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We consider the problem of identifying skilled funds among a large number of candidates under the linear factor pricing models containing both observable and latent market factors. Motivated by the existence of non-strong potential factors and diversity of error distribution types of the linear factor pricing models, we develop a distribution-free multiple testing procedure to solve this problem. The proposed procedure is established based on the statistical tool of symmetrized data aggregation, which makes it robust to the strength of potential factors and distribution type of the error terms. We then establish the asymptotic validity of the proposed procedure in terms of both the false discovery rate and true discovery proportion under some mild regularity conditions. Furthermore, we demonstrate the advantages of the proposed procedure over some existing methods through extensive Monte Carlo experiments. In an empirical application, we illustrate the practical utility of the proposed procedure in the context of selecting skilled funds, which clearly has much more satisfactory performance than its main competitors. [ABSTRACT FROM AUTHOR]

In this article, we study large-dimensional matrix factor models and estimate the factor loading matrices and factor score matrix by minimizing square loss function. Interestingly, the resultant estimators coincide with the Projected Estimators (PE) in Yu et al. which was proposed from the perspective of simultaneous reduction of the dimensionality and the magnitudes of the idiosyncratic error matrix. In other word, we provide a least-square interpretation of the PE for the matrix factor model, which parallels to the least-square interpretation of the PCA for the vector factor model. We derive the convergence rates of the theoretical minimizers under sub-Gaussian tails. Considering the robustness to the heavy tails of the idiosyncratic errors, we extend the least squares to minimizing the Huber loss function, which leads to a weighted iterative projection approach to compute and learn the parameters. We also derive the convergence rates of the theoretical minimizers of the Huber loss function under bounded fourth or even (2 + ϵ) th moment of the idiosyncratic errors. We conduct extensive numerical studies to investigate the empirical performance of the proposed Huber estimators relative to the state-of-the-art ones. The Huber estimators perform robustly and much better than existing ones when the data are heavy-tailed, and as a result can be used as a safe replacement in practice. An application to a Fama-French financial portfolio dataset demonstrates the empirical advantage of the Huber estimator. [ABSTRACT FROM AUTHOR]

Various parametric volatility models for financial data have been developed to incorporate high-frequency realized volatilities and better capture market dynamics. However, because high-frequency trading data are not available during the close-to-open period, the volatility models often ignore volatility information over the close-to-open period and thus may suffer from loss of important information relevant to market dynamics. In this article, to account for whole-day market dynamics, we propose an overnight volatility model based on Itô diffusions to accommodate two different instantaneous volatility processes for the open-to-close and close-to-open periods. We develop a weighted least squares method to estimate model parameters for two different periods and investigate its asymptotic properties. [ABSTRACT FROM AUTHOR]

The goal of this article is to evaluate the informational content of sentiment extracted from news articles about the state of the economy. We propose a fine-grained aspect-based sentiment analysis that has two main characteristics: (a) we consider only the text in the article that is semantically dependent on a term of interest (aspect-based) and, (b) assign a sentiment score to each word based on a dictionary that we develop for applications in economics and finance (fine-grained). Our dataset includes six large U.S. newspapers, for a total of over 6.6 million articles and 4.2 billion words. Our findings suggest that several measures of economic sentiment track closely business cycle fluctuations and that they are relevant predictors for four major macroeconomic variables. We find that there are significant improvements in forecasting when sentiment is considered along with macroeconomic factors. In addition, we also find that sentiment matters to explains the tails of the probability distribution across several macroeconomic variables. [ABSTRACT FROM AUTHOR]

