Dynamic Covariance Research Articles

Physics of failure-based degradation modeling and lifetime prediction of the momentum wheel in a dynamic covariate environment

We consider the problem of reliability modeling and evaluation of the Momentum Wheel (MW) in long-life satellites under small sample circumstances, proposing a physics-of-failure-based degradation model and life prediction method for such MWs in a dynamic covariate environment. From the results of a physics of failure experiment, we first derive models for the distribution and microcirculation of bearing lubricant. Next, we identify the qualitative and quantitative relationships between the key factors, e.g. rotation speed and bearing temperature, and the loss of lubricant. Then, taking the bearing temperature as a dynamic covariate, we build a degradation model for lubricant loss in the bearing assembly that corresponds to a Wiener process with drift that is positively associated with the covariate. To estimate the parameters of this degradation model, we use the method of maximum likelihood and the data from the physics of failure experiment. To predict the lifetime of an individual MW under orbital conditions, we suggest using Empirical Mode Decomposition (EMD) and regression analysis to model the trend in bearing temperature derived from telemetry data. Bootstrap simulation provides a satisfactory way of coping with the various sources of uncertainty in our prediction. Based on the predicted bearing temperature and the lubricant loss model, we estimate the amount of lubricant lost by an individual MW bearing, and hence obtain the lifetime of the lubrication system by comparing the predicted values for residual lubricant with the designed lubricant capacity. A case study involving data from a particular type of MW demonstrates the merits of this lifetime prediction method that we propose.

The role of realized ex-post covariance measures and dynamic model choice on the quality of covariance forecasts

Abstract Recently, consistent measures of the ex-post covariation of financial assets based on noisy high-frequency data have been proposed. A related strand of literature focuses on dynamic models and covariance forecasting for high-frequency data based covariance measures. The aim of this paper is to investigate whether more sophisticated estimation approaches lead to more precise covariance forecasts, both in a statistical precision sense and in terms of economic value. A further issue, we address, is the relative importance of the quality of the realized measure as an input in a given forecasting model vs. the model's dynamic specification. The main finding is that the largest gains result from switching from daily to high-frequency data. Further gains are achieved if a simple sparse sampling covariance measure is replaced with a more efficient and noise-robust estimator.

Dynamic Stock Market Covariances in the Eurozone

This paper examines the short-term dynamics, macroeconomic sensitivities, and longer-term trends in the variances and covariances of national equity market index daily returns for eleven countries in the Euro currency zone. We modify Colacito, Engle and Ghysel's Mixed Data Sampling Dynamic Conditional Correlation Garch model to include a new scalar measure for the degree of correlatedness in time-varying correlation matrices. We also explore the robustness of the findings with a less model-dependent realized covariance estimator. We find a secular trend toward higher correlation during our sample period, and significant linkages between macroeconomic and market-wide variables and dynamic correlation. One notable finding is that average correlation between these markets is lower when their average GDP growth rate is lower or when more of them have negative GDP growth.

Duration dependence and dynamic conditional covariance of seasonal food price shocks in semi-arid African countries

Every year in the months preceding harvests several African regions register higher malnutrition and morbidity levels, severe water shortages, and food price jumps. A previous study, focused on Niamey (Niger) with ‘hunger’ and ‘normal’ seasons modelled as a latent Markov process, found that in the last two decades the risk of food crises has tended to spread over longer periods and to shift forward in timing. To help better devise support programmes, it would be beneficial to test for this finding in other locations in Africa and extend the focus beyond conditional mean analysis. This paper first reviews measures of food insecurity/crisis risk, and considers determinants of spatial and temporal food price variability in drought-prone countries. Duration-dependent Markov-switching VAR models are then formulated and applied to monthly staple prices of food markets in Niger, Ethiopia and Somalia. This is complemented with multivariate GARCH models of volatility and dynamic correlations of food price shocks in major urban centres of five Sahel countries. In Niger, seasonal shocks in surplus-producing regions often anticipate by nearly 1 month those in deficit regions. ‘Steep’ regime probability switches are of concern especially in recent years. However, across semi-arid countries in East and West Africa, no systematic variation over time was detected in terms of onset and length of seasonal food insecurity periods, nor between seasons relative to food price volatility.

