Effects Of Autocorrelation Research Articles

The spectral color of natural and anthropogenic time series and its impact on the statistical significance of cross correlation

The cross-correlation between time series is a common tool to study and quantify the impact of climatic and anthropogenic changes on ecosystems. The traditional method for estimating the statistical significance of correlation relies on the assumption that the data are independent, but time series found in nature are often strongly auto-correlated because of low-frequency environmental variability and ecosystem inertia. Previous authors have used Monte Carlo simulations to study the impact of serial auto-correlation on the significance of cross-correlations. Most studies have used random time series that are often a poor representation of those found in nature, e.g., low-order auto-regressive models with normally distributed noise. Moreover, we are not aware of any tests of the applicability of those methods to anthropogenic time series. Here, we study the effect of serial auto-correlation on the performance of two methods for estimating the significance of cross-correlations determined from Monte Carlo simulations with time series that are generated synthetically based on power-law specification of spectral characteristics. Such time series have an auto-correlation structure defined by a single parameter, their spectral “color”, and are generally more convenient representations of natural time series than the autoregressive models. Our results show that one of the two methods considered here accurately reproduces prescribed error rates for the wide range of spectral colors representative of climatic, ecological and anthropogenic time series. For this, we characterized roughly 1800 observational records in different categories of spectral colors, including climate variability, abundance of vertebrate species, and pollution. We specifically focus on time series with annual sampling over data records of at least 40 years, which are particularly relevant for climate studies. The methodology advocated in this study provides a simple and realistic assessment of the significance of sample estimates of cross correlation for time series with any sample interval and record length.

Mediators of quality of life change in people with severe psychotic disorders treated in integrated care: ACCESS II study.

Patients with severe psychotic disorders exhibit a severely reduced quality of life (QoL) at all stages of the disease. Integrated care often led to an improvement in QoL. However, the specific mediators of QoL change are not yet well understood. The ACCESS II study is a prospective, long-term study investigating the effectiveness of an integrated care program for people with severe psychotic disorders (IC-TACT) that includes Therapeutic Assertive Community Treatment within a care network of in- and outpatient services at the University Medical Center Hamburg-Eppendorf, Germany. We examined longitudinal associations between QoL and the hypothesized mediators of change (i.e., negative symptoms, depression, and anxiety), using cross-lagged panel models. The sample includes 418 severely ill patients treated in IC-TACT for at least 1 year. QoL increased, whereas symptom severity decreased significantly from baseline to 6-month follow-up (p-values ≤ 0.001), and remained stable until 12-month follow-up. QoL and symptom severity demonstrated significant auto-correlated effects and significant cross-lagged effects from QoL at baseline to negative symptoms (6 months, β = -0.20, p < 0.001) to QoL (12 months, β = -0.19, p < 0.01) resulting in a significant indirect, mediated effect. Additionally, negative symptoms after 6 months had a significant effect on the severity of depression after 12 months (β = 0.13, p < 0.05). Negative symptoms appear to represent an important mechanism of change in IC-TACT indicating that improvement of QoL could potentially be achieved through optimized intervention on negative symptoms. Moreover, this may lead to a reduction in the severity of depression after 12 months.

Dynamic correlation between Crude Oil Price and Exchange rate: The Case of ASEAN-5

This study examines the relationship between exchange rate and crude oil price of five Southeast Asia countries including Indonesia, Malaysia, Philippines, Thailand and Singapore from January 1979 to January 2022 using monthly data. Augmented Dickey-Fuller test is used to examine the stationarity of the data. DCC-GARCH model is used to investigate the correlation between oil price and exchange rate. The result shows that skewness, kurtosis, autocorrelation and ARCH effects were found in both oil price and exchange rate. Results suggested that both short run persistence (α) and long run persistence(β) are found to be highly significant for oil price and exchange rate of all countries except Indonesia. Furthermore, the correlation coefficients vary over times for all the countries studied. Negative relationship was found between oil price and exchange rate over most of the periods studied in all countries studied.

