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Objective Dual-flow continuous culture (DFCC) fermentor systems have been historically used to simulate ruminant fermentation, but one most commonly used system was discontinued by the manufacturer. In response, modifications were made to construct new cost-effective units. Our objective was to evaluate the modifications relative to the original DFCC fermentors. Our hypothesis was that experiments using newly modified DFCC units would have decreased variance estimates for common dependent variables: nutrient digestibilities, VFA production, and bacterial N flow. Materials and Methods To evaluate impeller orientation, DFCC fermentors were randomized to either clockwise or counterclockwise fan blades on a counterclockwise-rotating motor. Fermentors (n = 8) were fed 37.2 g of DM of a pelleted 50:50 alfalfa:concentrate diet and run for 11 d with 7 d of adaptation and 4 d of sampling. To evaluate variance estimates, data were accumulated from 4 published fermentor experiments (n = 68) using original fermentors (The Virtis Company) and 2 fermentor experiments using modified DFCC units (n = 42). An F-test was conducted on the modified:original variance ratio, and a significant decrease in variance was declared at P Results and Discussion Impeller orientation decreased NDF digestibility in the clockwise rotation, whereas ADF digestibility was not affected. The modified DFCC system decreased variance of NDF and nonstructural carbohydrate digestibility. Variances of other measures were unaffected by the new system. Implications and Applications These data indicate the potential for the modified DFCC to primarily improve reliability of fiber digestibility, but more work may be needed to reduce variance of concentration-based fermentation parameters.

This project contains all data and code needed to reproduce our case study on the use of meta-analysis of variance. This study tests whether developmental stress affects both mean and variance in phenotype and fitness across animal species.

This article introduces a new unit root test that combines the variance ratio framework with the Flexible Fourier Form under the generalized least squares detrending mechanism. The advantage of the proposed method against its alternatives can be listed as: (1) it suggests a non-parametric procedure that does not require any parametric or semi-parametric model to remove serial correlation in the innovation process; (2) it can reasonably adapt itself to deal with the multiple structural breaks with various functional specifications. In the simulation exercises, we show that the proposed method exhibits satisfactory performance in the size and size-adjusted power analysis.

Aromatic rice (Oryza sativa L. Indica) is popular among consumers. They provide significant economic benefit to producing countries as well as farmers. Aromatic germplasm is huge and diverse in terms of agro-morphological characters, grain types and aroma content. Development of a representative coreset of aromatic germplasm can be a good source for novel alleles identification and is required for its improvement. A collection of 552 aromatic accessions were screened for 40 DUS traits and 60 SSR markers. The data were processed in PowerCore software that implements the advanced M (or maximization) strategy using a modified heuristic algorithm and a coreset of 99 accessions was identified. The average Nei diversity and Shannon–Weaver diversity indices of the coreset were 0.635 and 0.823, representing the entire diversity of the collection. Statistical parameters like mean difference and variance difference were analysed to compare the mean and variance ratio between core and entire collections. Coreset has 3.45% mean difference and 14.4% variance difference. The coreset has 99.04% coincidence rate and 106.31% variable range which indicated the optimum properties of the coreset against the entire collection. This is the first attempt of making coreset of aromatic rice from larger germplasm.

