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Linearly constrained multiple time series may be encountered in many practical contexts, such as the National Accounts (e.g., GDP disaggregated by Income, Expenditure and Output), and multilevel frameworks where the variables are organized according to hierarchies or groupings, like the total energy consumption of a country disaggregated by region and energy sources. In these cases, when multiple incoherent base forecasts for each individual variable are available, a forecast combination-and-reconciliation approach, that we call coherent forecast combination, may be used to improve the accuracy of the base forecasts and achieve coherence in the final result. In this paper, we develop an optimization-based technique that combines multiple unbiased base forecasts while assuring the constraints valid for the series. We present closed form expressions for the coherent combined forecast vector and its error covariance matrix in the general case where a different number of forecasts is available for each variable. We also discuss practical issues related to the covariance matrix that is part of the optimal solution. Through simulations and a forecasting experiment on the daily Australian electricity generation hierarchical time series, we show that the proposed methodology, in addition to adhering to sound statistical principles, may yield in significant improvement on base forecasts, single-task combination and single-expert reconciliation approaches as well.

Cross-temporal forecast reconciliation aims to ensure consistency across forecasts made at different temporal and cross-sectional levels. We explore the relationships between sequential, iterative, and optimal combination approaches, and discuss the conditions under which a sequential reconciliation approach (either first-cross-sectional-then-temporal, or first-temporal-then-cross-sectional) is equivalent to a fully (i.e., cross-temporally) coherent iterative heuristic. Furthermore, we show that for specific patterns of the error covariance matrix in the regression model on which the optimal combination approach grounds, iterative reconciliation naturally converges to the optimal combination solution, regardless the order of application of the uni-dimensional cross-sectional and temporal reconciliation approaches. Theoretical and empirical properties of the proposed approaches are investigated through a forecasting experiment using a dataset of hourly photovoltaic power generation. The study presents a comprehensive framework for understanding and enhancing cross-temporal forecast reconciliation, considering both forecast accuracy and the often overlooked computational aspects, showing that significant improvement can be achieved in terms of memory space and computation time, two particularly important aspects in the high-dimensional contexts that usually arise in cross-temporal forecast reconciliation.

We address the construction of Realized Variance (RV) forecasts by exploiting the hierarchical structure implicit in available decompositions of RV. By using data referred to the Dow Jones Industrial Average Index and to its constituents we show that exploiting the informative content of hierarchies improves the forecast accuracy. Forecasting performance is evaluated out-of-sample based on the empirical MSE and QLIKE criteria as well as using the Model Confidence Set approach.

Forecast reconciliation is the post-forecasting process aimed to revise a set of incoherent base forecasts into coherent forecasts in line with given data structures. Most of the point and probabilistic regression-based forecast reconciliation results ground on the so called "structural representation" and on the related unconstrained generalized least squares reconciliation formula. However, the structural representation naturally applies to genuine hierarchical/grouped time series, where the top- and bottom-level variables are uniquely identified. When a general linearly constrained multiple time series is considered, the forecast reconciliation is naturally expressed according to a projection approach. While it is well known that the classic structural reconciliation formula is equivalent to its projection approach counterpart, so far it is not completely understood if and how a structural-like reconciliation formula may be derived for a general linearly constrained multiple time series. Such an expression would permit to extend reconciliation definitions, theorems and results in a straightforward manner. In this paper, we show that for general linearly constrained multiple time series it is possible to express the reconciliation formula according to a "structural-like" approach that keeps distinct free and constrained, instead of bottom and upper (aggregated), variables, establish the probabilistic forecast reconciliation framework, and apply these findings to obtain fully reconciled point and probabilistic forecasts for the aggregates of the Australian GDP from income and expenditure sides, and for the European Area GDP disaggregated by income, expenditure and output sides and by 19 countries.

In this study structural and mechanical properties of a 1 um thick Al2O3 coating, deposited on 316L stainless steel by Pulsed Laser Deposition (PLD), subjected to high energy ion irradiation were assessed. Mechanical properties of pristine and ion-modified specimens were investigated using the nanoindentation technique. A comprehensive characterization combining Transmission Electron Microscopy and Grazing-Incidence X-ray Diffraction provided deep insight into the structure of the tested material at the nano- and micro- scale. Variation in the local atomic ordering of the irradiated zone at different doses was investigated using a reduced distribution function analysis obtained from electron diffraction data. Findings from nanoindentation measurements revealed a slight reduction in hardness of all irradiated layers. At the same time TEM examination indicated that the irradiated layer remained amorphous over the whole dpa range. No evidence of crystallization, void formation or element segregation was observed up to the highest implanted dose. Reported mechanical and structural findings were critically compared with each other pointing to the conclusion that under given irradiation conditions, over the whole range of doses used, alumina coatings exhibit excellent radiation resistance. Obtained data strongly suggest that investigated material may be considered as a promising candidate for next-generation nuclear reactors, especially LFR-type, where high corrosion protection is one of the highest prerogatives to be met.

