scholarly journals Optimal forecasting accuracy using Lp-norm combination

METRON ◽  
2021 ◽  
Author(s):  
Massimiliano Giacalone
Keyword(s):  
Real Data ◽  
Optimization Techniques ◽  
Combination Method ◽  
Forecast Combination ◽  
Forecasting Accuracy ◽  
Lp Norm ◽  
Combination Methods ◽  
Historical Series ◽  
Non Gaussian ◽  
Standard Regression

AbstractA well-known result in statistics is that a linear combination of two-point forecasts has a smaller Mean Square Error (MSE) than the two competing forecasts themselves (Bates and Granger in J Oper Res Soc 20(4):451–468, 1969). The only case in which no improvements are possible is when one of the single forecasts is already the optimal one in terms of MSE. The kinds of combination methods are various, ranging from the simple average (SA) to more robust methods such as the one based on median or Trimmed Average (TA) or Least Absolute Deviations or optimization techniques (Stock and Watson in J Forecast 23(6):405–430, 2004). Standard regression-based combination approaches may fail to get a realistic result if the forecasts show high collinearity in several situations or the data distribution is not Gaussian. Therefore, we propose a forecast combination method based on Lp-norm estimators. These estimators are based on the Generalized Error Distribution, which is a generalization of the Gaussian distribution, and they can be used to solve the cases of multicollinearity and non-Gaussianity. In order to demonstrate the potential of Lp-norms, we conducted a simulated and an empirical study, comparing its performance with other standard-regression combination approaches. We carried out the simulation study with different values of the autoregressive parameter, by alternating heteroskedasticity and homoskedasticity. On the other hand, the real data application is based on the daily Bitfinex historical series of bitcoins (2014–2020) and the 25 historical series relating to companies included in the Dow Jonson, were subsequently considered. We showed that, by combining different GARCH and the ARIMA models, assuming both Gaussian and non-Gaussian distributions, the Lp-norm scheme improves the forecasting accuracy with respect to other regression-based combination procedures.

Forecasting Tourism Demand With a New Time-Varying Forecast Averaging Approach

2021 ◽  
pp. 004728752110612
Author(s):  
Yuying Sun ◽  
Jian Zhang ◽  
Xin Li ◽  
Shouyang Wang
Keyword(s):  
Structural Changes ◽  
Model Averaging ◽  
Structural Instability ◽  
Time Varying ◽  
Forecast Combination ◽  
Tourism Demand ◽  
Single Model ◽  
Forecasting Accuracy ◽  
Combination Methods ◽  
Out Of Sample

Existing research has shown that combination can effectively improve tourism forecasting accuracy compared with single model. However, the model uncertainty and structural instability in combination for out-of-sample tourism forecasting may influence the forecasting performance. This paper proposes a novel forecast combination approach based on time-varying jackknife model averaging (TVJMA), which can more efficiently handle structural changes and nonstationary trends in tourism data. Using Hong Kong tourism demand from five major tourism source regions as an empirical study, we investigate whether our proposed nonparametric TVJMA-based approach can improve tourism forecasting accuracy further. Empirical results show that the proposed TVJMA-based approach outperforms other competitors including single model and three combination methods in most cases. Findings indicate the outstanding performance of our method is robust to various forecasting horizons and different estimation periods.

scholarly journals Day Ahead Hourly Global Horizontal Irradiance Forecasting—Application to South African Data

Energies ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 3569 ◽  
Author(s):  
Phathutshedzo Mpfumali ◽  
Caston Sigauke ◽  
Alphonce Bere ◽  
Sophie Mulaudzi
Keyword(s):  
Machine Learning ◽  
Solar Power ◽  
Prediction Interval ◽  
Combination Method ◽  
Support Vector ◽  
Forecast Combination ◽  
Learning Methods ◽  
Machine Learning Methods ◽  
Stochastic Gradient Boosting ◽  
Combination Methods

Due to its variability, solar power generation poses challenges to grid energy management. In order to ensure an economic operation of a national grid, including its stability, it is important to have accurate forecasts of solar power. The current paper discusses probabilistic forecasting of twenty-four hours ahead of global horizontal irradiance (GHI) using data from the Tellerie radiometric station in South Africa for the period August 2009 to April 2010. Variables are selected using a least absolute shrinkage and selection operator (Lasso) via hierarchical interactions and the parameters of the developed models are estimated using the Barrodale and Roberts’s algorithm. Two forecast combination methods are used in this study. The first is a convex forecast combination algorithm where the average loss suffered by the models is based on the pinball loss function. A second forecast combination method, which is quantile regression averaging (QRA), is also used. The best set of forecasts is selected based on the prediction interval coverage probability (PICP), prediction interval normalised average width (PINAW) and prediction interval normalised average deviation (PINAD). The results demonstrate that QRA gives more robust prediction intervals than the other models. A comparative analysis is done with two machine learning methods—stochastic gradient boosting and support vector regression—which are used as benchmark models. Empirical results show that the QRA model yields the most accurate forecasts compared to the machine learning methods based on the probabilistic error measures. Results on combining prediction interval limits show that the PMis the best prediction limits combination method as it gives a hit rate of 0.955 which is very close to the target of 0.95. This modelling approach is expected to help in optimising the integration of solar power in the national grid.

