Assessing Statistical Performance of Time Series Interpolators

Real-world time series data often contain missing values due to human error, irregular sampling, or unforeseen equipment failure. The ability of a computational interpolation method to repair such data greatly depends on the characteristics of the time series itself, such as the number of periodic and polynomial trends and noise structure, as well as the particular configuration of the missing values themselves. The interpTools package presents a systematic framework for analyzing the statistical performance of a time series interpolator in light of such data features. Its utility and features are demonstrated through evaluation of a novel algorithm, the Hybrid Wiener Interpolator.

Elucidating climatic controls of polynomial trends in interannual variations of northern ecosystem productivities

<p>Rapid warming in northern high latitudes during the past two decades may have profound impacts on the structures and functioning of ecosystems. Understanding how ecosystems respond to climatic change is crucial for the prediction of climate-induced changes in plant phenology and productivity. Here we investigate spatial patterns of polynomial trends in ecosystem productivity for northern (> 30 °N) biomes and their relationships with climatic drivers during 2000–2018. Based on a moderate resolution (0.05°) of satellite data and climate observations, we quantify polynomial trend types and change rates of ecosystem productivities using plant phenology index (PPI), a proxy of gross primary productivity (GPP), and a polynomial trend identification scheme (Polytrend). We find the yearly-integrated PPI (PPI<sub>INT</sub>) shows a high degree of agreement with an OCO-2-based solar‐induced chlorophyll fluorescence GPP product (GOSIF-GPP) for distinct spatial patterns of trend types of ecosystem productivities. The averaged slope for linear trends of GPP is found positive across all the biomes, among which deciduous broadleaved and evergreen needle-leaved forests show the highest and lowest rates respectively. The evergreen needle-leaved forests, low shrub, and permanent wetland show linear trends in PPI<sub>INT</sub> over more than 50% of the covered area and permanent wetland also shows a large fraction of the area with the quadratic and cubic trends. Spatial patterns of linear trends for growing season sum of temperature, precipitation, and photosynthetic active radiation have been quantified. Based on the partial correlations between PPI<sub>INT</sub> and climate drivers, we found that there is a consistent shift of dominant drivers from temperature or radiation to precipitation across all the biomes except the permeant wetland when the trend type of ecosystem productivity changes from linear to non-linear. This may imply precipitation changes in recent years may determine the linear or non-linear responses of ecosystem productivity to climate change. Our results highlight the importance of understanding how changes in climatic drivers may affect the overall responses of ecosystems productivity. Our findings will facilitate the sustainable management of ecosystems accounting for the resilience of ecosystem productivity and phenology to future climate change.</p>

A PROPERTY OF THE HODRICK–PRESCOTT FILTER AND ITS APPLICATION

This article explores a simple property of the Hodrick–Prescott (HP) filter: when the HP filter is applied to a series, the cyclical component is equal to the HP-filtered trend of the fourth difference of the series, except for the first and last two observations, for which different formulas are needed. We use this result to derive small sample results and asymptotic results for a fixed smoothing parameter. We first apply this property to analyze the consequences of a deterministic break. We find that the effect of a deterministic break on the cyclical component is asymptotically negligible for the points that are away from the break point, while for the points in the neighborhood of the break point, the effect is not negligible even asymptotically. Second, we apply this property to show that the cyclical component of the HP filter when applied to series that are integrated up to order 2 is weakly dependent, while the situation for series that are integrated up to order 3 or 4 is more subtle. Third, we characterize the behavior of the HP filter when applied to deterministic polynomial trends and show that in the middle of the sample, the cyclical component reduces the order of the polynomial by 4, while the end point behavior is different. Finally, we give a characterization of the HP filter when applied to an exponential deterministic trend, and this characterization shows that the filter is effectively incapable of dealing with a trend that increases this fast. Our results are compared with those of Phillips and Jin (2015, Business cycles, trend elimination, and the HP filter).

258 Intake, digestibility and rumen fermentation in sheep offered alfalfa silage alone or alfalfa and tall fescue-mixtures harvested after a killing frost

The objective of this study was to determine the effect of harvesting alfalfa and fescue after frost and ensiling mixtures of these forages on silage fermentation characteristics, intake, digestibility and ruminal fermentation by ewes. Forages were harvested in October of 2018, wilted, and blended as either alfalfa alone, 67% alfalfa +33% fescue, 33% alfalfa + 67% fescue, or 100% fescue. Twenty bins were lined with 2 plastic bags, packed (n = 5/trt), stored for 3 months, and then randomly assigned to ewes (n = 20; mean BW = 34.7 ± 6.65 kg) for ad libitum consumption, using 5 animals per treatment. Ewes were given 17 d of adaptation followed by 5 d of total feces and urine collection. Data were analyzed using PROC-MIXED of SAS and orthogonal polynomial trends were used to identify the effects of different proportions of fescue-to-alfalfa silage. Silage total acids, lactate, and acetate increased linearly (P < 0.01) while silage moisture and ammonia decreased linearly (P < 0.01) with increasing proportions of fescue in the diet. The proportions of lactate to total acids (mole/100 moles) increased linearly (P < 0.01) and quadratically (P < 0.05) by adding more fescue to alfalfa. Intake (g/kg BW), digestibility (%), and intake of digestible DM and OM (g/kg BW) decreased linearly (P < 0.05) as fescue proportion was increased in the silages. Ruminal acetate and butyrate (%) increased linearly (P < 0.01) with increasing fescue concentrations in the diet. Ensiling alfalfa with fescue may improve forage fermentation characteristics, but may reduce intake and digestibility in sheep compared to feeding alfalfa silage alone. This study was supported in part by USDA-ARS specific cooperative agreement 58-3655-4-052.

