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Over the last decade, latent growth modeling (LGM) utilizing hierarchical linear models or structural equation models has become a widely applied approach in the analysis of change. By analyzing two or more variables simultaneously, the current method provides a straightforward generalization of this idea. From a theory of change perspective, this chapter demonstrates ways to prescreen the covariance matrix in repeated measurement, which allows for the identification of major trends in the data prior to running the multivariate LGM. A three-step approach is suggested and explained using an empirical study published in the Journal of Applied Psychology.

A large literature over several decades reveals both extensive concern with the question of time-varying betas and an emerging consensus that betas are in fact time-varying, leading to the prominence of the conditional CAPM. Set against that background, we assess the dynamics in realized betas, vis-à-vis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recently popularized framework of realized volatility, we are led to a framework of nonlinear fractional cointegration: although realized variances and covariances are very highly persistent and well approximated as fractionally integrated, realized betas, which are simple nonlinear functions of those realized variances and covariances, are less persistent and arguably best modeled as stationary I(0) processes. We conclude by drawing implications for asset pricing and portfolio management.

Consumers’ product evaluations are often influenced by information contained in their memories. Prior to product evaluations, consumers are often exposed to data that permits them to judge the covariation relationships among different product attributes. However, these attribute covariance perceptions may lead to biased product evaluations. Using an experimental design, this study examines the accuracy of consumers’ product attribute covariance beliefs as a function of their product experience and the relevancy of product information to which they are exposed prior to evaluating product performances. The results indicate that even limited product information affects consumers’ beliefs about product performances on attributes for which no information is available. In other words, specific product information may serve as a cue or indicator for other product characteristics via attribute covariance inferences. The accuracy of these inferences appears to be, at least partly, the function of the consumers’ product experience. Consumers with high levels of product experience are more effective at encoding and retrieving product attribute performance information. Implications of the findings are discussed and suggestions for future research are provided.

The purpose of this paper is to investigate the return performance of different investment strategies in the hedge fund sector, with a particular emphasis on the recent US financial crisis of 2007‐2010. Additionally, the paper aims to investigate the comovement of hedge fund index returns.

The paper identifies broad hedge fund investment strategies using data from the Dow Jones Credit Suisse Hedge Fund Database. It examines the return comovement using the cross‐sectional volatility, covariance, and correlation metrics proposed in Adrian (2007). In addition, the paper examines whether correlations and covariance are important determinants of future volatility via traditional time‐series regressions.

The paper finds that the majority of the broad hedge fund investment strategies incurred record level losses and gains during the 2007‐2010 period. In addition, it finds that the crisis period was preceded by high correlations, attributed primarily to a rise in cross‐sectional hedge fund covariances. However, during the crisis period, a decrease in average correlations, stemming from an increase in hedge fund volatility, is documented. The time‐series regressions are supportive of a strong relationship between cross‐sectional covariances and subsequent volatility, suggesting that systemic risk occurs in the hedge fund sector when returns move significantly in dollar terms.

This study is one of the first investigations that focus on the comovement and volatility of hedge fund index returns during the US financial crisis of 2007‐2010.

Every “structural model” is defined by the set of covariance and mean expectations. These expectations are the source of parameter estimates, fit statistics, and substantive interpretation. The recent chapter by Cortina, Pant, and Smith-Darden ((this volume). In: F. Dansereau & F. J. Yammarino (Eds), Research in multi-level issues (vol. 4). Oxford, England: Elsevier) shows how a formal investigation of the data covariance matrix of longitudinal data can lead to an improved understanding of the estimates of covariance terms among linear growth models. The investigations presented by Cortina et al. (this volume) are reasonable and potentially informative for researchers using linear change growth models. However, it is quite common for behavioral researchers to consider more complex models, in which case a variety of more complex techniques for the calculation of expectations will be needed. In this chapter we demonstrate how available computer programs, such as Maple, can be used to automatically create algebraic expectations for the means and the covariances of every structural model. The examples presented here can be used for a latent growth model of any complexity, including linear and nonlinear processes, and any number of longitudinal measurements.

Existing multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models either impose strong restrictions on the parameters or do not guarantee a well-defined (positive-definite) covariance matrix. I discuss the main multivariate GARCH models and focus on the BEKK model for which it is shown that the covariance and correlation is not adequately specified under certain conditions. This implies that any analysis of the persistence and the asymmetry of the correlation is potentially inaccurate. I therefore propose a new Flexible Dynamic Correlation (FDC) model that parameterizes the conditional correlation directly and eliminates various shortcomings. Most importantly, the number of exogenous variables in the correlation equation can be flexibly augmented without risking an indefinite covariance matrix. Empirical results of daily and monthly returns of four international stock market indices reveal that correlations exhibit different degrees of persistence and different asymmetric reactions to shocks than variances. In addition, I find that correlations do not always increase with jointly negative shocks implying a justification for international portfolio diversification.