We introduce a novel two-step approach to predict implied volatility surfaces. Given any fitted parametric option pricing model, we train a feedforward neural network on the model-implied pricing errors to correct for mispricing and boost performance. Using a large dataset of S&P 500 options, we test our nonparametric correction on several parametric models ranging from ad-hoc Black–Scholes to structural stochastic volatility models and demonstrate the boosted performance for each model. Out-of-sample prediction exercises in the cross-section and in the option panel show that machine-corrected models always outperform their respective original ones, often by a large extent. Our method is relatively indiscriminate, bringing pricing errors down to a similar magnitude regardless of the misspecification of the original parametric model. Even so, correcting models that are less misspecified usually leads to additional improvements in performance and also outperforms a neural network fitted directly to the implied volatility surface. [ABSTRACT FROM AUTHOR]

This article proposes more efficient estimators for the leverage effect than the existing ones. The idea is to allow for nonuniform kernel functions in the spot volatility estimates or the aggregated returns. This finding highlights a critical difference between the leverage effect and integrated volatility functionals, where the uniform kernel is optimal. Another distinction between these two cases is that the overlapping estimators of the leverage effect are more efficient than the nonoverlapping ones. We offer two perspectives to explain these differences: one is based on the "effective kernel" and the other on the correlation structure of the nonoverlapping estimators. The simulation study shows that the proposed estimator with a nonuniform kernel substantially increases the estimation efficiency and testing power relative to the existing ones. [ABSTRACT FROM AUTHOR]

Realized covariance matrices are often constructed under the assumption that richness of intra-day return data is greater than the portfolio size, resulting in nonsingular matrix measures. However, when for example the portfolio size is large, assets suffer from illiquidity issues, or market microstructure noise deters sampling on very high frequencies, this relation is not guaranteed. Under these common conditions, realized covariance matrices may obtain as singular by construction. Motivated by this situation, we introduce the Singular Conditional Autoregressive Wishart (SCAW) model to capture the temporal dynamics of time series of singular realized covariance matrices, extending the rich literature on econometric Wishart time series models to the singular case. This model is furthermore developed by covariance targeting adapted to matrices and a sector wise BEKK-specification, allowing excellent scalability to large and extremely large portfolio sizes. Finally, the model is estimated to a 20-year long time series containing 50 stocks and to a 10-year long time series containing 300 stocks, and evaluated using out-of-sample forecast accuracy. It outperforms the benchmark models with high statistical significance and the parsimonious specifications perform better than the baseline SCAW model, while using considerably less parameters. [ABSTRACT FROM AUTHOR]

Selecting skilled mutual funds through the multiple testing framework has received increasing attention from finance researchers and statisticians. The intercept α of Carhart four-factor model is commonly used to measure the true performance of mutual funds, and positive α's are considered as skilled. We observe that the standardized ordinary least-square estimates of α's across the funds possess strong dependence and nonnormality structures, indicating that the conventional multiple testing methods are inadequate for selecting the skilled funds. We start from a decision theoretical perspective, and propose an optimal multiple testing procedure to minimize a combination of false discovery rate and false nondiscovery rate. Our proposed testing procedure is constructed based on the probability of each fund not being skilled conditional on the information across all of the funds in our study. To model the distribution of the information used for the testing procedure, we consider a mixture model under dependence and propose a new method called "approximate empirical Bayes" to fit the parameters. Empirical studies show that our selected skilled funds have superior long-term and short-term performance, for example, our selection strongly outperforms the S&P 500 index during the same period. [ABSTRACT FROM AUTHOR]

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semidefinite. Our simulation study indicates that the subsampling method is more robust than the plug-in method based on the asymptotic expression for the variance. We use our subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every 5 or 20 min. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe. [ABSTRACT FROM AUTHOR]