Forecast reconciliation is a post-forecasting process that involves transforming a set of incoherent forecasts into coherent forecasts which satisfy a given set of linear constraints for a multivariate time series. In this paper we extend the current state-of-the-art cross-sectional probabilistic forecast reconciliation approach to encompass a cross-temporal framework, where temporal constraints are also applied. Our proposed methodology employs both parametric Gaussian and non-parametric bootstrap approaches to draw samples from an incoherent cross-temporal distribution. To improve the estimation of the forecast error covariance matrix, we propose using multi-step residuals, especially in the time dimension where the usual one-step residuals fail. To address high-dimensionality issues, we present four alternatives for the covariance matrix, where we exploit the two-fold nature (cross-sectional and temporal) of the cross-temporal structure, and introduce the idea of overlapping residuals. We assess the effectiveness of the proposed cross-temporal reconciliation approaches through a simulation study that investigates their theoretical and empirical properties and two forecasting experiments, using the Australian GDP and the Australian Tourism Demand datasets. For both applications, the optimal cross-temporal reconciliation approaches significantly outperform the incoherent base forecasts in terms of the Continuous Ranked Probability Score and the Energy Score. Overall, the results highlight the potential of the proposed methods to improve the accuracy of probabilistic forecasts and to address the challenge of integrating disparate scenarios while coherently taking into account short-term operational, medium-term tactical, and long-term strategic planning.

In recent works by Yang et al. (2017a,b), and Yagli et al. (2019), geographical, temporal, and sequential deterministic reconciliation of hierarchical photovoltaic (PV) power generation have been considered for a simulated PV dataset in California. In the first two cases, the reconciliations are carried out in spatial and temporal domains separately. To further improve forecasting accuracy, in the third case these two reconciliation approaches are sequentially applied. During the replication of the forecasting experiment, some issues emerged about non-negativity and coherence (in space and/or in time) of the sequentially reconciled forecasts. Furthermore, while the accuracy improvement of the considered approaches over the benchmark persistence forecasts is clearly visible at any data granularity, we argue that an even better performance may be obtained by a thorough exploitation of cross-temporal hierarchies. In this paper the cross-temporal point forecast reconciliation approach is applied to generate non-negative, fully coherent (both in space and time) forecasts. In particular, some relationships between two-step, iterative and simultaneous cross-temporal reconciliation procedures are for the first time established, non-negativity issues of the final reconciled forecasts are correctly dealt with in a simple way, and the most recent cross-temporal reconciliation approaches are adopted. The normalised Root Mean Square Error is used to measure forecasting accuracy, and a statistical multiple comparison procedure is performed to rank the approaches. Besides assuring full coherence, and non-negativity of the reconciled forecasts, the results show that for the considered dataset, cross-temporal forecast reconciliation significantly improves on the sequential procedures proposed by Yagli et al. (2019), at any cross-sectional level of the hierarchy and for any temporal granularity., Comment: 43 pages, 16 figures

Edible electronics will facilitate point-of-care testing through safe and cheap devices that are digested or degraded in the body or environment after performing a specific function. Its thrive depends on creating a library of materials that are the basic building blocks for eatable technologies. Edible electrical conductors fabricated with green methods that allow production at a large scale and composed of food derivatives, ingestible in large amounts without risk for human health are needed. Here, conductive pastes made with materials with a high tolerable upper intake limit (major of mg/kg body weight /day) are proposed. Conductive oleogel paste composites, made with biodegradable and food-grade materials like natural waxes, oils, and activated carbon conductive fillers, are presented. The proposed pastes are compatible with manufacturing processes such as direct ink writing and thus are suitable for an industrial scale-up. These conductors are built without the use of solvents, and with tunable electromechanical features and adhesion depending on the composition. They have antibacterial and hydrophobic properties, so that they can be used in contact with food preventing contamination and preserving its organoleptic properties. As a proof-of-principle application, the edible conductive pastes are demonstrated to be effective edible contacts for food impedance analysis, to be integrated for example in smart fruit labels for ripening monitoring.

