Structural information in recursive VAR orderings

This paper investigates structural models that will permit a Cholesky decomposition of the covariance matrix of VAR residuals to identify some structural impulse response functions. Cholesky decompositions are found to be useful identification tools for the set of partially recursive structural models. A partially recursive structure is defined as any block recursive system where the equations in one block can be recursively ordered and where the structural shocks are uncorrelated. Using this class of models, we derive necessary and sufficient conditions for the moving average representation from a Cholesky decomposition to identify structure. The paper concludes by discussing implications of these results for empirical research.     

A Stein-type shrinkage estimator of the covariance matrix for portfolio selections

The covariance matrix plays a crucial role in portfolio optimization problems as the risk and correlation measure of asset returns. An improved estimation of the covariance matrix can enhance the performance of the portfolio. In this paper, based on the Cholesky decomposition of the covariance matrix, a Stein-type shrinkage strategy for portfolio weights is constructed under the mean-variance framework. Furthermore, according to the agent’s maximum expected utility value, a portfolio selection strategy is proposed. Finally, simulation experiments and an empirical study are used to test the feasibility of the proposed strategy. The numerical results show our portfolio strategy performs satisfactorily.     

Graphical Diagnostics for Modeling Unstructured Covariance Matrices

Prudent statistical analysis of correlated data requires accounting for the correlation among the measurements. Specifying a form for the covariance matrix of the data could reduce the high number of parameters of the covariance and increase efficiency of the inferences about the regression parameters. Motivated by the success of ordinary, partial and inverse correlograms in identifying parsimonious models for stationary time series, we introduce generalizations of these plots for nonstationary data. Their roles in detecting heterogeneity and correlation of the data and identifying parsimonious models for the covariance matrix are illuminated using a longitudinal dataset. Decomposition of a covariance matrix into "variance" and "dependence" components provides the necessary ingredients for the proposed graphs. This amounts to replacing a 3-D correlation plot by a pair of 2-D plots, providing complementary information about dependence and heterogeneity. Models identified and fitted using the variance-correlation decomposition of a covariance matrix are not guaranteed to be positive definite, but those using the modified Cholesky decomposition are. Limitations of our graphical diagnostics for general multivariate data where the measurements are not (time-) ordered are discussed.     

Distribution-free tests of mean vectors and covariance matrices for multivariate paired data

We study a permutation procedure to test the equality of mean vectors, homogeneity of covariance matrices, or simultaneous equality of both mean vectors and covariance matrices in multivariate paired data. We propose to use two test statistics for the equality of mean vectors and the homogeneity of covariance matrices, respectively, and combine them to test the simultaneous equality of both mean vectors and covariance matrices. Since the combined test has composite null hypothesis, we control its type I error probability and theoretically prove the asymptotic unbiasedness and consistency of the combined test. The new procedure requires no structural assumption on the covariances. No distributional assumption is imposed on the data, except that the permutation test for mean vector equality assumes symmetric joint distribution of the paired data. We illustrate the good performance of the proposed approach with comparison to competing methods via simulations. We apply the proposed method to testing the symmetry of tooth size in a dental study and to finding differentially expressed gene sets with dependent structures in a microarray study of prostate cancer.     

Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice

We consider modeling and forecasting large realized covariance matrices by penalized vector autoregressive models. We consider Lasso‐type estimators to reduce the dimensionality and provide strong theoretical guarantees on the forecast capability of our procedure. We show that we can forecast realized covariance matrices almost as precisely as if we had known the true driving dynamics of these in advance. We next investigate the sources of these driving dynamics as well as the performance of the proposed models for forecasting the realized covariance matrices of the 30 Dow Jones stocks. We find that the dynamics are not stable as the data are aggregated from the daily to lower frequencies. Furthermore, we are able beat our benchmark by a wide margin. Finally, we investigate the economic value of our forecasts in a portfolio selection exercise and find that in certain cases an investor is willing to pay a considerable amount in order get access to our forecasts. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis and short-term predictions of non-technical loss of electric power based on mixed effects models

In this paper we estimate, analyze and predict short-term non-technical loss (NTL) of electric power of Brazilian energy service companies based on different assumptions for the covariance structure of the errors and controlling for socio-economic confounding variables. Although the correlation among repeated responses is not usually of intrinsic interest, it is an important aspect of the data that must properly be accounted for to produce valid inferences in longitudinal or panel data analysis. In the extended linear mixed effects model, the covariance matrix of the response vector is comprised by two subcomponents, a random effect component that can represent between group variation and a intraclass or within group component. So, in order to adequately treat the longitudinal character of NTL data, we use the decomposition of these variance components to evaluate different architectures to the within group errors. Using data of 59 Brazilian distributing utilities from 2004 to 2012, we fit a conditionally independent errors model and three other models with autoregressive-moving average parametrization to the intraclass disturbances. Finally, we compare models using the MAD and MAPE metrics in the prediction of NTL for the year of 2013. The findings suggest that the approach can be satisfactorily implemented in future statistical analysis of NTL.     