Organisational Foundations and Performance of Banks in India – A Juxtaposition Study from 1991-92 to 2019-20

Banks are the pivot of development. The way the banking organisations function (Payer) will influence the performance of the banks as well as the target group (The Receiver). There will be always a business relationship between the banks and their customers. This relationship will be solidified and continue to exist for a lifetime and beyond (generation customers). When a bank lives longer, it means better performance by establishing a continuous customer relationship. It is in this context, a study on the organisational foundations to its performance is critical and essential. The present study aims at establishing a temporal relationship between organisational foundations – Vision, Mission, Objectives, Goals / Values, and Strategies and needs to be juxtaposed for a concomitant relationship. The study covers four types of banks in India – Public Sector (PSBs), Private Sector(Pvt_SBs), Foreign Banks(FBs), and All Scheduled Commercial Banks (ASCBs). The organisational foundational variables such as Vision, Mission, Objectives, Goals/ Values, and Strategies are culled out to test the hypothesis of the significance of organisational foundations as explicitly stated will lead to better performance of the banks by type.&#x0D; The above hypothesis is tested using ANOVA Fixed Effects Model for all performance variables at the aggregate level. The data are culled out from reports of eighty banks which form a major chunk of the banks in India. The sources of data are bank websites, annual reports, RBI websites, EPWRF data sets, and the like. The data have been tabulated by bank type from 1991-92 to 2019-20 – the post-liberalization period in India.&#x0D; The findings of the study are: PSBs although form 56.5% of the total transactions (credit) have mixed levels of performance. Some areas are statistically significant and some are not. The organisational foundational variables have moderate clarity and are in most of the cases, objectives and goals are not specified. The Pvt_SBs have a market share of 35.4% of total transactions that are urban-centric and have been performing well and most of the variables are documented. The FBs which are operating in India are clear about all the organisational variables except strategy. The share of the FBs in Indian urban transactions is 4.19% of the total and all the parameters of performance show the statistically significant result at 1% level. Generally, there will be no autocorrelation effect in the time model tested. This means Foreign Banks make very little or minimum time-oriented errors.&#x0D; The paper suggests that all types of banks in India must emulate the FBs to have stronger organisational foundations which in the long run facilitate better competitive performance.

Latitudinal patterns and environmental drivers of taxonomic, functional, and phylogenetic diversity of woody plants in western Amazonian terra firme forests.

Elucidating how environmental factors drive plant species distributions and how they affect latitudinal diversity gradients, remain essential questions in ecology and biogeography. In this study we aimed: 1) to investigate the relationships between all three diversity attributes, i.e., taxonomic diversity (TD), functional diversity (FD), and phylogenetic diversity (PD); 2) to quantify the latitudinal variation in these diversity attributes in western Amazonian terra firme forests; and 3) to understand how climatic and edaphic drivers contribute to explaining diversity patterns. We inventoried ca. 15,000 individuals from ca. 1,250 species, and obtained functional trait records for ca. 5,000 woody plant individuals in 50 plots of 0.1 ha located in five terra firme forest sites spread over a latitudinal gradient of 1200 km covering ca. 10°C in latitude in western Amazonia. We calculated all three diversity attributes using Hill numbers: q = 0 (richness), q = 1 (richness weighted by relative abundance), and q = 2 (richness weighted by dominance). Generalized linear mixed models were constructed for each diversity attribute to test the effects of different uncorrelated environmental predictors comprising the temperature seasonality, annual precipitation, soil pH and soil bulk density, as well as accounting for the effect of spatial autocorrelation, i.e., plots aggregated within sites. We confirmed that TD (q = 0, q = 1, and q = 2), FD (q = 0, q = 1, and q = 2), and PD (q = 0) increased monotonically towards the Equator following the latitudinal diversity gradient. The importance of rare species could explain the lack of a pattern for PD (q = 1 and q = 2). Temperature seasonality, which was highly correlated with latitude, and annual precipitation were the main environmental drivers of variations in TD, FD, and PD. All three diversity attributes increased with lower temperature seasonality, higher annual precipitation, and lower soil pH. We confirmed the existence of latitudinal diversity gradients for TD, FD, and PD in hyperdiverse Amazonian terra firme forests. Our results agree well with the predictions of the environmental filtering principle and the favourability hypothesis, even acting in a 10°C latitudinal range within tropical climates.