This work addresses the early stages ($\le$1000 h) of the dissolution corrosion behavior of 316L and DIN 1.4970 austenitic stainless steels in contact with oxygen-poor (C$_O$ < 10$^-$$^8$ mass%), static liquid lead-bismuth eutectic (LBE) at 500{\deg}C for 600-1000 h. The objective of this study was to determine the relative early-stage resistance of the uncoated steels to dissolution corrosion and to assess the protectiveness of select candidate coatings (Cr$_2$AlC, Al$_2$O$_3$, V$_2$Al$_x$C$_y$). The simultaneous exposure of steels with intended differences in microstructure and thermomechanical state showed the effects of steel grain size, density of annealing/deformation twins, and secondary precipitates on the steel dissolution corrosion behavior. The findings of this study provide recommendations on steel manufacturing with the aim of using the steels to construct Gen-IV lead-cooled fast reactors., Comment: 52 pages, 22 figures, 4 tables

In a recent paper, while elucidating the links between forecast combination and cross-sectional forecast reconciliation, Hollyman et al. (2021) have proposed a forecast combination-based approach to the reconciliation of a simple hierarchy. A new Level Conditional Coherent (LCC) point forecast reconciliation procedure was developed, and it was shown that the simple average of a set of LCC, and bottom-up reconciled forecasts (called Combined Conditional Coherent, CCC) results in good performance as compared to those obtained through the state-of-the-art cross-sectional reconciliation procedures. In this paper, we build upon and extend this proposal along some new directions. (1) We shed light on the nature and the mathematical derivation of the LCC reconciliation formula, showing that it is the result of an exogenously linearly constrained minimization of a quadratic loss function in the differences between the target and the base forecasts with a diagonal associated matrix. (2) Endogenous constraints may be considered as well, resulting in level conditional reconciled forecasts of all the involved series, where both the upper and the bottom time series are coherently revised. (3) As the LCC procedure does not guarantee the non-negativity of the reconciled forecasts, we argue that - when non-negativity is a natural attribute of the variables to be forecast - its interpretation as an unbiased top-down reconciliation procedure leaves room for some doubts. (4) The new procedures are used in a forecasting experiment on the classical Australian Tourism Demand (Visitor Nights) dataset. Due to the crucial role played by the (possibly different) models used to compute the base forecasts, we re-interpret the CCC reconciliation of Hollyman et al. (2021) as a forecast pooling approach, showing that accuracy improvement may be gained by adopting a simple forecast averaging strategy., Comment: 33 pages, 6 figures

Forecast reconciliation is a post-forecasting process aimed to improve the quality of the base forecasts for a system of hierarchical/grouped time series (Hyndman et al., 2011). Contemporaneous (cross-sectional) and temporal hierarchies have been considered in the literature, but - except for Kourentzes and Athanasopoulos (2019) - generally these two features have not been fully considered together. Adopting a notation able to simultaneously deal with both forecast reconciliation dimensions, the paper shows two new results: (i) an iterative cross-temporal forecast reconciliation procedure which extends, and overcomes some weaknesses of, the two-step procedure by Kourentzes and Athanasopoulos (2019), and (ii) the closed-form expression of the optimal (in least squares sense) point forecasts which fulfill both contemporaneous and temporal constraints. The feasibility of the proposed procedures, along with first evaluations of their performance as compared to the most performing `single dimension' (either cross-sectional or temporal) forecast reconciliation procedures, is studied through a forecasting experiment on the 95 quarterly time series of the Australian GDP from Income and Expenditure sides considered by Athanasopoulos et al. (2019)., Comment: Main text: 49 pages, 10 figures, 2 tables. Appendix: 68 pages, 29 figures, 17 tables

Lead halide perovskite-based photoactive layers are nowadays employed for a large number of optoelectronic applications, from solar cells to photodetectors and light-emitting diodes, because of their excellent absorption, emission and charge-transport properties. Unfortunately, their commercialization is still hindered by an intrinsic instability towards classical environmental conditions. Water in particular promotes fast decomposition, leading to a drastic decrease in device performance. An innovative functional approach to overcome this major issue could derive from integrating water-splitting active species within charge extracting layers adjacent to the perovskite photoactive layer, converting incoming water molecules into molecular oxygen and hydrogen before they reach this last one, thus preserving device performance in time. In this work we report for the first time on a perovskite-ancillary layer based on CuSCN nanoplateletes dispersed in a p-type semiconducting polymeric matrix, combining hole extraction/transport properties with good water-oxidation activity, that transforms incoming water molecules and further triggers the in situ p-doping of the conjugated polymer by means of the produced dioxygen, further improving transport of photogenerated charges. This composite layer enables the long-term stabilization of a mixed cation lead halide perovskite within a direct solar cell architecture, maintaining a stable performance for 28 days in high-moisture simulated conditions. Our findings demonstrate that the engineering of a hole extraction layer with water-splitting active additives represent a valuable strategy to mitigate the degradation of perovskite solar cells exposed to atmospheric humidity. A similar approach could be employed in the future to improve stabilities of other optoelectronic devices based on water-sensitive species.

We propose a complete reconciliation procedure, resulting in a 'one number forecast' of the GDP figure, coherent with both Income and Expenditure sides' forecasted series, and evaluate its performance on the Australian quarterly GDP series, as compared to the original proposal by Athanasopoulos et al. (2019)., Comment: 7 pages, 3 figures. Accepted for presentation at the Italian Statistical Society Meeting - SIS 2020