Linear Correlation Structure Research Articles

Structured multifractal scaling of the principal cryptocurrencies: Examination using a self‐explainable machine learning

AbstractThis paper introduces a novel statistical testing technique known as segmented detrended multifractal fluctuation analysis (SMF‐DFA) to analyze the structured scaling properties of financial returns and predict the long‐term memory of financial markets. The proposed methodology is applied to assess the efficiency of major cryptocurrencies, expanding upon conventional approaches by incorporating different fluctuation regimes identified through a change‐point detection test. A single‐factor model is employed to characterize the endogenous factors influencing scaling behavior, leading to the development of a self‐explanatory machine learning approach for price forecasting. The proposed method is evaluated using daily data from three major cryptocurrencies spanning from April 2017 to December 2022. The analysis aims to determine whether the digital market has experienced significant changes in recent years and assess whether this has resulted in structured multifractal behavior. The study identifies common periods of local scaling among the three prices, with a noticeable decrease in multifractality observed after 2018. Furthermore, complementary tests on shuffled and surrogate data are conducted to explore the distribution, linear correlation, and nonlinear structure, shedding light on the explanation of structured multifractality to some extent. Additionally, prediction experiments based on neural networks fed with multi‐fractionally differentiated data demonstrate the utility of this new self‐explanatory algorithm for decision‐makers and investors seeking more accurate and interpretable forecasts.

Neurophysiological signatures of cortical micro-architecture

Systematic spatial variation in micro-architecture is observed across the cortex. These micro-architectural gradients are reflected in neural activity, which can be captured by neurophysiological time-series. How spontaneous neurophysiological dynamics are organized across the cortex and how they arise from heterogeneous cortical micro-architecture remains unknown. Here we extensively profile regional neurophysiological dynamics across the human brain by estimating over 6800 time-series features from the resting state magnetoencephalography (MEG) signal. We then map regional time-series profiles to a comprehensive multi-modal, multi-scale atlas of cortical micro-architecture, including microstructure, metabolism, neurotransmitter receptors, cell types and laminar differentiation. We find that the dominant axis of neurophysiological dynamics reflects characteristics of power spectrum density and linear correlation structure of the signal, emphasizing the importance of conventional features of electromagnetic dynamics while identifying additional informative features that have traditionally received less attention. Moreover, spatial variation in neurophysiological dynamics is co-localized with multiple micro-architectural features, including gene expression gradients, intracortical myelin, neurotransmitter receptors and transporters, and oxygen and glucose metabolism. Collectively, this work opens new avenues for studying the anatomical basis of neural activity.

Rainfall Generation Revisited: Introducing CoSMoS‐2s and Advancing Copula‐Based Intermittent Time Series Modeling

AbstractWhat elements should a parsimonious model reproduce at a single scale to precisely simulate rainfall at many scales? We posit these elements are: (a) the probability of dry and linear correlation structure of the wet/dry sequence as a proxy reproducing the distribution of wet/dry spells, and (b) the marginal distribution of nonzero rainfall and its correlation structure. We build a two‐state rainfall model, the CoSMoS‐2s, that explicitly reproduces these elements and is easily applicable at any timescale. Additionally, the paper: (a) introduces the Generalized Exponential () distribution system comprising six flexible distributions with desired properties to describe nonzero rainfall and facilitate time series generation; (b) extends the CoSMoS framework to allow simulations with negative correlations; (c) simplifies the generation of binary sequences with any correlation structure by analytical approximations; (d) introduces the rank‐based CoSMoS‐2s that preserves Spearman's correlations, has an analytical formulation, and is also applicable for infinite variance time series, (e) introduces the copula‐based CoSMoS‐2s enabling intermittent times series generation with nonzero values having the dependence structure of any desired copula, and (f) offers conceptual generalizations for rainfall modeling and beyond, with specific ideas for future improvements and extensions. The CoSMoS‐2s is tested using four long hourly rainfall records; the simulations reproduce rainfall properties at multiple scales including the wet/dry spells, probability of dry, characteristics of nonzero rainfall, and the behavior of extremes.