Research on Ultra-Short-Term Load Forecasting Based on Real-Time Electricity Price and Window-Based XGBoost Model

With the continuous development of new power systems, the load demand on the user side is becoming more and more diverse and random, which also brings difficulties in the accurate prediction of power load. Although the introduction of deep learning algorithms has improved the prediction accuracy to a certain extent, it also faces problems such as large data requirements and low computing efficiency. An ultra-short-term load forecasting method based on the windowed XGBoost model is proposed, which not only reduces the complexity of the model, but also helps the model to capture the autocorrelation effect of the forecast object. At the same time, the real-time electricity price is introduced into the model to improve its forecast accuracy. By simulating the load data of Singapore’s electricity market, it is proved that the proposed model has fewer errors than other deep learning algorithms, and the introduction of the real-time electricity price helps to improve the prediction accuracy of the model. Furthermore, the broad applicability of the proposed method is verified by a sensitivity analysis on data with different sample sizes.

How Are Macro-Scale and Micro-Scale Built Environments Associated with Running Activity? The Application of Strava Data and Deep Learning in Inner London

Running can promote public health. However, the association between running and the built environment, especially in terms of micro street-level factors, has rarely been studied. This study explored the influence of built environments at different scales on running in Inner London. The 5Ds framework (density, diversity, design, destination accessibility, and distance to transit) was used to classify the macro-scale features, and computer vision (CV) and deep learning (DL) were used to measure the micro-scale features. We extracted the accumulated GPS running data of 40,290 sample points from Strava. The spatial autoregressive combined (SAC) model revealed the spatial autocorrelation effect. The result showed that, for macro-scale features: (1) running occurs more frequently on trunk, primary, secondary, and tertiary roads, cycleways, and footways, but runners choose tracks, paths, pedestrian streets, and service streets relatively less; (2) safety, larger open space areas, and longer street lengths promote running; (3) streets with higher accessibility might attract runners (according to a spatial syntactic analysis); and (4) higher job density, POI entropy, canopy density, and high levels of PM 2.5 might impede running. For micro-scale features: (1) wider roads (especially sidewalks), more streetlights, trees, higher sky openness, and proximity to mountains and water facilitate running; and (2) more architectural interfaces, fences, and plants with low branching points might hinder running. The results revealed the linkages between built environments (on the macro- and micro-scale) and running in Inner London, which can provide practical suggestions for creating running-friendly cities.

Stock Price Prediction Based on Spatio-Temporal Coupling with Deep Learning

Stock price prediction is a nonlinear dynamic problem, and the stock price is susceptible to its autocorrelation and inertia effect, as well as other stock price fluctuation on the same plate. Traditional Autoregressive Integrated Moving Average Model (ARIMA) only builds a linear prediction model, but the neural network model has strong nonlinear modeling ability. In this paper, we propose a Convolutional neural networks with Long short-term memory (CNN-LSTM) method to predict stock price fluctuations. This is because the selective memory advanced deep learning function of LSTM is used to deeply mine the internal rules of time series information, and the convolution in CNN is used to integrate the original stock data to extract the relationship between features of different variables. Finally, the feasibility of the method and the model's applicability are analyzed by comparing with the results of other prediction models and a conclusion is drawn. The results show that, compared with the prediction model based on time series alone, the model has a significant accuracy advantage. In addition, the hybrid model can better help investors make decisions, expand returns, and avoid risks.