In this article, we consider statistical inference for high-dimensional approximate factor models. We posit a weak factor structure, in which the factor loading matrix can be sparse and the signal eigenvalues may diverge more slowly than the cross-sectional dimension, N. We propose a novel inferential procedure to decide whether each component of the factor loadings is zero or not, and prove that this controls the false discovery rate (FDR) below a preassigned level, while the power tends to unity. This "factor selection" procedure is primarily based on a debiased version of the sparse orthogonal factor regression (SOFAR) estimator; but is also applicable to the principal component (PC) estimator. After the factor selection, the resparsified SOFAR and sparsified PC estimators are proposed and their consistency is established. Finite sample evidence supports the theoretical results. We apply our method to the FRED-MD dataset of macroeconomic variables and the monthly firm-level excess returns which constitute the S&P 500 index. The results give very strong statistical evidence of sparse factor loadings under the identification restrictions and exhibit clear associations of factors and categories of the variables. Furthermore, our method uncovers a very weak but statistically significant factor in the residuals of Fama-French five factor regression. [ABSTRACT FROM AUTHOR]

This article proposes the new grid bootstrap to construct confidence intervals (CI) for the persistence parameter in a class of continuous-time models. It is different from the standard grid bootstrap of Hansen in dealing with the initial condition. The asymptotic validity of the CI is discussed under the in-fill scheme. The modified grid bootstrap leads to uniform inferences on the persistence parameter. Its improvement over in-fill asymptotics is achieved by expanding the coefficient-based statistic around its in-fill asymptotic distribution that is non-pivotal and depends on the initial condition. Monte Carlo studies show that the modified grid bootstrap performs better than Hansen's grid bootstrap. Empirical applications to the U.S. interest rates and volatilities suggest significant differences between the two bootstrap procedures when the initial condition is large. [ABSTRACT FROM AUTHOR]

This article develops an inferential theory for state-varying factor models of large dimensions. Unlike constant factor models, loadings are general functions of some recurrent state process. We develop an estimator for the latent factors and state-varying loadings under a large cross-section and time dimension. Our estimator combines nonparametric methods with principal component analysis. We derive the rate of convergence and limiting normal distribution for the factors, loadings, and common components. In addition, we develop a statistical test for a change in the factor structure in different states. We apply the estimator to the U.S. Treasury yields and S&P500 stock returns. The systematic factor structure in treasury yields differs in times of booms and recessions as well as in periods of high market volatility. State-varying factors based on the VIX capture significantly more variation and pricing information in individual stocks than constant factor models. [ABSTRACT FROM AUTHOR]

Identifying interaction effects is fundamentally important in many scientific discoveries and contemporary applications, but it is challenging since the number of pairwise interactions increases quadratically with the number of covariates and that of higher-order interactions grows even faster. Although there is a growing literature on interaction detection, little work has been done on the prediction and false sign rate on interaction detection in ultrahigh-dimensional regression models. This article fills such a gap. More specifically, in this article we establish some theoretical results on interaction selection for ultrahigh-dimensional quadratic regression models under random designs. We prove that the examined method enjoys the same oracle inequalities as the lasso estimator and further admits an explicit bound on the false sign rate. Moreover, the false sign rate can be asymptotically vanishing. These new theoretical characterizations are confirmed by simulation studies. The performance of our proposed approach is further illustrated through a real data application. [ABSTRACT FROM AUTHOR]

We present a model for direct semi-parametric estimation of the state price density (SPD) implied by quoted option prices. We treat the observed prices as expected values of possible pay-offs at maturity, weighted by the unknown probability density function. We model the logarithm of the latter as a smooth function, using P-splines, while matching the expected values of the potential pay-offs with the observed prices. This leads to a special case of the penalized composite link model. Our estimates do not rely on any parametric assumption on the underlying asset price dynamics and are consistent with no-arbitrage conditions. The model shows excellent performance in simulations and in applications to real data. [ABSTRACT FROM AUTHOR]

This article introduces structured machine learning regressions for high-dimensional time series data potentially sampled at different frequencies. The sparse-group LASSO estimator can take advantage of such time series data structures and outperforms the unstructured LASSO. We establish oracle inequalities for the sparse-group LASSO estimator within a framework that allows for the mixing processes and recognizes that the financial and the macroeconomic data may have heavier than exponential tails. An empirical application to nowcasting US GDP growth indicates that the estimator performs favorably compared to other alternatives and that text data can be a useful addition to more traditional numerical data. Our methodology is implemented in the R package midasml, available from CRAN. [ABSTRACT FROM AUTHOR]