The use of the “Rational” system of global marketing communications in management of international enterprises

The modern system of global marketing communications is not ideal, that is why management of international enterprises needs to use creativity in their attempts to predict the results of the marketing activities. They often fail in forecasting, because specialists do not have necessary practical models and data. The article deals with the questions of developing a model of the “rational” system of global marketing communications, which will be ready for the implementation into managerial processes of the Ukrainian firms. The model in the research is based on one-factor and multi-factor equations with calculations on the example of the well-known American company Nike, which works in the segment of apparel and footwear industry and can be a bright example of building a strong marketing communication strategy. Methods of linear and polynomial trends, smoothing average and exponential smoothing were used for the development of the proposed model. The examination of the correlation between global income, costs on marketing communication activities of the international company and index of satisfaction by this enterprise on the market in the frames of the econometric model’s work showed the dependency, which can become a basis for future analysis. The invented model of the “rational” system of global marketing communications shows how managers can calculate the resultativity of specific marketing instruments, which they plan to accept as appropriate. Different indicators can be used in forecasting the effects of global marketing communications on the performance of international enterprises. The article shows that the more indicators are used in the model, the more accurate is the result.

Analysis of Emergency Situations in the Russian Federation

Introduction:Emergency situations (ES) are situations within a certain territory, which have arisen because of an accident, a dangerous natural phenomenon, natural disaster, or other that may cause or have caused human casualties, damage to human health or the environment, significant material losses, and unbalance of living conditions of people. Important characteristics of ES are suddenness and involvement of a significant number of victims who need first aid and emergency medical care. These characteristics determined the organization of the Unified State System for Emergency Prevention and Elimination of the Russian Federation.Aim:To study the structure of ES in Russia. By the scale of spread and damage caused, ES can be local, municipal, inter-municipal, regional, interregional, or federal, by the source of origin – technogenic, natural, biological, or social. The terrorist acts are usually allocated in a separate group of ES. The structure of ES, according to the EMERCOM of Russia in 2005-2017, is as follows: 1.Technogenic (59.61%)2.Natural (29.42%)3.Biological and social (9.91%)4.Major terrorist acts (1.06%)Methods:Statistical analysis was conducted. According to the EMERCOM of Russia, every year in 2005-2017 there were 422.5 ± 46.5 ES, resulting in the death of 796 ± 56 people. Polynomial trends in the number of ES and deaths, according to the EMERCOM of Russia, (with significant coefficients of determination R2 = 0.85 and R2 = 0.64, respectively) show a decrease in the number of ES and deaths.Discussion:The resulting analysis of the structure and number of ES, the number of deaths, the risk of being in an emergency, and the individual risk of death in an emergency can predict the forces and means necessary for the elimination of the consequences of ES.

FINANCIAL MANAGEMENT MODELING FOR ENTERPRISES

The purpose of the study was to model the financial management processes of enterprises to ensure the qualitative and complete forecasting of enterprise development. The analysis of the strategic matrix of interconnections through the use of power, logarithmic and polynomial trends during the determination of the tightness of the connection between the financial resources’ volumes and the coefficients of liquidity and financial sustainability at the enterprise was carried out. It is established that effective organization of scenario activity as an element of strategic planning is one of the main factors that will allow improving the system of financial management at the enterprise.

EFFECTS OF POLYNOMIAL TRENDS ON DETRENDING MOVING AVERAGE ANALYSIS

The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. As many long-term correlated time series in real systems contain various trends, we investigate the effects of polynomial trends on the scaling behaviors and the performances of three widely used DMA methods including backward algorithm (BDMA), centered algorithm (CDMA) and forward algorithm (FDMA). We derive a general framework for polynomial trends and obtain analytical results for constant shifts and linear trends. We find that the behavior of the CDMA method is not influenced by constant shifts. In contrast, linear trends cause a crossover in the CDMA fluctuation functions. We also find that constant shifts and linear trends cause crossovers in the fluctuation functions obtained from the BDMA and FDMA methods. When a crossover exists, the scaling behavior at small scales comes from the intrinsic time series while that at large scales is dominated by the constant shifts or linear trends. We also derive analytically the expressions of crossover scales and show that the crossover scale depends on the strength of the polynomial trends, the Hurst index, and in some cases (linear trends for BDMA and FDMA) the length of the time series. In all cases, the BDMA and the FDMA behave almost the same under the influence of constant shifts or linear trends. Extensive numerical experiments confirm excellently the analytical derivations. We conclude that the CDMA method outperforms the BDMA and FDMA methods in the presence of polynomial trends.