studied for power grid company considering the impact of customer churn on the agency electricity consumption. Firstly, a customer churn model based on life cycle theory is proposed to predict the customer churn rate of a power grid company in a specific period of the development process of China’s electricity retail reform. The seasonal and trend decomposition algorithm for decomposing user monthly electricity consumption series is presented, based on which the trend, seasonal, and remainder components of user load are predicted respectively by using polynomial curve fitting methods. Then, the monthly load forecasting model for agent users is proposed according to the expected customer churn rate and the prediction of different load components. A simple electricity market is served for demonstrating the proposed method, and the simulation results show that the proposed method has higher accuracy of monthly load forecasting than the other model that does not consider the predicted customer churn rate of power grid companies.

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“…Piecewise polynomial fitting is a popular method used to observe the trend in time series and to identify the timing of change points by minimizing the residual sum of squares of all possible combinations of segments representing time intervals of several years [36,37]. Breakpoint years, which showed significant changes in the PWD-damaged forest distribution, were estimated, and separate periods with significant trend changes were identified.…”

Section: Piecewise Polynomial Fittingmentioning

confidence: 99%

Spatiotemporal Dynamics and Factors Driving the Distributions of Pine Wilt Disease-Damaged Forests in China

Wei

Peng

Liu

et al. 2022

Forests

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Many forests have suffered serious economic losses and ecological consequences of pine wilt disease (PWD) outbreaks. Climate change and human activities could accelerate the distribution of PWD, causing the exponential expansion of damaged forest areas in China. However, few studies have analyzed the spatiotemporal dynamics and the factors driving the distribution of PWD-damaged forests using continuous records of long-term damage, focusing on short-term environmental factors that influence multiple PWD outbreaks. We used a maximum entropy (MaxEnt) model that incorporated annual meteorological and human activity factors, as well as temporal dependence (the PWD distribution in the previous year), to determine the contributions of environmental factors to the annual distribution of PWD-damaged forests in the period 1982–2020. Overall, the MaxEnt showed good performance in modeling the PWD-damaged forest distributions between 1982 and 2020. Our results indicate that (i) the temporal lag dependence term for the presence/absence of PWD was the best predictor of the distribution of PWD-damaged forests; and (ii) Bio14 (precipitation in the driest month) was the most important meteorological factor for affecting the PWD-damaged forests. These results are essential to understanding the factors governing the distribution of PWD-damaged forests, which is important for forest management and pest control worldwide.

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Fast Piecewise Polynomial Fitting of Time-Series Data for Streaming Computing

Cited by 19 publications

References 42 publications

ANN–polynomial–Fourier series modeling and Monte Carlo forecasting of tourism data

ANN–polynomial–Fourier series modeling and Monte Carlo forecasting of tourism data

Monthly load forecasting for China’s delegate power purchase mechanism considering customer churn

Spatiotemporal Dynamics and Factors Driving the Distributions of Pine Wilt Disease-Damaged Forests in China

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