High-dimensional time series datasets are becoming increasingly common in various fields of economics and finance. Given the ubiquity of time series data, it is crucial to develop efficient variable screening methods that use the unique features of time series. This article introduces several model-free screening methods based on partial distance correlation and developed specifically to deal with time-dependent data. Methods are developed both for univariate models, such as nonlinear autoregressive models with exogenous predictors (NARX), and multivariate models such as linear or nonlinear VAR models. Sure screening properties are proved for our methods, which depend on the moment conditions, and the strength of dependence in the response and covariate processes, amongst other factors. We show the effectiveness of our methods via extensive simulation studies and an application on forecasting U.S. market returns. [ABSTRACT FROM AUTHOR]

This article studies a high-dimensional factor model with sparse idiosyncratic covariance matrix in continuous time, using asynchronous high-frequency financial data contaminated by microstructure noise. We focus on consistent estimations of the number of common factors, the integrated covariance matrix and its inverse, based on the flat-top realized kernels introduced by Varneskov. Simulation results illustrate the satisfactory performance of our estimators in finite samples. We apply our methodology to the high-frequency price data on a large number of stocks traded in Shanghai and Shenzhen stock exchanges, and demonstrate its value for capturing time-varying covariations and portfolio allocation. [ABSTRACT FROM AUTHOR]

We study a class of nonparametric volatility estimators based on the Laplace transform, which are robust to the presence of the endogeneity of observation times. Asymptotic properties and feasible central limit theorems are established. In the presence of time endogeneity, our bias-corrected Laplace estimator takes advantage of the informational content of time endogeneity, which leads to narrower confidence bounds. The finite sample properties of the estimator are studied through Monte Carlo simulations. Through the simulation study, we also find that due to the presence of the kernel, Laplace estimator could be adopted in a model with microstructure noise. The performance of the Laplace estimator is compared with other commonly used estimators through forecasting exercises by employing high frequency data. We conclude that the bias-corrected Laplace estimator performs better than most estimators in terms of forecasting equity return volatility in the presence of both time endogeneity and market microstructure noise. [ABSTRACT FROM AUTHOR]

We develop new high-frequency-based inference procedures for analyzing the relationship between jumps in instantaneous moments of stochastic processes. The estimation consists of two steps: the nonparametric determination of the jumps as differences in local averages, followed by a minimum-distance type estimation of the parameters of interest under general loss functions that include both least-square and more robust quantile regressions as special cases. The resulting asymptotic distribution of the estimator, derived under an infill asymptotic setting, is highly nonstandard and generally not mixed normal. In addition, we establish the validity of a novel bootstrap algorithm for making feasible inference including bias-correction. The new methods are applied in a study on the relationship between trading intensity and spot volatility in the U.S. equity market at the time of important macroeconomic news announcement. [ABSTRACT FROM AUTHOR]

Text data is ultra-high dimensional, which makes machine learning techniques indispensable for textual analysis. Text is often selected—journalists, speechwriters, and others craft messages to target their audiences' limited attention. We develop an economically motivated high-dimensional selection model that improves learning from text (and from sparse counts data more generally). Our model is especially useful when the choice to include a phrase is more interesting than the choice of how frequently to repeat it. It allows for parallel estimation, making it computationally scalable. A first application revisits the partisanship of the U.S. congressional speech. We find that earlier spikes in partisanship manifested in increased repetition of different phrases, whereas the upward trend starting in the 1990s is due to distinct phrase selection. Additional applications show how our model can backcast, nowcast, and forecast macroeconomic indicators using newspaper text, and that it substantially improves out-of-sample fit relative to alternative approaches. [ABSTRACT FROM AUTHOR]