The association of COVID-19 incidence with temperature, humidity, and UV radiation – A Global multi-city analysis

Background and Aim. The possible associations of COVID 19 transmission and meteorological factors is a topic of scientific debate. A multitude of studies have been conducted worldwide, with inconsistent findings. However, often these had methodological issues, e.g. did not exclude important confounding factors, or had limited geographic or temporal resolution. Methods. We analysed data from 455 cities across 20 countries around the globe over an observation period before the vaccine roll out began, ranging from 3 February to 31 October 2020. We used a time-series analysis that assumes a quasi-Poisson distribution of the cases and incorporates distributed lag non-linear modelling for the exposure association at city-levels while considering effects of autocorrelation, long-term trends and day of the week. The confounding by governmental measures was accounted by incorporating the Oxford Governmental Stringency Index. The effects of daily mean air temperature, relative and absolute humidity, and UV radiation were estimated by applying a meta-regression of local estimates with multi-level random effects for location, country, and climatic zone. Results. We found that air temperature and absolute humidity influenced the spread of COVID-19 over a lag period of 15 days. Pooling the evidence globally showed that overall low temperatures (7.5&amp;#xb0;C compared to 17.0&amp;#xb0;C) and low absolute humidity (6.0 g/m³ compared to 11.0 g/m³) were associated with higher COVID 19 incidences (RRtemp=1.33 with 95%CI: 1.08; 1.64 and RRAH=1.33 with 95%CI: 1.12; 1.57). For RH and UV no evidence of an association was found. These results were robust to sensitivity analysis. However, the study results also emphasised the heterogeneity of these associations in different countries. Conclusion. Globally, our results suggest that comparatively low temperatures and low absolute humidity were associated with increased risks of COVID 19 incidence. However, this study underlines regional heterogeneity of weather-related effects on COVID-19 transmission. Key words: Temperature, Humidity, UV Radiation, COVID-19

What drives the spatio-temporal distribution and spillover of air quality in China’s three urban agglomerations? Evidence from a two-stage approach

Beijing-Tianjin-Hebei urban agglomeration (BTH), Yangtze River Delta (YRD), and Pearl River Delta (PRD) are the most important economic hinterlands in China, offering high levels of economic development. In 2020, their proportion of China’s total GDP reached 39.28%. Over the 5 years of 2014–2018, the annual maximum air quality index (AQI) of the three major urban agglomerations was greater than 100, thus maintaining a grade III light pollution (100 &amp;lt; AQI &amp;lt; 200) in Chinese air standards. This research thus uses a two-stage empirical analysis method to explore the spatial-temporal dispersal physiognomies and spillover effects of air quality in these three major urban agglomerations. In the first stage, the Kriging interpolation method regionally estimates and displays the air quality monitoring sampling data. The results show that the air quality of these three major urban agglomerations is generally good from 2014 to 2018, the area of good air is gradually expanding, the AQI value is constantly decreasing, the air pollution of YRD is shifting from southeast to northwest, and the air pollution of PRD is increasing. The dyeing industry shows a trend of concentration from northwest to south-central. In the second stage, Moran’s I and Spatial Durbin Model (SDM) explore the spatial autocorrelation and spillover effects of air quality related variables. The results show that Moran’s I values in the spatial autocorrelation analysis all pass the significance test. Moreover, public transport, per capita GDP, science and technology expenditure, and the vegetation index all have a significant influence on the spatial dispersal of air quality in the three urban agglomerations, among which the direct effect of public transport and the indirect effect and total effect of the vegetation index are the most significant. Therefore, the China’s three major urban agglomerations (TMUA) ought to adjust the industrial structure, regional coordinated development, and clean technology innovation.