A Kalman filter-based hybridization model of statistical and intelligent approaches for exchange rate forecasting

Purpose The purpose of this paper is to propose a comprehensive version of a hybrid autoregressive integrated moving average (ARIMA), and artificial neural networks (ANNs) in order to yield a more general and more accurate hybrid model for exchange rates forecasting. For this purpose, the Kalman filter technique is used in the proposed model to preprocess and detect the trend of raw data. It is basically done to reduce the existing noise in the underlying data and better modeling, respectively. Design/methodology/approach In this paper, ARIMA models are applied to construct a new hybrid model to overcome the above-mentioned limitations of ANNs and to yield a more general and more accurate model than traditional hybrid ARIMA and ANNs models. In our proposed model, a time series is considered as a function of a linear and nonlinear component, so, in the first phase, an ARIMA model is first used to identify and magnify the existing linear structures in data. In the second phase, a multilayer perceptron is used as a nonlinear neural network to model the preprocessed data, in which the existing linear structures are identified and magnified by ARIMA and to predict the future value of time series. Findings In this paper, a new Kalman filter based hybrid artificial neural network and ARIMA model are proposed as an alternate forecasting technique to the traditional hybrid ARIMA/ANNs models. In the proposed model, similar to the traditional hybrid ARIMA/ANNs models, the unique strengths of ARIMA and ANN in linear and nonlinear modeling are jointly used, aiming to capture different forms of relationship in the data; especially, in complex problems that have both linear and nonlinear correlation structures. However, there are no aforementioned assumptions in the modeling process of the proposed model. Therefore, in the proposed model, in contrast to the traditional hybrid ARIMA/ANNs, it can be generally guaranteed that the performance of the proposed model will not be worse than either of their components used separately. In addition, empirical results in both weekly and daily exchange rate forecasting indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by traditional hybrid ARIMA/ANNs models. Originality/value In the proposed model, in contrast to the traditional hybrid ARIMA/ANNs, it can be guaranteed that the performance of the proposed model will not be worse than either of the components used separately. In addition, empirical results in exchange rate forecasting indicate that the proposed model can be an effective way to improve forecasting accuracy achieved by traditional hybrid ARIMA/ANNs models. Therefore, it can be used as an appropriate alternate model for forecasting in exchange ratemarkets, especially when higher forecasting accuracy is needed.

Arrow of time across five centuries of classical music

The concept of time series irreversibility -- the degree by which the statistics of signals are not invariant under time reversal -- naturally appears in non-equilibrium physics in stationary systems which operate away from equilibrium and produce entropy. This concept has not been explored to date in the realm of musical scores as these are typically short sequences whose time reversibility estimation could suffer from strong finite size effects which preclude interpretability. Here we show that the so-called Horizontal Visibility Graph method -- which recently was shown to quantify such statistical property even in non-stationary signals -- is a method that can estimate time reversibility of short symbolic sequences, thus unlocking the possibility of exploring such properties in the context of musical compositions. Accordingly, we analyse over 8000 musical pieces ranging from the Renaissance to the early Modern period and certify that, indeed, most of them display clear signatures of time irreversibility. Since by construction stochastic processes with a linear correlation structure (such as 1/f noise) are time reversible, we conclude that musical compositions have a considerably richer structure, that goes beyond the traditional properties retrieved by the power spectrum or similar approaches. We also show that musical compositions display strong signs of nonlinear correlations, that nonlinearity is correlated to irreversibility, and that these are also related to asymmetries in the abundance of musical intervals, which we associate to the narrative underpinning a musical composition. These findings provide tools for the study of musical periods and composers, as well as criteria related to music appreciation and cognition.