Turkey is one of the poultry species that is declining in Nigeria due to its importation as frozen turkey. In this study, a total of 78 day-old random-bred Nigerian local turkey poults were used to generate another 232 day-old poults to discriminate Nigerian local turkey based on linear body measurements. Three phenotypic classes (Black, White and Spotted) were obtained as base population and used to generate F1 progeny. Experimental design was a randomized complete block (RCBD) with phenotypic class as major factor of interest and hatch as block. Linear body measurements (LBMs), namely body length (BDL), shank length (SHL), keel length (KLL), breast width (BW), wing length (WGL) and drumstick length (DSL) were significantly different at weeks 7, 9, 11 and 19. There were two discriminant functions. The variance ratio (eigenvalue) of each of the two discriminant functions were not significant (p>0.05). The percentage of the total variance explained was 87.7% and 12.3% for the two functions respectively. Group centroids for the phenotypic classes were 7.210, -1.254 and -5.956 for Black, White and Spotted turkeys respectively. The magnitudes and signs of the group centroids indicate that the three phenotypes are distinctly different from one another when BDL (weeks 7, 11, 13 and 15), WGL (weeks 7, 9 and 11), KLL (weeks 7, 9 and 15) and SHL (weeks 11 and 21) are used as the discriminating factors. The study shows that linear body measurement is a reliable classification criterion for discriminating among the phenotypes, which are therefore, correctly described as different breeds/strains. Therefore, for rapid improvement in local turkeys and breed development, these linear body traits could be used to enhance its discrimination, classification and appropriate grouping into breeds. The present findings could assist in the design of long-term genetic improvement programmes for local turkey breeding and production in Nigeria.

This study forecasts the return and volatility dynamics of S&P BSE Sensex and S&P BSE IT indices of the Bombay Stock Exchange. To achieve the objectives, the study uses descriptive statistics; tests including variance ratio, Augmented Dickey-Fuller, Phillips-Perron, and Kwiatkowski Phillips Schmidt and Shin; and Autoregressive Integrated Moving Average (ARIMA). The analysis forecasts daily stock returns for the S&P BSE Sensex and S&P BSE IT time series, using the ARIMA model. The results reveal that the mean returns of both indices are positive but near zero. This is indicative of a regressive tendency in the long-term. The forecasted values of S&P BSE Sensex and S&P BSE IT are almost equal to their actual values, with few deviations. Hence, the ARIMA model is capable of predicting medium- or long-term horizons using historical values of S&P BSE Sensex and S&P BSE IT.

Reducing the input data of tactile sensory systems brings a large degree of freedom to real-world implementations from the perspectives of bandwidth and computational complexity. For this, in this letter, we suggest efficient active-cell formations with a high classification accuracy of tactile materials. By revealing that averaged Kullback–Leibler-divergence and common frequency component power to variance ratio are proportional to the classification accuracy, we showed that those methods can be useful in estimating valid active-cell formations.

This study evaluates the varying degree of predictability of commodities return through empirical analysis of AMH (Adaptive Market Hypothesis). We divide daily returns data (from 1996 to 2013) of commodities indices (Gold, Metal, Oil& Silver) into different crisis periods. We subject all the subsamples to linear/nonlinear tests to reveal how market efficiency (independency of returns) has behaved over time. All the linear (except variance ratio) and nonlinear tests are evident that commodity indices returns have been predictable (dependent) in some crisis periods while unpredictable (dependence) in the others thus consistent with the implication of AMH. Therefore, commodities markets are adaptive markets. The findings suggest the behavior of commodities’ markets is best explained by AMH than conventional/traditional EMH (Efficient Market Hypothesis).

Synchronous dynamics (fluctuations that occur in unison) are universal phenomena with widespread implications for ecological stability. Synchronous dynamics can amplify the destabilizing effect of environmental variability on ecosystem functions such as productivity, whereas the inverse, compensatory dynamics, can stabilize function. Here we combine simulation and empirical analyses to elucidate mechanisms that underlie patterns of synchronous versus compensatory dynamics. In both simulated and empirical communities, we show that synchronous and compensatory dynamics are not mutually exclusive but instead can vary by timescale. Our simulations identify multiple mechanisms that can generate timescale-specific patterns, including different environmental drivers, diverse life histories, dispersal, and non-stationary dynamics. We find that traditional metrics for quantifying synchronous dynamics are often biased toward long-term drivers and may miss the importance of short-term drivers. Our findings indicate key mechanisms to consider when assessing synchronous versus compensatory dynamics and our approach provides a pathway for disentangling these dynamics in natural systems.

