Interval forecasting of time series using orderstatistics

In the traditional approach of obtaining time series forecasts based on the selected model, the model parameters are first estimated, then a point forecast using the obtained estimatesis made and then an interval forecast with a given probability is made. In the article the authors propose a nonparametric method for obtaining a single-stage interval forecasting of a time series based on constructing predictive and target variables sets using robust statistics and obtaining the forecast boundaries by constructing linear regression models. The predictive algorithm is based on the problems of estimating the parameters of linear multiple regression using a model regularization methods. The results of forecasting prove the expediency and effectiveness of the proposed method.

The Impact of the Internal Expenditures on R&D in the Growth of Small and Medium-Sized Businesses in the Republic of Kazakhstan

The aim of the article is to investigate the relationship between the number of active small and medium-sized businesses in Kazakhstan and the number of internal costs for research and development projects based on the use of economic and mathematical forecasting methods. As a result of the application of statistical and mathematical methods, the analysis of changes in the number of active SMEs and the volume of R&D expenditures in the Republic of Kazakhstan for the period 1999-2019 was carried out on the basis of constructing a paired linear regression model. The quality of the model was assessed, the interval for the lower and upper boundaries of the forecast of changes in the indicators of the number of active SMEs from the volume of R&D expenditures was calculated. An economic interpretation of the calculated data obtained because of constructing a linear paired regression model is given. It was revealed that the number of active SMEs by 94.5% is explained by the volume of internal R&D expenditures. A point forecast for the number of active SMEs has been calculated when the volume of internal R&D expenditures changes for 2022. The calculation of indicators of the lower and upper boundaries of the predicted value of the number of active SMEs has been carried out. With an increase in the volume of internal expenditures on R&D in the GDP of the Republic of Kazakhstan to 92,178 million tenge, the number of active small and medium-sized enterprises will be in the range from 1,244,436 to 1,669,622 units.

Assessing Point Forecast Bias Across Multiple Time Series: Measures and Visual Tools

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well known and well researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy to implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series. /// Note: This is the final version of the paper, which appeared in the International Journal of Statistics and Probability. The first draft of this paper was uploaded to Preprints.org on 11 May, 2021: https://doi.org/10.20944/preprints202105.0261.v1 /// Copyrights: This is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

Assessing Point Forecast Bias Across Multiple Time Series: Measures and Visual Tools

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under-represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well-known and well-researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling-origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy-to-implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series.

Peculiarities of Implementing the State’s Strategic Narrative based on the Public Opinion

The main purpose of the article is the peculiarities of implementing of the state’s strategic narrative based on the the statistical analysis of the public opinion. The scenarios of the public opinion development are forecasted. The main results are: the graphs of the statistical series of change in public opinion have been constructed; the approximating functions for the trend of change in public opinion have been determined; the parameters of the approximating function have been calculated; a point forecast of the change in public opinion has been made. The main scientific method ia the method of statistical extrapolation. The main results are: to identify the features of the implementation of the strategic narrative of the state system in strategic communications; it is obtained the necessary minimum value of efficiency. This value of efficienct should be achieved by the system of strategic communications, when taking appropriate measures to promote and support of the appropriate course of the state by the population. This result is actually such as in the controlled territory and in the temporarily occupied territories (Donetsk and Luhansk regions, the Crimea). Keywords—strategic narrative, target audience, informational and psychological influence, strategic communications

If You Like It, GAN It—Probabilistic Multivariate Times Series Forecast with GAN

The contribution of this paper is two-fold. First, we present ProbCast—a novel probabilistic model for multivariate time-series forecasting. We employ a conditional GAN framework to train our model with adversarial training. Second, we propose a framework that lets us transform a deterministic model into a probabilistic one with improved performance. The motivation of the framework is to either transform existing highly accurate point forecast models to their probabilistic counterparts or to train GANs stably by selecting the architecture of GAN’s component carefully and efficiently. We conduct experiments over two publicly available datasets—an electricity consumption dataset and an exchange-rate dataset. The results of the experiments demonstrate the remarkable performance of our model as well as the successful application of our proposed framework.

Hierarchical forecasts of Diabetes mortality in Mexico by marginalization and sex to establish resource allocation

Objective: The mexican population has experimented an astounding rise in type II Diabetes mortality as well as a growing trend for the economic burden in the recent years. The paper’s purpose is to propose an approach to establish a distribution of resource allocation objectively to face the future economic burden. Methodology: Hierarchical forecasts of Diabetes mortality to 2030 by sub-domains of the population are estimated based on marginalization and sex. Results: The forecasts confirm that differences related to sub-domains will be significant. In fact, the rates will increase most notably both in low and high marginalized. Limitations: The hierarchical method just provide point forecast without prediction intervals. Originality: There is not a similar application for mexican data to do that objectively. Conclusions: The most recommendable budget distribution should be mainly addressed among the low and high levels. Implications of these estimates should support unpostponable health policy in general and for the mentioned sub-domains in particular.

Assessing Point Forecast Bias Across Multiple Time Series: Measures and Visual Tools

Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under-represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well-known and well-researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling-origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy-to-implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series.

Interval Optimization to Schedule a Multi-Energy System with Data-Driven PV Uncertainty Representation

Recently, multi-energy systems (MESs), whereby different energy carriers are coupled together, have become popular. For a more efficient use of MESs, the optimal operation of these systems needs to be considered. This paper focuses on the day-ahead optimal schedule of an MES, including a combined heat and electricity (CHP) unit, a gas boiler, a PV system, and energy storage devices. Starting from a day-ahead PV point forecast, a non-parametric probabilistic forecast method is proposed to build the predicted interval and represent the uncertainty of PV generation. Afterwards, the MES is modeled as mixed-integer linear programming (MILP), and the scheduling problem is solved by interval optimization. To demonstrate the effectiveness of the proposed method, a case study is performed on a real industrial MES. The simulation results show that, by using only historical PV measurement data, the point forecaster reaches a normalized root-mean square error (NRMSE) of 14.24%, and the calibration of probabilistic forecast is improved by 10% compared to building distributions around point forecast. Moreover, the results of interval optimization show that the uncertainty of the PV system not only has an influence on the electrical part of the MES, but also causes a shift in the behavior of the thermal system.

Bootstrap joint prediction regions for sequences of missing values in spatio-temporal datasets

Missing data reconstruction is a critical step in the analysis and mining of spatio-temporal data. However, few studies comprehensively consider missing data patterns, sample selection and spatio-temporal relationships. To take into account the uncertainty in the point forecast, some prediction intervals may be of interest. In particular, for (possibly long) missing sequences of consecutive time points, joint prediction regions are desirable. In this paper we propose a bootstrap resampling scheme to construct joint prediction regions that approximately contain missing paths of a time components in a spatio-temporal framework, with global probability $$1-\alpha $$ 1 - α . In many applications, considering the coverage of the whole missing sample-path might appear too restrictive. To perceive more informative inference, we also derive smaller joint prediction regions that only contain all elements of missing paths up to a small number k of them with probability $$1-\alpha $$ 1 - α . A simulation experiment is performed to validate the empirical performance of the proposed joint bootstrap prediction and to compare it with some alternative procedures based on a simple nominal coverage correction, loosely inspired by the Bonferroni approach, which are expected to work well standard scenarios.