Data-driven prediction for volatile processes based on real option theories

This paper presents a new prediction model for time series data by integrating a time-varying Geometric Brownian Motion model with a pricing mechanism used in financial engineering. Typical time series models such as Auto-Regressive Integrated Moving Average assumes a linear correlation structure in time series data. When a stochastic process is highly volatile, such an assumption can be easily violated, leading to inaccurate predictions. We develop a new prediction model that can flexibly characterize a time-varying volatile process without assuming linearity. We formulate the prediction problem as an optimization problem with unequal overestimation and underestimation costs. Based on real option theories developed in finance, we solve the optimization problem and obtain a predicted value, which can minimize the expected prediction cost. We evaluate the proposed approach using multiple datasets obtained from real-life applications including manufacturing, and finance. The numerical results demonstrate that the proposed model shows competitive prediction capability, compared with alternative approaches.

Precise Temporal Disaggregation Preserving Marginals and Correlations (DiPMaC) for Stationary and Nonstationary Processes

AbstractHydroclimatic variables such as precipitation and temperature are often measured or simulated by climate models at coarser spatiotemporal scales than those needed for operational purposes. This has motivated more than half a century of research in developing disaggregation methods that break down coarse‐scale time series into finer scales, with two primary objectives: (a) reproducing the statistical properties of the fine‐scale process and (b) preserving the original coarse‐scale data. Existing methods either preserve a limited number of statistical moments at the fine scale, which is often insufficient and can lead to an unrepresentative approximation of the actual marginal distribution, or are based on a limited number of a priori distributional assumptions, for example, lognormal. Additionally, they are not able to account for potential nonstationarity in the underlying fine‐scale process. Here we introduce a novel disaggregation method, named Disaggregation Preserving Marginals and Correlations (DiPMaC), that is able to disaggregate a coarse‐scale time series to any finer scale, while reproducing the probability distribution and the linear correlation structure of the fine‐scale process. DiPMaC is also generalized for arbitrary nonstationary scenarios to reproduce time varying marginals. Additionally, we introduce a computationally efficient algorithm, based on Bernoulli trials, to optimize the disaggregation procedure and guarantee preservation of the coarse‐scale values. We focus on temporal disaggregation and demonstrate the method by disaggregating monthly precipitation to hourly, and time series with trends (e.g., climate model projections), while we show its potential to disaggregate based on general nonstationary scenarios. The example applications demonstrate the performance and robustness of DiPMaC.

Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency

Abstract Hydroclimatic processes come in all “shapes and sizes”. They are characterized by different spatiotemporal correlation structures and probability distributions that can be continuous, mixed-type, discrete or even binary. Simulating such processes by reproducing precisely their marginal distribution and linear correlation structure, including features like intermittency, can greatly improve hydrological analysis and design. Traditionally, modelling schemes are case specific and typically attempt to preserve few statistical moments providing inadequate and potentially risky distribution approximations. Here, a single framework is proposed that unifies, extends, and improves a general-purpose modelling strategy, based on the assumption that any process can emerge by transforming a specific “parent” Gaussian process. A novel mathematical representation of this scheme, introducing parametric correlation transformation functions, enables straightforward estimation of the parent-Gaussian process yielding the target process after the marginal back transformation, while it provides a general description that supersedes previous specific parameterizations, offering a simple, fast and efficient simulation procedure for every stationary process at any spatiotemporal scale. This framework, also applicable for cyclostationary and multivariate modelling, is augmented with flexible parametric correlation structures that parsimoniously describe observed correlations. Real-world simulations of various hydroclimatic processes with different correlation structures and marginals, such as precipitation, river discharge, wind speed, humidity, extreme events per year, etc., as well as a multivariate example, highlight the flexibility, advantages, and complete generality of the method.