scholarly journals Short-Term Wind Speed Forecasting Using Statistical and Machine Learning Methods

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 132 ◽  
Author(s):  
Lucky O. Daniel ◽  
Caston Sigauke ◽  
Colin Chibaya ◽  
Rendani Mbuvha
Keyword(s):  
Wind Speed ◽  
Quantile Regression ◽  
Predictive Performance ◽  
Additive Models ◽  
Combination Method ◽  
Forecast Combination ◽  
Primary Input ◽  
Stochastic Gradient Boosting ◽  
Combination Methods ◽  
Forecasts Combination

Wind offers an environmentally sustainable energy resource that has seen increasing global adoption in recent years. However, its intermittent, unstable and stochastic nature hampers its representation among other renewable energy sources. This work addresses the forecasting of wind speed, a primary input needed for wind energy generation, using data obtained from the South African Wind Atlas Project. Forecasting is carried out on a two days ahead time horizon. We investigate the predictive performance of artificial neural networks (ANN) trained with Bayesian regularisation, decision trees based stochastic gradient boosting (SGB) and generalised additive models (GAMs). The results of the comparative analysis suggest that ANN displays superior predictive performance based on root mean square error (RMSE). In contrast, SGB shows outperformance in terms of mean average error (MAE) and the related mean average percentage error (MAPE). A further comparison of two forecast combination methods involving the linear and additive quantile regression averaging show the latter forecast combination method as yielding lower prediction accuracy. The additive quantile regression averaging based prediction intervals also show outperformance in terms of validity, reliability, quality and accuracy. Interval combination methods show the median method as better than its pure average counterpart. Point forecasts combination and interval forecasting methods are found to improve forecast performance.

scholarly journals A Changing Weights Spatial Forecast Combination Approach with an Application to Housing Price Prediction

2020 ◽  
Vol 12 (4) ◽  
pp. 11
Author(s):  
Chuanhua Wei ◽  
Chenping Du ◽  
Nana Zheng
Keyword(s):  
Spatial Data ◽  
Time Series Data ◽  
House Prices ◽  
Housing Price ◽  
Combination Method ◽  
Series Data ◽  
Forecast Combination ◽  
Combination Methods ◽  
Seminal Article ◽  
Combination Approach

Forecast combination has been widely applied in various fields since the seminal article of Bates and Granger (1969). However, these research were focused only on time series data. Few study focus on the spatial data, this paper proposes a novel adaptive spatial forecast combination method with varying weights based on the geographically weighted regression technique. Finally, the proposed method is applied to the Boston house prices prediction, and the results indicate that our procedure performs better than the other forecast combination methods.

scholarly journals MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

scholarly journals An improved conflicting-evidence combination method based on the redistribution of the basic probability assignment

2021 ◽  
Author(s):  
Zezheng Yan ◽  
Hanping Zhao ◽  
Xiaowen Mei
Keyword(s):  
Evidence Theory ◽  
Combination Method ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Combination Methods ◽  
Conflicting Evidence ◽  
Basic Probability ◽  
The Right ◽  
Conflict Intensity ◽  
Dempster’S Rule Of Combination

AbstractDempster–Shafer evidence theory is widely applied in various fields related to information fusion. However, the results are counterintuitive when highly conflicting evidence is fused with Dempster’s rule of combination. Many improved combination methods have been developed to address conflicting evidence. Nevertheless, all of these approaches have inherent flaws. To solve the existing counterintuitive problem more effectively and less conservatively, an improved combination method for conflicting evidence based on the redistribution of the basic probability assignment is proposed. First, the conflict intensity and the unreliability of the evidence are calculated based on the consistency degree, conflict degree and similarity coefficient among the evidence. Second, the redistribution equation of the basic probability assignment is constructed based on the unreliability and conflict intensity, which realizes the redistribution of the basic probability assignment. Third, to avoid excessive redistribution of the basic probability assignment, the precision degree of the evidence obtained by information entropy is used as the correction factor to modify the basic probability assignment for the second time. Finally, Dempster’s rule of combination is used to fuse the modified basic probability assignment. Several different types of examples and actual data sets are given to illustrate the effectiveness and potential of the proposed method. Furthermore, the comparative analysis reveals the proposed method to be better at obtaining the right results than other related methods.