To move or not to move to find a new job: spatial duration time model with dynamic covariate effects

The aim of this paper is to show the flexibility and capacity of penalized spline smoothing as estimation routine for modelling duration time data. We analyse the unemployment behaviour in Germany between 2000 and 2004 using a massive database from the German Federal Employment Agency. To investigate dynamic covariate effects and differences between competing job markets depending on the distance between former and recent working place, a functional duration time model with competing risks is used. It is build upon a competing hazard function where some of the smooth covariate effects are allowed to vary with unemployment duration. The focus of our analysis is on contrasting the spatial, economic and individual covariate effects of the competing job markets and on analysing their general influence on the unemployed's re-employment probabilities. As a result of our analyses, we reveal differences concerning gender, age and education. We also discover an effect between the newly formed and the old West German states. Moreover, the spatial pattern between the considered job markets differs.

Dynamical Locality and Covariance: What Makes a Physical Theory the Same in all Spacetimes?

The question of what it means for a theory to describe the same physics on all spacetimes (SPASs) is discussed. As there may be many answers to this question, we isolate a necessary condition, the SPASs property, that should be satisfied by any reasonable notion of SPASs. This requires that if two theories conform to a common notion of SPASs, with one a subtheory of the other, and are isomorphic in some particular spacetime, then they should be isomorphic in all globally hyperbolic spacetimes (of given dimension). The SPASs property is formulated in a functorial setting broad enough to describe general physical theories describing processes in spacetime, subject to very minimal assumptions. By explicit constructions, the full class of locally covariant theories is shown not to satisfy the SPASs property, establishing that there is no notion of SPASs encompassing all such theories. It is also shown that all locally covariant theories obeying the time-slice property possess two local substructures, one kinematical (obtained directly from the functorial structure) and the other dynamical (obtained from a natural form of dynamics, termed relative Cauchy evolution). The covariance properties of relative Cauchy evolution and the kinematic and dynamical substructures are analyzed in detail. Calling local covariant theories dynamically local if their kinematical and dynamical local substructures coincide, it is shown that the class of dynamically local theories fulfills the SPASs property. As an application in quantum field theory, we give a model independent proof of the impossibility of making a covariant choice of preferred state in all spacetimes, for theories obeying dynamical locality together with typical assumptions.

Does the Diversification Potential of Securitized Real Estate Vary Over Time and Should Investors Care?

This paper examines the dynamics of the covariance matrix of return rates for securitized real estate, other company stocks, and government bonds for a cross-section of eight countries. In-sample analysis establishes that in all countries the covariance matrix is time-varying and reacts stronger to bad than to good news. Using a realistic out-of-sample exercise, we find that portfolios selected with a forecasted dynamic covariance matrix are less risky than portfolios constructed with the static matrix. However, benefits of using the dynamic covariance matrix for active portfolio management are mostly offset by rebalancing cost. Passive buy-and-hold investors benefit, because the forecasted dynamic covariance matrix provides better risk assessment.

A framework for analysis of brain cine MR sequences

In this paper, we propose a framework to automate the assessment of the movements of a third cerebral ventricle in a cine MR sequence. Indeed, the goal of this assessment is to build an atlas of the movements of the healthy ventricles in the context of the hydrocephalus pathology. This approach is composed of two phases: a contour extraction, using fractional integration and a registration method, based on dynamic evolutionary optimization. The first phase of the framework is based on the fractional integration thresholding, that allows delineating the contours of the area of interest. In order to track over time each point of the primitive and achieve the assessment of the deformation, a matching method, based on a new dynamic optimization algorithm, called Dynamic Covariance Matrix Adaptation Evolution Strategy (D-CMAES), is used. The obtained results for quantification have been clinically validated by an expert and compared to those presented in the literature.

Time series behavior of average dynamic conditional correlations in European real estate securities markets

PurposeThe purpose of this paper is to investigate the time series behavior of co‐movements among 11 European real estate securities markets, with each other as well as between country‐averages, over the sample period from January 1999 to January 2010 by utilizing the asymmetric dynamic conditional correlation (ADCC) technique, long‐memory tests and multiple structural break methodology.Design/methodology/approachFirst the ADCC from the multivariate GJR‐GARCH model is used to estimate the pair‐wise conditional correlations between the 11 securitized real estate markets. Then, the 11 country‐average conditional correlation series is subject to a battery of four long‐memory tests to form an “on the balance of evidence” picture; the semi‐parametric Geweke and Porter‐Hudak procedure and Robinson test, as well as the non‐parametric Hurst‐Mandelbrot R/S and Lo's modified R/S tests. Finally, the Bai and Perron's multiple structural break methodology seeks to test whether the average conditional correlations are subject to regime switching via the detection of breaks in the co‐movements of real estate securities returns.FindingsLow to moderate conditional correlations are found for these European real estate securities market and a higher level of correlation in the aftermath of the global financial crisis. The long‐memory correlation effect is present for nine European real estate securities markets. In addition, the conditional correlations are subject to regime switching with two structural breaks in four country‐average correlation series. Across the regimes, a higher level of correlation is linked to a higher level of volatility and a lower level of return, and this happened around the global financial crisis period.Research limitations/implicationsThe findings that national real estate securities correlations exhibit time‐varying and asymmetric behavior can help investors understand how real estate securities will co‐move in different market scenarios (e.g. “crisis” and “non‐crisis” times). Moreover, the process of dynamic covariance analysis and forecasting (the ultimate objective in portfolio management) should not rely too much on short‐term autoregressive moving average models. Instead, a combination of some appropriate long‐range dependence models and regime‐switching specifications is needed.Originality/valueThis paper offers useful insights into the time series behavior of average dynamic conditional correlations in European public property markets.