We propose a statistical procedure to determine the dimension of the nonstationary subspace of cointegrated functional time series taking values in the Hilbert space of square-integrable functions defined on a compact interval. The procedure is based on sequential application of a proposed test for the dimension of the nonstationary subspace. To avoid estimation of the long-run covariance operator, our test is based on a variance ratio-type statistic. We derive the asymptotic null distribution and prove consistency of the test. Monte Carlo simulations show good performance of our test and provide evidence that it outperforms the existing testing procedure. We apply our methodology to three empirical examples: age-specific US employment rates, Australian temperature curves, and Ontario electricity demand.

Measure–correlate–predict (MCP) approaches are often used to correct wind measurements to the long-term wind conditions on-site. This paper investigates systematic errors in MCP-based long-term corrections which occur if the measurement on-site covers only a few months (seasonal biases). In this context, two common linear MCP methods are tested and compared with regard to accuracy in mean, variance, and turbine energy production – namely, variance ratio (VR) and linear regression with residuals (LR). Wind measurement data from 18 sites with different terrain complexity in Germany are used (measurement heights between 100 and 140 m). Six different reanalysis data sets serve as the reference (long-term) wind data in the MCP calculations. All these reanalysis data sets showed an overpronounced annual course of wind speed (i.e., wind speeds too high in winter and too low in summer). However, despite the mathematical similarity of the two MCP methods, these errors in the data resulted in very different seasonal biases when either the VR or LR methods were used for the MCP calculations. In general, the VR method produced overestimations of the mean wind speed when measuring in summer and underestimations in the case of winter measurements. The LR method, in contrast, predominantly led to opposite results. An analysis of the bias in variance did not show such a clear seasonal variation. Overall, the variance error plays only a minor role for the accuracy in energy compared to the error in mean wind speed. Besides the experimental analysis, a theoretical framework is presented which explains these phenomena. This framework enables us to trace the seasonal biases to the mechanics of the methods and the properties of the reanalysis data sets. In summary, three aspects are identified as the main influential factors for the seasonal biases in mean wind speed: (1) the (dis-)similarity of the real wind conditions on-site in correlation and correction period (representativeness of the measurement period), (2) the capability of the reference data to reproduce the seasonal course of wind speed, and (3) the regression parameter β1 (slope) of the linear MCP method. This theoretical framework can also be considered valid for different measurement durations, other reference data sets, and other regions of the world.

Synchrony among population fluctuations of multiple coexisting species has a major impact on community stability, i.e. on the relative temporal constancy of aggregate properties such as total community biomass. However, synchrony and its impacts are usually measured using covariance methods, which do not account for whether species abundances may be more correlated when species are relatively common than when they are scarce, or vice versa. Recent work showed that species commonly exhibit such ‘asymmetric tail associations’. We here consider the influence of asymmetric tail associations on community stability. We develop a ‘skewness ratio’ which quantifies how much species relationships and tail associations modify stability. The skewness ratio complements the classic variance ratio and related metrics. Using multi-decadal grassland datasets, we show that accounting for tail associations gives new viewpoints on synchrony and stability; e.g. species associations can alter community stability differentially for community crashes or explosions to high values, a fact not previously detectable. Species associations can mitigate explosions of community abundance to high values, increasing one aspect of stability, while simultaneously exacerbating crashes to low values, decreasing another aspect of stability; or vice versa. Our work initiates a new, more flexible paradigm for exploring species relationships and community stability. This article is part of the theme issue ‘Synchrony and rhythm interaction: from the brain to behavioural ecology’.

Abstract. Equivalence tests (also known as similarity or parity tests) have become more and more popular in addition to equality tests. However, in testing the equivalence of two population means, approximate sample sizes developed using conventional techniques found in the literature on this topic have usually been under-valued as having less statistical power than is required. In this paper, the authors first address the reason for this problem and then provide a solution using an exhaustive local search algorithm to find the optimal sample size. The proposed method is not only accurate but is also flexible so that unequal variances or sampling unit costs for different groups can be considered using different sample size allocations. Figures and a numerical example are presented to demonstrate various configurations. An R Shiny App is also available for easy use ( https://optimal-sample-size.shinyapps.io/equivalence-of-means/ ).