The analysis of the intraday dynamics of covariances among high-frequency returns is challenging due to asynchronous trading and market microstructure noise. Both effects lead to significant data reduction and may severely affect the estimation of the covariances if traditional methods for low-frequency data are employed. We propose to model intraday log-prices through a multivariate local-level model with score-driven covariance matrices and to treat asynchronicity as a missing value problem. The main advantages of this approach are: (i) all available data are used when filtering the covariances, (ii) market microstructure noise is taken into account, (iii) estimation is performed by standard maximum likelihood. Our empirical analysis, performed on 1-sec NYSE data, shows that opening hours are dominated by idiosyncratic risk and that a market factor progressively emerges in the second part of the day. The method can be used as a nowcasting tool for high-frequency data, allowing to study the real-time response of covariances to macro-news announcements and to build intraday portfolios with very short optimization horizons. [ABSTRACT FROM AUTHOR]

This article studies the estimation of integrated volatility functionals, which is a semiparametric two-step estimation problem in the nonstationary continuous-time setting. We generalize the asymptotic normality results of Jacod and Rosenbaum to a wider range of bandwidths. Moreover, we employ matrix calculus to obtain a new analytical bias correction and variance estimation method. The proposed method gives more succinct expressions than the element-by-element analytical method of the above cited article. In addition, it has a computational advantage over the jackknife/simulation-based method proposed by Li, Liu, and Xiu. Comprehensive simulation studies demonstrate that our method has good finite sample performance for a variety of volatility functionals, including quadraticity, determinant, continuous beta, and eigenvalues. [ABSTRACT FROM AUTHOR]

Motivated by the empirical evidence of high-frequency lead-lag effects and cross-asset linkages, we introduce a multi-asset price formation model which generalizes standard univariate microstructure models of lagged price adjustment. Econometric inference on such model provides: (i) a unified statistical test for the presence of lead-lag correlations in the latent price process and for the existence of a multi-asset price formation mechanism; (ii) separate estimation of contemporaneous and lagged dependencies; (iii) an unbiased estimator of the integrated covariance of the efficient martingale price process that is robust to microstructure noise, asynchronous trading, and lead-lag dependencies. Through an extensive simulation study, we compare the proposed estimator to alternative approaches and show its advantages in recovering the true lead-lag structure of the latent price process. Our application to a set of NYSE stocks provides empirical evidence for the existence of a multi-asset price formation mechanism and sheds light on its market microstructure determinants. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

This article investigates the large sample properties of the variance, weights, and risk of high-dimensional portfolios where the inverse of the covariance matrix of excess asset returns is estimated using a technique called nodewise regression. Nodewise regression provides a direct estimator for the inverse covariance matrix using the least absolute shrinkage and selection operator to estimate the entries of a sparse precision matrix. We show that the variance, weights, and risk of the global minimum variance portfolios and the Markowitz mean-variance portfolios are consistently estimated with more assets than observations. We show, empirically, that the nodewise regression-based approach performs well in comparison to factor models and shrinkage methods. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

Employing tick-by-tick maximum likelihood estimation on several leading models from the financial economics literature, we find that the market microstructure noise is mostly explained by a linear model where the trade direction, that is, whether the trade is buyer or seller initiated, is multiplied by the dynamic quoted bid-ask spread. Although reasonably stable intraday, this model manifests variability across days and stocks. Among different observable high frequency financial characteristics of the underlying stocks, this variability is best explained by the tick-to-spread ratio, implying that discreteness is the first residual source of noise. We determine the bid-ask bounce effect as the next source of noise. [ABSTRACT FROM AUTHOR]

Inflation forecasting is an important but difficult task. Here, we explore advances in machine learning (ML) methods and the availability of new datasets to forecast U.S. inflation. Despite the skepticism in the previous literature, we show that ML models with a large number of covariates are systematically more accurate than the benchmarks. The ML method that deserves more attention is the random forest model, which dominates all other models. Its good performance is due not only to its specific method of variable selection but also the potential nonlinearities between past key macroeconomic variables and inflation. for this article are available online. [ABSTRACT FROM AUTHOR]