The association of COVID-19 incidence with temperature, humidity, and UV radiation – A global multi-city analysis

Background and aimThe associations between COVID-19 transmission and meteorological factors are scientifically debated. Several studies have been conducted worldwide, with inconsistent findings. However, often these studies had methodological issues, e.g., did not exclude important confounding factors, or had limited geographic or temporal resolution. Our aim was to quantify associations between temporal variations in COVID-19 incidence and meteorological variables globally. MethodsWe analysed data from 455 cities across 20 countries from 3 February to 31 October 2020. We used a time-series analysis that assumes a quasi-Poisson distribution of the cases and incorporates distributed lag non-linear modelling for the exposure associations at the city-level while considering effects of autocorrelation, long-term trends, and day of the week. The confounding by governmental measures was accounted for by incorporating the Oxford Governmental Stringency Index. The effects of daily mean air temperature, relative and absolute humidity, and UV radiation were estimated by applying a meta-regression of local estimates with multi-level random effects for location, country, and climatic zone. ResultsWe found that air temperature and absolute humidity influenced the spread of COVID-19 over a lag period of 15 days. Pooling the estimates globally showed that overall low temperatures (7.5 °C compared to 17.0 °C) and low absolute humidity (6.0 g/m3 compared to 11.0 g/m3) were associated with higher COVID-19 incidence (RR temp =1.33 with 95%CI: 1.08; 1.64 and RR AH =1.33 with 95%CI: 1.12; 1.57). RH revealed no significant trend and for UV some evidence of a positive association was found. These results were robust to sensitivity analysis. However, the study results also emphasise the heterogeneity of these associations in different countries. ConclusionGlobally, our results suggest that comparatively low temperatures and low absolute humidity were associated with increased risks of COVID-19 incidence. However, this study underlines regional heterogeneity of weather-related effects on COVID-19 transmission.

Probabilistic Predictions of Ecologically Relevant Hydrologic Indices Using a Hydrological Model

AbstractThis study evaluated the effects of prior knowledge obtained from multi‐objective optimization on the uncertainty quantification of simulated ecologically relevant hydrologic indices (ERHIs) using a hydrological model. Two experiments were formulated considering contrasting conditions in prior knowledge when implementing Bayesian parameter estimation. In the first experiment, we reproduced a common modeling practice in the absence of previous information where uniform priors are considered when calibrating hydrological and error model parameters. In the second experiment, near‐optimal Pareto solutions from multi‐objective calibration were used to build a multivariate prior distribution for estimating hydrological and error model parameters using Bayesian calibration. In both experiments, a likelihood function considering heteroscedasticity and autocorrelation effects was employed. The Unified Non‐dominated Sorting Algorithm III was used for multi‐objective calibration, whereas the multiple‐try differential evolution adaptive metropolis algorithm was used for Markov Chain Monte Carlo sampling. The experiments were tested using a hydrologic model. We selected a subset of ERHIs comprised of 32 central tendency Indicators of Hydrologic Alteration and seven additional indices describing basic streamflow statistical properties. In general, using near‐optimal Pareto parameter distributions as prior knowledge in Bayesian calibration reduced both the bias and variability ranges in ERHIs prediction. Furthermore, there was no significant loss in the reliability of streamflow predictions (from 2% to 6%, p = 0.07) when targeting the selected ERHIs, while improving precision (from 66% to 58%, p &lt; 0.05) and reducing the bias (from 6% to 4%, p &lt; 0.05). Moreover, parametric uncertainty substantially shrank by 72% when linking multi‐objective calibration and Bayesian parameter estimation.

Autokorelasi Laba Dan Volatilitas Laba: Peningkat Audit Delay?

This study aims to test the effect of earnings autocorrelation and earnings volatility on audit delay. In the process of the test, researchers used multiple regression analysis using a research sample of 105 manufacturing companies or 525 observations with the observation range of 2015 – 2019. The result, it showed that earnings autocorrelation had an effect on increasing audit delay. It is similar that the earnings correlation which also affects audit delays. The results of this study provide implications that auditors must be more careful in carrying out the audit process, especially in capturing earnings information from time to time. This is because earnings are the information that is often used by the users in assessing a company and used to manipulate earnings. For future research, it is suggested to use specialist industrial auditors as a coding variable in an effort to suppress the occurrence of long audit delays

Impacts of urban forms and socioeconomic factors on CO2 emissions: A spatial econometric analysis