Hodges–Lehmann Detection of Structural Shocks – An Analysis of Macroeconomic Dynamics in the Euro Area

Structural shocks in multivariate dynamic systems are hidden and often identified with reference to a priori economic reasoning. Based on a non‐Gaussian framework of independent shocks, this work provides an approach to discriminate between alternative identifying assumptions on the basis of dependence diagnostics. Relying on principles of Hodges–Lehmann estimation, we suggest a decomposition of reduced form covariance matrices that yields implied least dependent (structural) shocks. A Monte Carlo study underlines the discriminatory strength of the proposed identification strategy. Applying the approach to a stylized model of the Euro Area economy, independent shocks conform with features of demand, supply and monetary policy shocks.     

Conditions for invariance of the multivariate versions of grubbs’ test and bartlett’s test under a general dependency structure

Summary This paper generalizes a result by Stadje (1984) by deriving conditions for which a general dependency structure for multivariate observations, given in Pavur (1987), yields a positive definite covariance structure. This general dependency structure allows the sample covariance matrix to be distributed as a constant times a Wishart random matrix. It is then demonstrated that the maximum squared-radii test and a test for equal population covariance matrices have null distributions which remain unchanged when the new general dependency structure, rather than the usual independence structure, for the vector observations, is assumed. Moreover, under a general dependency structure for which the population covariance matrices are unequal, it is shown that the distribution of the test statistic for testing equal covariance matrices is identical to the distribution of the same test statistic when the population covariance matrices are equal and the observations are independent.     

Order-invariant tests for proper calibration of multivariate density forecasts

Established tests for proper calibration of multivariate density forecasts based on Rosenblatt probability integral transforms can be manipulated by changing the order of variables in the forecasting model. We derive order-invariant tests. The new tests are applicable to densities of arbitrary dimensions and can deal with parameter estimation uncertainty and dynamic misspecification. Monte Carlo simulations show that they often have superior power relative to established approaches. We use the tests to evaluate generalized autoregressive conditional heteroskedasticity-based multivariate density forecasts for a vector of stock market returns and macroeconomic forecasts from a Bayesian vector autoregression with time-varying parameters.     

A TVM-Copula-MIDAS-GARCH model with applications to VaR-based portfolio selection

This paper develops a novel time-varying multivariate Copula-MIDAS-GARCH (TVM-Copula-MIDAS-GARCH) model with exogenous explanatory variables to model the joint distribution of returns. The model accounts for mixed frequency factors that affect the time-varying dependence structure of financial assets. Furthermore, we examine the effectiveness of the proposed model in VaR-based portfolio selection. We conduct an empirical analysis on estimating the 90%, 95%, 99% VaRs of the portfolio constituted of the Shanghai Composite Index, Shanghai SE Fund Index, and Shanghai SE Treasury Bond Index. The empirical results show that the proposed TVM-Copula-MIDAS-GARCH model is effective to investigate the nonlinear time-varying dependence among those three indices and performs better in portfolio selection.     

NETS: Network estimation for time series

We model a large panel of time series as a vector autoregression where the autoregressive matrices and the inverse covariance matrix of the system innovations are assumed to be sparse. The system has a network representation in terms of a directed graph representing predictive Granger relations and an undirected graph representing contemporaneous partial correlations. A LASSO algorithm called NETS is introduced to estimate the model. We apply the methodology to analyze a panel of volatility measures of 90 blue chips. The model captures an important fraction of total variability, on top of what is explained by volatility factors, and improves out‐of‐sample forecasting.     

A PREDICTIVE APPROACH TO MODEL SELECTION AND MULTICOLLINEARITY

We argue for the adoption of a predictive approach to model specification. Specifically, we derive the difference between means and the ratio of determinants of covariance matrices when a subset of explanatory variables is included or excluded from a regression. Results for an economic application are presented as an example. © 1997 by John Wiley & Sons, Ltd.     

Combining survey long-run forecasts and nowcasts with BVAR forecasts using relative entropy

This paper constructs hybrid forecasts that combine forecasts from vector autoregressive (VAR) model(s) with both short- and long-term expectations from surveys. Specifically, we use the relative entropy to tilt one-step-ahead and long-horizon VAR forecasts to match the nowcasts and long-horizon forecasts from the Survey of Professional Forecasters. We consider a variety of VAR models, ranging from simple fixed-parameter to time-varying parameters. The results across models indicate meaningful gains in multi-horizon forecast accuracy relative to model forecasts that do not incorporate long-term survey conditions. Accuracy improvements are achieved for a range of variables, including those that are not tilted directly but are affected through spillover effects from tilted variables. The accuracy gains for hybrid inflation forecasts from simple VARs are substantial, statistically significant, and competitive to time-varying VARs, univariate benchmarks, and survey forecasts. We view our proposal as an indirect approach to accommodating structural change and moving end points.     