Fourier spectral factor model for prediction of multidimensional signals

A prediction model for multidimensional weakly stationary signals positing fewer number of common dynamic unobserved factors than the number of measured signals is presented. The strategy involves decomposing the measured signals into two independent parts such that one of them is multidimensional idiosyncratic noise while the other is enforced to bear the dynamic covariances using an appropriately transformed lower dimensional factor. The autocovariance functions of the two components are estimated using a Fourier spectral factor model – Spector – by the principle of maximum likelihood. Using the asymptotic properties of discrete Fourier transform, an estimation method based on eigenvalue decomposition of the spectral density function is presented. The predictability using Spector is validated by vector autoregression on publicly available database of signals.

The analysis and impact of simulated high-resolution surface observations in addition to radar data for convective storms with an ensemble Kalman filter

Observing system simulation experiments are performed using an ensemble Kalman filter to investigate the impact of surface observations in addition to radar data on convective storm analysis and forecasting. A multi-scale procedure is used in which different covariance localization radii are used for radar and surface observations. When the radar is far enough away from the main storm so that the low level data coverage is poor, a clear positive impact of surface observations is achieved when the network spacing is 20 km or smaller. The impact of surface data increases quasi-linearly with decreasing surface network spacing until the spacing is close to the grid interval of the truth simulation. The impact of surface data is sustained or even amplified during subsequent forecasts when their impact on the analysis is significant. When microphysics-related model error is introduced, the impact of surface data is reduced but still evidently positive, and the impact also increases with network density. Through dynamic flow-dependent background error covariance, the surface observations not only correct near-surface errors, but also errors at the mid- and upper levels. State variables different from observed are also positively impacted by the observations in the analysis.

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, P f. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model

We propose a semiparametric conditional covariance (SCC) estimator that combines the first-stage parametric conditional covariance (PCC) estimator with the second-stage nonparametric correction estimator in a multiplicative way. We prove the asymptotic normality of our SCC estimator, propose a nonparametric test for the correct specification of PCC models, and study its asymptotic properties. We evaluate the finite sample performance of our test and SCC estimator and compare the latter with that of the PCC estimator, purely nonparametric estimator, and Hafner, Dijk, and Franses’s (2006) estimator in terms of mean squared error and Value-at-Risk losses via simulations and real data analyses.

A new localization implementation scheme for ensemble data assimilation of non-local observations

Localization technique is commonly used in ensemble data assimilation of small-size ensemble members. It effectively eliminates the spurious correlations of the background and increases the rank of the system. However, one disadvantage in current localization schemes is that it is difficult to implement the assimilation of non-local observations. In this paper, we test a new localized implementation scheme that can directly assimilate non-local observations without pinpointing them. A classical local support correlation functionmatrix is first sampled by a set of local correlation function ensemble members (the size is M). Then, the dynamical ensemble (the size is N) is combined with the local correlation function ensemble to form an N × M ensemble by multiplying each dynamical member with each local correlation function member using the Schur product. The covariance matrix constructed by the N×M members is proved to approximate the Schur product of the local support correlation matrix and the dynamical covariance matrix. This scheme is verified through assimilating both local and non-local observations with a linear advection model and an intermediate coupled model. The analysis results show that this scheme is feasible and effective in providing reasonable and high-quality analysis fields with a relatively small dynamical ensemble size.