We give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps. The quantity of interest is defined as the integrated value over time of the parameter process Θ = T − 1 ∫ 0 T θ t * d t . We provide a local parametric estimator (LPE) of Θ and conditions under which we can show the central limit theorem. Roughly speaking those conditions correspond to some uniform limit theory in the parametric version of the problem. The framework is restricted to the specific convergence rate n1∕2. Several examples of LPE are studied: estimation of volatility, powers of volatility, volatility when incorporating trading information and time-varying MA(1). [ABSTRACT FROM AUTHOR]

Spatial econometric models allow for interactions among variables through the specification of a spatial weight matrix. Practitioners often face the risk of misspecification of such a matrix. In many problems a number of potential specifications exist, such as geographic distances, or various economic quantities among variables. We propose estimating the best linear combination of these specifications, added with a potentially sparse adjustment matrix. The coefficients in the linear combination, together with the sparse adjustment matrix, are subjected to variable selection through the adaptive least absolute shrinkage and selection operator (LASSO). As a special case, if no spatial weight matrices are specified, the sparse adjustment matrix becomes a sparse spatial weight matrix estimator of our model. Our method can therefore, be seen as a unified framework for the estimation and selection of a spatial weight matrix. The rate of convergence of all proposed estimators are determined when the number of time series variables can grow faster than the number of time points for data, while oracle properties for all penalized estimators are presented. Simulations and an application to stocks data confirms the good performance of our procedure. [ABSTRACT FROM AUTHOR]

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semimartingale log asset price process, which is subject to noise and nonsynchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM), which recently has been introduced by Bibinger et al.. We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects, and general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations, and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a test for the rank of a cross-section of processes at a set of jump events. The jump events are either specific known times or are random and associated with jumps of some process. The test is formed from discretely sampled data on a fixed time interval with asymptotically shrinking mesh. In the first step, we form nonparametric estimates of the jump events via thresholding techniques. We then compute the eigenvalues of the outer product of the cross-section of increments at the identified jump events. The test for rank r is based on the asymptotic behavior of the sum of the squared eigenvalues excluding the largest r. A simple resampling method is proposed for feasible testing. The test is applied to financial data spanning the period 2007–2015 at the times of stock market jumps. We find support for a one-factor model of both industry portfolio and Dow 30 stock returns at market jump times. This stands in contrast with earlier evidence for higher-dimensional factor structure of stock returns during "normal" (nonjump) times. We identify the latent factor driving the stocks and portfolios as the size of the market jump. [ABSTRACT FROM AUTHOR]

In this article, we develop a new goodness-of-fit test for multivariate jump diffusion models. The test statistic is constructed by a contrast between an "in-sample" likelihood (or a likelihood of observed data) and an"out-of-sample" likelihood (or a likelihood of predicted data). We show that under the null hypothesis of a jump diffusion process being correctly specified, the proposed test statistic converges in probability to a constant that equals to the number of model parameters in the null model. We also establish the asymptotic normality for the proposed test statistic. To implement this method, we invoke a closed-form approximation to transition density functions, which results in a computationally efficient algorithm to evaluate the test. Using Monte Carlo simulation experiments, we illustrate that both exact and approximate versions of the proposed test perform satisfactorily. In addition, we demonstrate the proposed testing method in several popular stochastic volatility models for time series of weekly S&P 500 index during the period of January 1990 and December 2014, in which we invoke a linear affine relationship between latent stochastic volatility and the implied volatility index. [ABSTRACT FROM AUTHOR]

We develop a theoretical framework for covariance stationary but persistent positively valued processes which combines a semi-nonparametric expansion of the Gamma distribution with a component version of the multiplicative error model. Our conditional mean assumption allows for slow, possibly nonmonotonic mean-reversion, while our distribution assumption provides more flexibility than a traditional Laguerre expansion while preserving positivity of the density. We apply our framework to a dynamic portfolio allocation for Exchange Traded Notes tracking short- and mid-term VIX futures indices, which are increasingly popular but risky financial instruments. We show the superior performance of the strategies based on our econometric model. [ABSTRACT FROM AUTHOR]