Change-point analysis through integer-valued autoregressive process with application to some COVID-19 data

In this article, we consider the problem of change-point analysis for the count time series data through an integer-valued autoregressive process of order 1 (INAR(1)) with time-varying covariates. These types of features we observe in many real-life scenarios especially in the COVID-19 data sets, where the number of active cases over time starts falling and then again increases. In order to capture those features, we use Poisson INAR(1) process with a time-varying smoothing covariate. By using such model, we can model both the components in the active cases at time-point t namely, (i) number of nonrecovery cases from the previous time-point and (ii) number of new cases at time-point t. We study some theoretical properties of the proposed model along with forecasting. Some simulation studies are performed to study the effectiveness of the proposed method. Finally, we analyze two COVID-19 data sets and compare our proposed model with another PINAR(1) process which has time-varying covariate but no change-point, to demonstrate the overall performance of our proposed model.     

The nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator

Several limited-information type estimators of the nonlinear simultaneous equation model are considered and their asymptotic covariance matrices are compared. Amemiya (1974) proposed the general class of nonlinear two-stage least-squares estimators. In this paper, its two specific members are considered and, in addition, the nonlinear limited-information maximum- likelihood estimator and the modified nonlinear two-stage least-squares estimator are proposed. Both are shown to be asymptotically more efficient than the nonlinear two-stage least-squares estimator, and the second has the advantage of being computationally simple.     

The structure of dynamic correlations in multivariate stochastic volatility models

This paper proposes two types of stochastic correlation structures for Multivariate Stochastic Volatility (MSV) models, namely the constant correlation (CC) MSV and dynamic correlation (DC) MSV models, from which the stochastic covariance structures can easily be obtained. Both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices, and for calculating Value-at-Risk (VaR) forecasts and optimal capital charges under the Basel Accord through the use of covariance matrices. A technique is developed to estimate the DC MSV model using the Markov Chain Monte Carlo (MCMC) procedure, and simulated data show that the estimation method works well. Various multivariate conditional volatility and MSV models are compared via simulation, including an evaluation of alternative VaR estimators. The DC MSV model is also estimated using three sets of empirical data, namely Nikkei 225 Index, Hang Seng Index and Straits Times Index returns, and significant dynamic correlations are found. The Dynamic Conditional Correlation (DCC) model is also estimated, and is found to be far less sensitive to the covariation in the shocks to the indexes. The correlation process for the DCC model also appears to have a unit root, and hence constant conditional correlations in the long run. In contrast, the estimates arising from the DC MSV model indicate that the dynamic correlation process is stationary.     

Evaluating New‐Keynesian Models of a Small Open Economy*

We suggest a strategy to evaluate members of a class of New‐Keynesian models of a small open economy. As an example, we estimate a modified version of the model in Svensson [Journal of International Economics (2000) Vol. 50, pp. 155–183] and compare its impulse response and variance decomposition functions with those a structural vector autoregression (VAR) model. The focus is on responses to foreign rather than to domestic shocks, which facilitates identification. Some results are that US shocks account for large shares of the variance of Canadian variables, that little of this influence is due to real exchange rate movements, and that Canadian monetary policy is not adequately described by a Taylor rule.     

A comparison of several approximations to the power function of the likelihood ratio test in covariance structure analysis*

In this paper we compare alternative asymptotic approximations to the power of the likelihood ratio test used in covariance structure analysis for testing the fit of a model. Alternative expressions for the noncentrality parameter (ncp) lead to different approximations to the power function. It appears that for alternative covariance matrices close to the null hypothesis, the alternative ncp's lead to similar values, while for alternative covariance matrices far from H_o the different expressions for the ncp can conflict substantively. Monte Carlo evidence shows that the ncp proposed in Satorra and Saris (1985) gives the most accurate power approximations.     

A Markov Switching Factor‐Augmented VAR Model for Analyzing US Business Cycles and Monetary Policy

This paper develops a Markov switching factor‐augmented vector autoregression to investigate the transmission mechanisms of monetary policy for distinct stages of the US business cycle. We assume that autoregressive parameters and covariance matrices of the error terms are regime dependent, driven by an unobserved Markov indicator. Endogenously determined transition probabilities are governed by an underlying probit model that features a large set of possible predictors. The empirical findings provide evidence for differences in the transmission of monetary policy shocks that mainly stem from heterogeneity in the responses of financial market quantities.     

经济转型期山东省经济增长与出口贸易的长期均衡关系——状态空间模型及变协整分析

利用状态空间模型建立了经济增长与出口贸易之间的变参数模型,并利用E-G两步法检验了两者之间的关系,得到如下结论:(1)考虑制度变迁因素,GDP与出口贸易之间存在着均衡比例变化的变协整关系;(2)该时变均衡比例总体上有平稳的趋势且伴随着制度变迁及政策变动上下波动。