Environmental drivers of sardine (Sardina pilchardus) in the Catalan Sea (NW Mediterranean Sea)

ABSTRACTIn the area surrounding the Ebro Delta, similar to the rest of the north-western Mediterranean Sea, the sardine (Sardina pilchardus), one of the most exploited small pelagic fishes, has suffered a decreasing trend in abundance and biomass in the last decade, with low values in evidence since 2007. The dependence of this species on environmental factors makes it vulnerable to environmental changes; consequently, the abundance of the species is highly variable. Using segmented regression, we evaluated the presence of discontinuities in the temporal pattern of the seasonally adjusted landings per unit effort (LPUE), which was used as a proxy for abundance, between 2000 and 2013. The results suggested a sudden increase in mid-2005, followed by a sharp decrease starting in 2006. A generalized additive mixed model (GAMM), incorporating the linear correlation structure, was used to identify relationships between the seasonally adjusted LPUE and trends of the Western Mediterranean Oscillation index (WeMOI), sea surface temperature (SST), salinity (SAL) and the Zonal and Meridional Currents (ZC and MC, respectively). The variance inflation factors (VIFs) were calculated between all environmental variables to avoid high-dimensional collinearities. The final GAMM, selected using the Akaike information criterion, indicated that positive WeMOI values, which favour the productivity of the area, along with SAL (at ca. 38) and a northward-flowing MC, favoured LPUE. Our results, obtained by applying a method in which variation due to season, non-linearity, autocorrelation and collinearity of the covariates was taken into account, provided further evidence of the dependence of the sardine population upon specific hydrographic variables.

On composite likelihood in bivariate meta-analysis of diagnostic test accuracy studies

The composite likelihood is amongst the computational methods used for estimation of the generalized linear mixed model (GLMM) in the context of bivariate meta-analysis of diagnostic test accuracy studies. Its advantage is that the likelihood can be derived conveniently under the assumption of independence between the random effects, but there has not been a clear analysis of the merit or necessity of this method. For synthesis of diagnostic test accuracy studies, a copula mixed model has been proposed in the biostatistics literature. This general model includes the GLMM as a special case and can also allow for flexible dependence modelling, different from assuming simple linear correlation structures, normality and tail independence in the joint tails. A maximum likelihood (ML) method, which is based on evaluating the bi-dimensional integrals of the likelihood with quadrature methods, has been proposed, and in fact it eases any computational difficulty that might be caused by the double integral in the likelihood function. Both methods are thoroughly examined with extensive simulations and illustrated with data of a published meta-analysis. It is shown that the ML method has no non-convergence issues or computational difficulties and at the same time allows estimation of the dependence between study-specific sensitivity and specificity and thus prediction via summary receiver operating curves.

Simulation of multivariate non-gaussian autoregressive time series with given autocovariance and marginals

A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes, transforming the autocorrelation of the non-Gaussian process to that of a Gaussian process based on a piece-wise linear marginal transform from non-Gaussian to Gaussian marginal. The extension to multivariate processes involves the derivation of the autocorrelation matrix from the marginal transforms, which determines the generating vector autoregressive process. The effectiveness of the approach is demonstrated on systems designed under different scenarios of autocovariance and marginals.

What Can Causal Networks Tell Us about Metabolic Pathways?

Graphical models describe the linear correlation structure of data and have been used to establish causal relationships among phenotypes in genetic mapping populations. Data are typically collected at a single point in time. Biological processes on the other hand are often non-linear and display time varying dynamics. The extent to which graphical models can recapitulate the architecture of an underlying biological processes is not well understood. We consider metabolic networks with known stoichiometry to address the fundamental question: “What can causal networks tell us about metabolic pathways?”. Using data from an Arabidopsis BaySha population and simulated data from dynamic models of pathway motifs, we assess our ability to reconstruct metabolic pathways using graphical models. Our results highlight the necessity of non-genetic residual biological variation for reliable inference. Recovery of the ordering within a pathway is possible, but should not be expected. Causal inference is sensitive to subtle patterns in the correlation structure that may be driven by a variety of factors, which may not emphasize the substrate-product relationship. We illustrate the effects of metabolic pathway architecture, epistasis and stochastic variation on correlation structure and graphical model-derived networks. We conclude that graphical models should be interpreted cautiously, especially if the implied causal relationships are to be used in the design of intervention strategies.