The aim of the article is to examine the martingale hypothesis of market efficiency on high-frequency data of the soya bean futures traded in National Commodity and Derivatives Exchange (NCDEX) of India using multiple variance ratio (VR) tests from February 2015 to August 2015. The study employs high-frequency future prices of 5, 10, 15, 30 and 60 min time intervals mainly to decipher the efficiency of processing information by soya bean traders during intraday sessions of futures trading. The results of VR tests confirm that except prices of 5 and 10 min intervals which displays weak form of market efficiency, all other samples follow martingale hypothesis. The findings suggest that as information gets absorbed promptly in the intraday NCDEX soya bean futures prices, there exists fairly less opportunities to explore any trading strategy for profitable outcomes in the soya bean futures market in India.

Earthquakes (EQs) are potential agents of damage and destruction to life and property. Scientists have been on the lookout for precursors and signatures of EQs. This work attempts to isolate earthquake precursors by analysing the coupling between interplanetary magnetic field (IMF) and geomagnetic (GM) field. The vertical variance (VV) method is employed to quantify disturbance content in the data and thereby analyse such coupling. Since IMF–GM field coupling is a global phenomenon, this variation is strongly correlated between stations. However, this correlation is disturbed by local events like earthquakes. We have analysed the role of earthquakes in the loss of IMF–GM field coupling by observing such correlation between selected geomagnetic observatories, viz. Alibag, Huancayo, Phu Thuy, Qsaybeh, Addis Ababa and Hyderabad. Analysis for the months of December 2004 and April 2012 is presented. Critical dips are observed in the inter-station GM–IMF vertical variance ratio correlations of the analysed station pairs in association with occurrence of earthquakes. This inference has been substantiated by the fact that the anomaly is absent during earthquake free intervals. The veracity of this anomaly has been crosschecked for agreement with earthquake precursors that have already been reported by parallel studies.

Investigation of locomotion patterns provides a useful scenario for many applications like locomotion classification in the prosthesis, gait rehabilitation, and pathological gait analysis. Locomotion classification for prosthesis use has been of great importance for the development of intelligent prosthesis. Electromyography (EMG) has shown promising results in the past as a sensing modality to represent the locomotion patterns in different terrain. However, EMG suffers from various limitations to be widely accepted. A force myography (FMG) system has been developed to analyze its feasibility as an alternate sensing modality to EMG. Data from eight force sensitive resistors (FSR) along with foot switches were collected from six healthy subjects for five different locomotion modes i.e. level walk (LW), ramp ascent (RA), ramp descent (RD), stair ascent (SA) and stair descent (SD). To estimate the characteristics of FMG, the variance ratio and correlation coefficient were calculated for intra and inter-class locomotion respectively. A lower variance ratio in anterior FMG in all locomotion modes was observed, indicating the high repeatability of FMG signal. Further, the lower correlation coefficient between level walking (LW) and other locomotion modes SA & SD, promises FMG to be a potential information source for future application in locomotion classification. Results of the present study demonstrate the prospective of FMG in the representation of different locomotion and its possible application in lower limb prosthetic control.

In this paper, we propose a wavelet-based cointegration test for fractionally integrated time series. The proposed test is nonparametric and asymptotically invariant to different forms of short-run dynamics. The use of wavelets allows us to take advantage of the wavelet-based bootstrapping method mainly known as wavestrapping. In this regard, we introduce to the literature a new wavestrapping algorithm for multivariate time series processes specifically for cointegration tests. The Monte Carlo simulations indicate that this new wavestrapping procedure can alleviate the severe size distortions which we generally observe in cointegration tests with time series containing innovations that possess highly negative moving average roots.

This article extends the variance ratio test of Lo and MacKinlay (1988) to tests of skewness and kurtosis ratios using the generalized methods of moments. In particular, overlapping observations are used in which dependencies are explicitly modeled to make the tests more powerful and have better size properties. The proposed higher-order ratio tests can be useful in risk management where risk models are estimated using daily data but multiperiod forecasts of tail risks are required for the determination of risk capital. Application of the tests finds significant higher moment dependence in the U.S. stock market returns.