A Measure of Explained Variation for Event History Data

There is no shortage of proposed measures of prognostic value of survival models in the statistical literature. They come under different names, including explained variation, correlation, explained randomness, and information gain, but their goal is common: to define something analogous to the coefficient of determination R(2) in linear regression. None however have been uniformly accepted, none have been extended to general event history data, including recurrent events, and many cannot incorporate time-varying effects or covariates. We present here a measure specifically tailored for use with general dynamic event history regression models. The measure is applicable and interpretable in discrete or continuous time; with tied data or otherwise; with time-varying, time-fixed, or dynamic covariates; with time-varying or time-constant effects; with single or multiple event times; with parametric or semiparametric models; and under general independent censoring/observation. For single-event survival data with neither censoring nor time dependency it reduces to the concordance index. We give expressions for its population value and the variance of the estimator and explore its use in simulations and applications. A web link to R software is provided.

Recurrent events and the exploding Cox model.

Counting process models have played an important role in survival and event history analysis for more than 30 years. Nevertheless, almost all models that are being used have a very simple structure. Analyzing recurrent events invites the application of more complex models with dynamic covariates. We discuss how to define valid models in such a setting. One has to check carefully that a suggested model is well defined as a stochastic process. We give conditions for this to hold. Some detailed discussion is presented in relation to a Cox type model, where the exponential structure combined with feedback lead to an exploding model. In general, counting process models with dynamic covariates can be formulated to avoid explosions. In particular, models with a linear feedback structure do not explode, making them useful tools in general modeling of recurrent events.

Evaluating the Performances of Adaptive Kalman Filter Methods in GPS/INS Integration

One of the most important tasks in integration of GPS/INS is to choose the realistic dynamic model covariance matrix Q and measurement noise covariance matrix R for use in the Kalman filter. The performance of the methods to estimate both of these matrices depends entirely on the minimization of dynamic and measurement update errors that lead the filter to converge. This paper evaluates the performances of adaptive Kalman filter methods with different adaptations. Innovation and residual based adaptive Kalman filters were employed for adapting R and Q. These methods were implemented in a loose GPS/INS integration system and tested using real data sets. Their performances have been evaluated and compared. Their limitations in real-life engineering applications are discussed.

The Volatility of Market Returns: A Comparative Study of Emerging versus Mature Markets

This paper will examine the volatility of markets returns, dynamic conditional covariance and dynamic conditional correlation between the equity markets of developed countries (US and UK) and the equity markets of developing countries (Kuwait and United Arab Emirates). A multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model will be used; Diagonal VEC (DVEC) - MGARCH to identify the source and magnitude of volatility. The results will show the relation between the global mature market of USA and the UK on the emerging markets of Kuwait (K) and UAE.

Pragmatic Analysis of Longitudinal Data on Disease Activity in Systemic Lupus Erythematosus

The multiple clinical manifestations of systemic lupus erythematosus are a challenge to rheumatologists managing patients with the disease, and there is a need to better understand predictors of disease activity in order to improve and standardize therapy and prevent the development of permanent damage. In this article, we present the analysis of a clinical database for patients with lupus. The database consists of data collected on 440 patients over a period of 10 years. The analysis is based on logistic regression methodology with outcomes defined at the times of clinic visits and develops an approach to examine the interrelationships between disease activity in different systems. The usefulness of separate logistic regressions with dynamic covariates for the analysis of multinomial panel data is illustrated and the efficiency of the approach relative to modeling disease activity in continuous time is investigated.

A “dressed” Ensemble Kalman Filter using the Hybrid Coordinate Ocean Model in the Pacific

The computational cost required by the Ensemble Kalman Filter (EnKF) is much larger than that of some simpler assimilation schemes, such as Optimal Interpolation (OI) or three-dimension variational assimilation (3DVAR). Ensemble optimal interpolation (EnOI), a crudely simplified implementation of EnKF, is sometimes used as a substitute in some oceanic applications and requires much less computational time than EnKF. In this paper, to compromise between computational cost and dynamic covariance, we use the idea of “dressing” a small size dynamical ensemble with a larger number of static ensembles in order to form an approximate dynamic covariance. The term “dressing” means that a dynamical ensemble seed from model runs is perturbed by adding the anomalies of some static ensembles. This dressing EnKF (DrEnKF for short) scheme is tested in assimilation of real altimetry data in the Pacific using the HYbrid Coordinate Ocean Model (HYCOM) over a four-year period. Ten dynamical ensemble seeds are each dressed by 10 static ensemble members selected from a 100-member static ensemble. Results are compared to two EnKF assimilation runs that use 10 and 100 dynamical ensemble members. Both temperature and salinity fields from the DrEnKF and the EnKF are compared to observations from Argo floats and an OI SST dataset. The results show that the DrEnKF and the 100-member EnKF yield similar root mean square errors (RMSE) at every model level. Error covariance matrices from the DrEnKF and the 100-member EnKF are also compared and show good agreement.