A Hierarchical Model of Tail Dependent Asset Returns for Assessing Portfolio Credit Risk

This paper introduces a multivariate pure-jump Levy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a two-stage stochastic time change to Brownian motions, I derive a hierarchical structure with different properties of inter- and intra-sector dependence. I investigate the properties of the implied static copula families and come to the conclusion that they are ordered with respect to their parameters and that the lower-tail dependence of the intra-sector copula is increasing in the absolute values of skewness parameters. Furthermore, I show that the joint characteristic function of the VCG asset returns can be explicitly given as a nested Archimedean copula of their marginal characteristic functions. Applied to credit portfolio modelling, the framework introduced results in a more conservative tail risk assessment than a Gaussian framework with the same linear correlation structure, as I show in a simulation study. To foster the simulation efficiency, I provide an Importance Sampling algorithm for the VCG portfolio setting.

A Hierarchical Model of Tail Dependent Asset Returns for Assessing Portfolio Credit Risk

This paper introduces a multivariate pure-jump Levy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a two-stage stochastic time change to Brownian motions, I derive a hierarchical structure with different properties of inter- and intra-sector dependence. I investigate the properties of the implied static copula families and come to the conclusion that they are ordered with respect to their parameters and that the lower-tail dependence of the intra-sector copula is increasing in the absolute values of skewness parameters. Furthermore, I show that the joint characteristic function of the VCG asset returns can be explicitly given as a nested Archimedean copula of their marginal characteristic functions. Applied to credit portfolio modelling, the framework introduced results in a more conservative tail risk assessment than a Gaussian framework with the same linear correlation structure, as I show in a simulation study. To foster the simulation efficiency, I provide an Importance Sampling algorithm for the VCG portfolio setting.

Nonlinear ensemble prediction of chaotic daily rainfall

The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955–2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on the phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996–2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature.

Quasi-least squares with mixed linear correlation structures

Quasi-least squares (QLS) is a two-stage computational approach for estimation of the correlation parameters in the framework of generalized estimating equations. We prove two general results for the class of mixed linear correlation structures: namely, that the stage one QLS estimate of the correlation parameter always exists and is feasible (yields a positive definite estimated correlation matrix) for any correlation structure, while the stage two estimator exists and is unique (and therefore consistent) with probability one, for the class of mixed linear correlation structures. Our general results justify the implementation of QLS for particular members of the class of mixed linear correlation structures that are appropriate for analysis of data from families that may vary in size and composition. We describe the familial structures and implement them in an analysis of optical spherical values in the Old Order Amish (OOA). For the OOA analysis, we show that we would suffer a substantial loss in efficiency, if the familial structures were the true structures, but were misspecified as simpler approximate structures. To help bridge the interface between Statistics and Medicine, we also provide R software so that medical researchers can implement the familial structures in a QLS analysis of their own data.

A multivariate Lévy process model with linear correlation

In this paper, we develop a multivariate risk-neutral Lévy process model and discuss its applicability in the context of the volatility smile of multiple assets. Our formulation is based upon a linear combination of independent univariate Lévy processes and can easily be calibrated to a set of one-dimensional marginal distributions and a given linear correlation matrix. We derive conditions for our formulation and the associated calibration procedure to be well-defined and provide some examples associated with particular Lévy processes permitting a closed-form characteristic function. Numerical results of the option premiums on three currencies are presented to illustrate the effectiveness of our formulation with different linear correlation structures.