Planning and development of urban is one of the key factors that affect CO2 emissions. Sustainable urban planning and development is crucial to achieving carbon neutrality. However, there are relatively less studies in quantifying the impacts of urban forms and socioeconomic development on CO2 emissions with considering its spatial autocorrelation effects at the city-level. Thus, this study aimed to analyze the impacts of urban forms and socioeconomic factors on CO2 emissions of cities in Guangdong province during 2000–2017 based on a spatial panel econometric model. The results showed that CO2 emissions of Guangdong province increased significantly with a growth rate of 151% and had obvious spatial clustering characteristics. Urban form and socioeconomic development had a significant impact on CO2 emissions. Specifically, the results indicated that increasing the continuity of urban areas and improving the traffic coupling factor can help reduce CO2 emissions. The economic growth, population increase and economic openness degree increase would lead to stronger CO2 emission. In addition, the spatial spillover effects would enhance such impacts of the driving factors. Specifically, when the spillover effect of spatial Dubin model was taken into account, every 1% increase in urban class area, mean perimeter-area ratio, GDP, population, technology level and urbanization rate would lead a total CO2 emissions change by −0.53%, 1.3%, 1.1%, 0.18%, 12% and 1.4%, respectively. The results suggested that cities in Guangdong province should develop a more compact pattern, urban development with a scattered or disperse pattern should transform towards one continuous core city cluster and city belt, thus enhancing integration and sharing of infrastructure and related policies for low carbon development.

Climate signals in stable carbon and hydrogen isotopes of lignin methoxy groups from southern German beech trees

Abstract. Stable hydrogen and carbon isotope ratios of wood lignin methoxy groups (δ13CLM and δ2HLM values) have been shown to be reliable proxies of past temperature variations. Previous studies showed that δ2HLM values even work in temperate environments where classical tree-ring width and maximum latewood density measurements are less successful for climate reconstructions. Here, we analyse the annually resolved δ13CLM values from 1916–2015 of four beech trees (Fagus sylvatica) from a temperate site near Hohenpeißenberg in southern Germany and compare these data with regional- to continental-scale climate observations. Initial δ13CLM values were corrected for the Suess effect (a decrease of δ13C in atmospheric CO2) and physiological tree responses to increasing atmospheric CO2 concentrations considering a range of published discrimination factors. The calibration of δ13CLM chronologies against instrumental data reveals the highest correlations with regional summer (r=0.68) and mean annual temperatures (r=0.66), as well as previous-year September to current-year August temperatures (r=0.61), all calculated from 1916–2015 and reaching p&lt;0.001. Additional calibration trials using detrended δ13CLM values and climate data (to constrain effects of autocorrelation on significance levels) returned rsummer=0.46 (p&lt;0.001), rannual=0.25 (p&lt;0.05) and rprev.September-August=0.18 (p&gt;0.05). The new δ13CLM chronologies were finally compared with the previously produced δ2HLM values of the same trees in order to evaluate the additional gain of assessing past climate variability using a dual-isotope approach. Compared to δ13CLM, δ2HLM values correlate substantially more strongly with large-scale temperatures averaged over western Europe (rprev.September-August=0.69), whereas only weak and mainly insignificant correlations are obtained between precipitation and both isotope chronologies (δ13CLM and δ2HLM values). Our results indicate the great potential of using δ13CLM values from temperate environments as a proxy for local temperatures and, in combination with δ2HLM values, to assess regional- to sub-continental scale temperature patterns.

A new approach to detecting patterns of ENSO teleconnections with temperature and rainfall patterns in the Western Kenya Highlands separates seasonal, auto-correlated, and random effects

A new approach to detecting patterns of ENSO teleconnections with temperature and rainfall patterns in the Western Kenya Highlands separates seasonal, auto-correlated, and random effects

Asymmetric influences on Latin American stock markets: A quantile approach

This study examines the impact of international crude oil prices on quantiles of the distribution of stock market returns in Argentina, Brazil, Chile, and Mexico, from May 1, 2015 to January 15, 2021. For this purpose, quantile and ordinary least squares regression analysis methods were compared, controlling for the effects of autocorrelation, exchange rates, the S&P 500, and the COVID-19 pandemic period. We performed the analyses considering five quantiles associated with different states of stock market performance. The results showed that oil price fluctuations exhibited positive influences on Latin American stock markets, more prominent when oil prices were positive, as well as across all quantiles for the S&P 500 index. However, the exchange rate had a negative impact, except in Argentina. Asymmetric responses were found under negative and positive influences in previous trading sessions, as well for the pandemic period.

