scholarly journals Practical Considerations for Optimal Weights in Density Forecast Combination

2013 ◽  
Author(s):  
Andrey L. L. Vasnev ◽  
Laurent Pauwels
Keyword(s):  
Forecast Combination ◽  
Density Forecast ◽  
Optimal Weights

scholarly journals Probability Forecast Combination via Entropy Regularized Wasserstein Distance

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 929
Author(s):  
Ryan Cumings-Menon ◽  
Minchul Shin
Keyword(s):  
Wasserstein Distance ◽  
Tuning Parameter ◽  
Forecast Combination ◽  
Probability Forecast ◽  
Density Forecast ◽  
Combination Methods ◽  
Multivariate Gaussian ◽  
Density Forecasting ◽  
Gaussian Input

We propose probability and density forecast combination methods that are defined using the entropy regularized Wasserstein distance. First, we provide a theoretical characterization of the combined density forecast based on the regularized Wasserstein distance under the assumption. More specifically, we show that the regularized Wasserstein barycenter between multivariate Gaussian input densities is multivariate Gaussian, and provide a simple way to compute mean and its variance–covariance matrix. Second, we show how this type of regularization can improve the predictive power of the resulting combined density. Third, we provide a method for choosing the tuning parameter that governs the strength of regularization. Lastly, we apply our proposed method to the U.S. inflation rate density forecasting, and illustrate how the entropy regularization can improve the quality of predictive density relative to its unregularized counterpart.

scholarly journals On the Forecast Combination Puzzle

Econometrics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 39
Author(s):  
Wei Qian ◽  
Craig A. Rolling ◽  
Gang Cheng ◽  
Yuhong Yang
Keyword(s):  
Estimation Error ◽  
Real Data ◽  
Forecast Combination ◽  
Optimal Weights ◽  
Multi Level ◽  
Simple Average ◽  
Combining Methods

It is often reported in the forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the “forecast combination puzzle”. Motivated by this puzzle, we explore its possible explanations, including high variance in estimating the target optimal weights (estimation error), invalid weighting formulas, and model/candidate screening before combination. We show that the existing understanding of the puzzle should be complemented by the distinction of different forecast combination scenarios known as combining for adaptation and combining for improvement. Applying combining methods without considering the underlying scenario can itself cause the puzzle. Based on our new understandings, both simulations and real data evaluations are conducted to illustrate the causes of the puzzle. We further propose a multi-level AFTER strategy that can integrate the strengths of different combining methods and adapt intelligently to the underlying scenario. In particular, by treating the simple average as a candidate forecast, the proposed strategy is shown to reduce the heavy cost of estimation error and, to a large extent, mitigate the puzzle.

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

An adaptive forecast combination approach based on meta intuitionistic fuzzy functions

2021 ◽  
Vol 40 (5) ◽  
pp. 9567-9581
Author(s):  
Nihat Tak ◽  
Erol Egrioglu ◽  
Eren Bas ◽  
Ufuk Yolcu
Keyword(s):  
Meta Analysis ◽  
Forecast Combination ◽  
Specific Topic ◽  
Fuzzy C Means ◽  
Intuitionistic Fuzzy ◽  
Forecasting Methods ◽  
Combination Approach ◽  
Combination Function ◽  
Fuzzy Forecast

Intuitionistic meta fuzzy forecast combination functions are introduced in the paper. There are two challenges in the forecast combination literature, determining the optimum weights and the methods to combine. Although there are a few studies on determining the methods, there are numerous studies on determining the optimum weights of the forecasting methods. In this sense, the questions like “What methods should we choose in the combination?” and “What combination function or the weights should we choose for the methods” are handled in the proposed method. Thus, the first two contributions that the paper aims to propose are to obtain the optimum weights and the proper forecasting methods in combination functions by employing meta fuzzy functions (MFFs). MFFs are recently introduced for aggregating different methods on a specific topic. Although meta-analysis aims to combine the findings of different primary studies, MFFs aim to aggregate different methods based on their performances on a specific topic. Thus, forecasting is selected as the specific topic to propose a novel forecast combination approach inspired by MFFs in this study. Another contribution of the paper is to improve the performance of MFFs by employing intuitionistic fuzzy c-means. 14 meteorological datasets are used to evaluate the performance of the proposed method. Results showed that the proposed method can be a handy tool for dealing with forecasting problems. The outstanding performance of the proposed method is verified in terms of RMSE and MAPE.

Shipping market forecasting by forecast combination mechanism

2021 ◽  
pp. 1-16
Author(s):  
Ruobin Gao ◽  
Jiahui Liu ◽  
Liang Du ◽  
Kum Fai Yuen
Keyword(s):  
Forecast Combination

scholarly journals The Optimal Selection for Restricted Linear Models with Average Estimator

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Qichang Xie ◽  
Meng Du
Keyword(s):  
Model Selection ◽  
Linear Models ◽  
Weighted Average ◽  
Selection Procedure ◽  
Information Criterion ◽  
Optimal Weights ◽  
Model Average ◽  
Squared Error ◽  
Generalized Information Criterion ◽  
Risk Investment

The essential task of risk investment is to select an optimal tracking portfolio among various portfolios. Statistically, this process can be achieved by choosing an optimal restricted linear model. This paper develops a statistical procedure to do this, based on selecting appropriate weights for averaging approximately restricted models. The method of weighted average least squares is adopted to estimate the approximately restricted models under dependent error setting. The optimal weights are selected by minimizing ak-class generalized information criterion (k-GIC), which is an estimate of the average squared error from the model average fit. This model selection procedure is shown to be asymptotically optimal in the sense of obtaining the lowest possible average squared error. Monte Carlo simulations illustrate that the suggested method has comparable efficiency to some alternative model selection techniques.

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