scholarly journals Robust Weighted l1,2 Norm Filtering in Passive Radar Systems

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3270 ◽  
Author(s):  
Baris Satar ◽  
Gokhan Soysal ◽  
Xue Jiang ◽  
Murat Efe ◽  
Thiagalingam Kirubarajan
Keyword(s):  
Target Detection ◽  
Impulsive Noise ◽  
Simulated Data ◽  
Real Data ◽  
Detection Performance ◽  
Passive Radar ◽  
Mobile Telecommunication ◽  
Telecommunication System ◽  
Conventional Methods ◽  
Non Gaussian

Conventional methods such as matched filtering, fractional lower order statistics cross ambiguity function, and recent methods such as compressed sensing and track-before-detect are used for target detection by passive radars. Target detection using these algorithms usually assumes that the background noise is Gaussian. However, non-Gaussian impulsive noise is inherent in real world radar problems. In this paper, a new optimization based algorithm that uses weighted l 1 and l 2 norms is proposed as an alternative to the existing algorithms whose performance degrades in the presence of impulsive noise. To determine the weights of these norms, the parameter that quantifies the impulsiveness level of the noise is estimated. In the proposed algorithm, the aim is to increase the target detection performance of a universal mobile telecommunication system (UMTS) based passive radars by facilitating higher resolution with better suppression of the sidelobes in both range and Doppler. The results obtained from both simulated data with α stable distribution, and real data recorded by a UMTS based passive radar platform are presented to demonstrate the superiority of the proposed algorithm. The results show that the proposed algorithm provides more robust and accurate detection performance for noise models with different impulsiveness levels compared to the conventional methods.

Modeling CO2 Emissions of Top 5 Emitters with Combination Technique

2012 ◽  
Vol 616-618 ◽  
pp. 1143-1147
Author(s):  
Wei Sun ◽  
Jing Min Wang ◽  
Jun Jie Kang
Keyword(s):  
Forecast Error ◽  
Combination Method ◽  
Future Projection ◽  
Forecasting Accuracy ◽  
Combination Technique ◽  
Combination Forecast ◽  
Forecast Models ◽  
Model Time Series ◽  
Grey Verhulst Model ◽  
Better Than

In this paper, the performance of combination forecast methods for CO2 emissions prediction is investigated. Linear model, time series model, GM (1, 1) model and Grey Verhulst model are selected in study as the separate models. And, four kinds of combination forecast models, i.e. the equivalent weight (EW) combination method, variance-covariance (VACO) combination method, regression combination (R) method, and discounted mean square forecast error (MSFE) method are chosen to employ for top 5 CO2 emitters. The forecasting accuracy is compared between these combination models and single models. This research suggests that the combination forecasts are almost certain to outperform the worst individual forecasts and maybe even better than most individual ones. Furthermore the combination forecasts can avoid the risk of model choosing in future projection. For CO2 emissions forecast with many uncertain factors in the future, combining the single forecast would be safer in such forecasting situations.

scholarly journals Computing the Partial Correlation of ICA Models for Non-Gaussian Graph Signal Processing

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 22 ◽  
Author(s):  
Jordi Belda ◽  
Luis Vergara ◽  
Gonzalo Safont ◽  
Addisson Salazar
Keyword(s):  
Signal Processing ◽  
Partial Correlation ◽  
Correlation Coefficients ◽  
Real Data ◽  
Linear Estimation ◽  
Precision Matrix ◽  
Conditional Mean ◽  
Graph Signal Processing ◽  
Gaussian Case ◽  
Non Gaussian

Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context.

scholarly journals Research on Improvement of the Combination Method for Conflicting Evidence Based on Historical Data

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 762
Author(s):  
Shuai Yuan ◽  
Honglei Wang
Keyword(s):  
Decision Rule ◽  
Historical Data ◽  
Evidence Theory ◽  
Weighted Average ◽  
Combination Method ◽  
Final Decision ◽  
Evidence Based ◽  
Combination Methods ◽  
Conflicting Evidence ◽  
The Difference

In a multi-sensor system, due to the difference of performance of sensors and the environment in which the sensor collects evidence, evidence collected will be highly conflicting, which leads to the failure of D-S evidence theory. The current research on combination methods of conflicting evidence focuses on eliminating the problem of "Zadeh paradox" brought by conflicting evidence, but do not distinguish the evidence from different sources effectively. In this paper, the credibility of each piece of evidence to be combined is weighted based on historical data, and the modified evidence is obtained by weighted average. Then the final result is obtained by combining the modified evidence using D-S evidence theory, and the improved decision rule is used for the final decision. After the decision, the system updates and stores the historical data based on actual results. The improved decision rule can solve the problem that the system cannot make a decision when there are two or more propositions corresponding to the maximum support in the final combination result. This method satisfies commutative law and associative law, so it has the symmetry that can meet the needs of the combination of time-domain evidence. Numerical examples show that the combination method of conflict evidence based on historical data can not only solve the problem of “Zadeh paradox”, but also obtain more reasonable results.

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