Monitoring the multivariate coefficient of variation in presence of autocorrelation with variable parameters control charts

ABSTRACT The coefficient of variation is a very important process parameter in many processes. A few control charts have been considered so far for monitoring its multivariate counterpart, i.e., the multivariate coefficient of variation (MCV). In addition, autocorrelation is very likely to occur in processes with high sampling frequency. Hence, designing suitable control charts and investigating the effect of autocorrelation on these charts is necessary. However, no control chart has been developed so far for the coefficient of variation that is capable of accounting for autocorrelation in either univariate or multivariate cases. This paper fills the gap by developing multivariate Shewhart-type control charts to monitor MCV with different autocorrelation structures for the observations: vector autoregressive, vector moving average, and vector mixed autoregressive and moving average. In addition, we add variable parameters adaptive features to the Shewhart-type scheme, in order to improve its performance. We develop a Markov chain model to get the statistical performance measures; then, we perform extensive numerical analyses to evaluate the effect of autocorrelation on adaptive and non-adaptive charts in the presence of downward and upward MCV shifts. Finally, we present an illustrative example from a healthcare process to show the implementation of this scheme in real practice.

Applications of the sampling uncertainty (SU)

The Sampling Uncertainty (SU) recently proposed allows the estimation of the sampling uncertainty including the Grouping and Segregation Error (GSE), the Fundamental Sampling Error (FSE) or the Fundamental Sampling Uncertainty (FSU) and the long range sampling errors for 1-dimensional sampling. SU is calculated from the spatial distribution of the analyte in a manner similar to cyclic convolution. For 1-dimensional sampling SU is shown to be better than variogram integration in case of cyclic or non-stationary variations and by being independent of the nugget effect when the nugget effect is close to zero. Three cases will be treated in detail: The problems with a low nugget effect, the effect of autocorrelation on 1-dimensional sampling and the effect of cyclic variations. For the effect of cyclic variations discrete Fourier transform (DFT) analysis is included to explain the findings and to filter the data. Finally, it is shown that DFT and SU give similar results for the cyclic pattern in the data when SU is calculated for a sampling ratio mass(lot)/mass(sample) = 2. Even though SU itself can estimate the sampling uncertainty correctly, it is proposed always to include a variographic analysis and a DFT analysis to characterize the spatial heterogeneity of the data.

Applications of the sampling uncertainty (SU)

The Sampling Uncertainty (SU) recently proposed allows the estimation of the sampling uncertainty including the Grouping and Segregation Error (GSE), the Fundamental Sampling Error (FSE) or the Fundamental Sampling Uncertainty (FSU) and the long range sampling errors for 1-dimensional sampling. SU is calculated from the spatial distribution of the analyte in a manner similar to cyclic convolution. For 1-dimensional sampling SU is shown to be better than variogram integration in case of cyclic or non-stationary variations and by being independent of the nugget effect when the nugget effect is close to zero. Three cases will be treated in detail: The problems with a low nugget effect, the effect of autocorrelation on 1-dimensional sampling and the effect of cyclic variations. For the effect of cyclic variations discrete Fourier transform (DFT) analysis is included to explain the findings and to filter the data. Finally, it is shown that DFT and SU give similar results for the cyclic pattern in the data when SU is calculated for a sampling ratio mass(lot)/mass(sample) = 2. Even though SU itself can estimate the sampling uncertainty correctly, it is proposed always to include a variographic analysis and a DFT analysis to characterize the spatial heterogeneity of the data.