The successful use of the standard extended Kalman filter (EKF) is restricted by the requirement on the statistics information of the measurement noise. The covariance of the measurement noise may deviate from its nominal value in practical environment, and the filtering performance may decline because of the statistical uncertainty. Although the adaptive EKF (AEKF) is available for recursive covariance estimation, it is often less accurate than the EKF with accurate noise statistics.

Aiming at this problem, this paper develops a parallel adaptive EKF (PAEKF) by combining the EKF and the AEKF with an adaptive law, such that the final state estimate is dominated by the EKF when the prior noise covariance is accurate, while the AEKF is activated when the actual noise covariance deviates from its nominal value.

The PAEKF can reduce the sensitivity of the algorithm to the model uncertainty and ensure the estimation accuracy in the normal case. The simulation results demonstrate that the PAEKF has the advantage of both the AEKF and the EKF.

The presented algorithm is applicable for spacecraft relative attitude and position estimation.

The PAEKF is presented for a kind of nonlinear uncertain systems. Stability analysis is provided to show that the error of the estimator is bounded under certain assumptions.

This research aims to select the best-fitting model(s) of equal risk contribution portfolios (ERC). ERC is a robust estimation in the absence of reasonable expectations about future returns.

The portfolio consists of five environmental-friendly exchange-traded funds (ETFs). It applies equal risk optimization, beneficial when the assets are firmly linked, such as the ETFs. This paper operationalizes 20 covariance models in portfolio construction, and a portfolio with classic covariance is the benchmark to beat. To select the best-fitting model(s), the paper applies statistical inferences of the model confidence set. This research also constructs the newly-developed minimum connectedness optimization method and utilizes maximum drawdown as the primary evaluation tool.

The outbreak of COVID-19 hugely impacts the portfolio drawdown. The results also show that the classic covariance is hard to beat, partly explained by estimation error and model misspecification. This paper suggests that equal risk contribution can benefit from copula-based covariance. It consistently and significantly outperforms the other models in various robustness tests.

In the absence of substantial predictions about future returns and the existence of strongly linked assets, selecting appropriate portfolio components by risk contribution is a sound choice.

This is the first paper to select the best-fitting model(s) of ERC portfolio during the COVID-19.

The purpose of this paper is twofold: to improve the traditional conditional autoregressive Wishart (CAW) and heterogeneous autoregressive (HAR)-CAW model to account for heterogeneous leverage effect and to adjust the high-frequency volatility. The other is to confirm whether CAW-type models that have statistical advantages have economic advantages.

Based on the high-frequency data, this study proposed a new model to describe the volatility process according to the heterogeneous market hypothesis. Thus, the authors acquire needed and credible high-frequency data.

By designing two mean-variance frameworks and considering several economic performance measures, the authors find that compared with five other models based on daily data, CAW-type models, especially LHAR-CAW and HAR-CAW, indeed generate the substantial economic values, and matrix adjustment method significantly improves the three CAW-type performances.

The findings in this study suggest that from the aspect of economics, LHAR-CAW model can more accurately built the dynamic process of return rates and covariance matrix, respectively, and the matrix adjustment can reduce bias of realized volatility as covariance matrix estimator of return rates, and greatly improves the performance of unadjusted CAW-type models.

Compared with traditional low-frequency models, investors should allocate assets according to the LHAR-CAW model so as to get more economic values.

This study proposes LHAR-CAW model with the matrix adjustment, to account for heterogeneous leverage effect and empirically show their economic advantage. The new model and the new bias adjustment approach are pioneering and promote the evolution of financial econometrics based on high-frequency data.

The purpose of this paper is to analyze the implications of the risk versus characteristic debate from the perspective of a mean-variance investor.

Expected returns and the variance-covariance matrix are estimated based on various characteristic and risk models and evaluated for the purpose of mean-variance portfolios.

Return estimates from characteristic models are most informative to investors. Risk-factor models provide the most informative estimates of the risk. A mean-variance investor should rely on combinations of the two model types.

Although the risk vs characteristic debate is a binary academic debate, our findings from an investor's perspective suggest to make use of the best of both worlds.