Pretreatment of Mass Spectral Profiles: Application to Proteomic Data

Mass spectral profiles are influenced by several factors that have no relation to compositional differences between samples: baseline effects, shifts in mass-to-charge ratio (m/z) (synchronization/alignment problem), structured noise (heteroscedasticity), and, differences in signal intensities (normalization problem). Different procedures for pretreatment of whole mass spectral profiles described by almost 50,000 m/z values are investigated in order to find optimal approaches with respect to revealing the information content in the data. In order to quantitatively assess the impact of different procedures for pretreatment of mass spectral profiles, we use factorial designs with the ratio between intergroup and intragroup (replicate) variance as response. We have examined the influence of smoothing, binning, alignment/synchronization, noise pattern, and normalization on data interpretation. Our analysis shows that the spectral profiles have to be corrected for heteroscedastic noise prior to normalization. An nth root transform, where n is a small, positive integer, is used to create a homoscedastic noise structure without destroying the linear correlation structures describing individual components when using whole mass spectral profiles. The choice of n is decided by a simple graphic procedure using replicate information. Log transform is shown to change the heteroscedastic noise structure from being dominant in high-intensity regions, to produce the largest noise in the low-intensity regions. In addition, log transform has a negative effect on the collinearity in the profiles. Factorial designs reveal strong interactions between several of the pretreatment steps, e.g., noise structure and normalization. This underlines the limited usability of looking at the different pretreatment steps in isolation. Binning turns out to be able to substitute smoothing of spectra by, for example, moving average or Savitsky-Golay, while, at the same time, reducing the data point description of the profiles by 1 order of magnitude. Thus, if the sampling density is high, binning seems to be an attractive option for data reduction without the risk of losing information accompanying the integration of profiles into peaks. In the absence of smoothing, binning should be executed prior to alignment. If binning is not performed, the order of pretreatment should be smoothing, alignment, nth root transform, and normalization.

Fitting copulas to bivariate earthquake data: the seismic gap hypothesis revisited

AbstractThe seismic gap hypothesis assumes that the intensity of an earthquake and the time elapsed from the previous one are positively related. Previous works on this topic were based on particular assumptions for the joint distribution implying specific type of dependence. We investigate this hypothesis using copulas. Copulas are flexible for modelling the dependence structure far from assuming simple linear correlation structures and, thus, allow for better examination of this controversial aspect of geophysical research. In fact, via copulas, marginal properties and dependence structure can be separated. We propose a model averaging approach in order to allow for model uncertainty and diminish the effect of the choice of a particular copula. This enlarges the range of potential dependence structures that can be investigated. Application to a real data set is provided. Copyright © 2007 John Wiley & Sons, Ltd.

Effect of clinical mastitis on the lactation curve: a mixed model estimation using daily milk weights.

The objective of this study was to estimate the milk production losses associated with clinical mastitis using mixed linear models and correlation structures that have not been available previously. Data used included computer-recorded daily milk yields and detailed and accurate recordings of clinical mastitis cases. Two commercial Holstein dairy farms in New York State participated in the study, one with 650 lactating cows and another that began the study with 830 lactating cows and increased to 1120 cows by the end of the study. Cows on both farms were housed in free stall barns and milked 3 times daily in milking parlors. Electrical conductivity was used as a diagnostic aid for clinical mastitis on both farms. Date of clinical onset was recorded for every episode of clinical mastitis as well as for 8 other diseases defined using standardized case definitions (dystocia, milk fever, retained placenta, metritis, ketosis, displaced abomasum, lameness, and cystic ovarian disease) during the study period of October 1, 1999 to July 31, 2001. The mixed linear model for explaining variation in the outcome variable daily milk yield relative to non-mastitic herdmates found the terms for all 9 diseases studied, including clinical mastitis, significant. The model with an autoregressive correlation structure was preferred based on -2 * log likelihood, Akaike's information criterion, and Bayesian information criterion as well as savings in degrees of freedom. Separate analyses were run for first lactation cows and for second-plus lactation cows because their lactation curves were shaped differently. Adjusting for the effects of the other 8 diseases, milk production loss from clinical mastitis during the whole lactation was estimated as approximately 598 kg for second-plus lactation cows. However, cows that contracted mastitis had a daily production advantage of 2.6 kg over their herdmates until they contracted the disease. When compared with this potentially higher milk production, the total loss from clinical mastitis was estimated as 1181 kg.