It is widely accepted that some financial data exhibit long memory or long dependence, and that the observed data usually possess noise. In the continuous time situation, the factional Brownian motion BH and its extension are an important class of models to characterize the long memory or short memory of data, and Hurst parameter H is an index to describe the degree of dependence. In this article, we estimate the Hurst parameter of a discretely sampled fractional integral process corrupted by noise. We use the preaverage method to diminish the impact of noise, employ the filter method to exclude the strong dependence, and obtain the smoothed data, and estimate the Hurst parameter by the smoothed data. The asymptotic properties such as consistency and asymptotic normality of the estimator are established. Simulations for evaluating the performance of the estimator are conducted. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

It is well known that in finance variances and covariances of asset returns move together over time. Recently, much interest has been aroused by an approach involving the use of the realized covariance (RCOV) matrix constructed from high-frequency returns as the ex-post realization of the covariance matrix of low-frequency returns. For the analysis of dynamics of RCOV matrices, we propose the generalized conditional autoregressive Wishart (GCAW) model. Both the noncentrality matrix and scale matrix of the Wishart distribution are driven by the lagged values of RCOV matrices, and represent two different sources of dynamics, respectively. The GCAW is a generalization of the existing models, and accounts for symmetry and positive definiteness of RCOV matrices without imposing any parametric restriction. Some important properties such as conditional moments, unconditional moments, and stationarity are discussed. Empirical examples including sequences of daily RCOV matrices from the New York Stock Exchange illustrate that our model outperforms the existing models in terms of model fitting and forecasting. [ABSTRACT FROM AUTHOR]

We document a striking block-diagonal pattern in the factor model residual covariances of the S&P 500 Equity Index constituents, after sorting the assets by their assigned Global Industry Classification Standard (GICS) codes. Cognizant of this structure, we propose combining a location-based thresholding approach based on sector inclusion with the Fama-French and SDPR sector Exchange Traded Funds (ETF’s). We investigate the performance of our estimators in an out-of-sample portfolio allocation study. We find that our simple and positive-definite covariance matrix estimator yields strong empirical results under a variety of factor models and thresholding schemes. Conversely, we find that the Fama-French factor model is only suitable for covariance estimation when used in conjunction with our proposed thresholding technique. Theoretically, we provide justification for the empirical results by jointly analyzing the in-fill and diverging dimension asymptotics. [ABSTRACT FROM PUBLISHER]

We consider an approach to analyze big data of time series. Big dependent data are first transformed into functional time series of densities via nonparametric density estimation. We then discuss some tools for exploratory data analysis of the resulting functional time series. The tools employed include K-means cluster analysis and tree-based classification. For modeling, we propose a threshold approximate-factor model and a Hellinger distance autoregressive model for functional time series of continuous densities. The latent factors of factor models are estimated by functional principal component analysis. Cross-validation and Hellinger distance are used to select the number of principal component functions. For prediction of high-dimensional time series, we use the results of cluster analysis to obtain parsimonious models. We demonstrate the proposed analysis by considering the demand of electricity, the behavior of daily U.S. stock returns, and U.S. income distributions. [ABSTRACT FROM PUBLISHER]

We propose a composite realized kernel to estimate the ex-post covariation of asset prices. These measures can in turn be used to forecast the covariation of future asset returns. Composite realized kernels are a data-efficient method, where the covariance estimate is composed of univariate realized kernels to estimate variances and bivariate realized kernels to estimate correlations. We analyze the merits of our composite realized kernels in an ultra high-dimensional environment, making asset allocation decisions every day solely based on the previous day’s data or a short moving average over very recent days. The application is a minimum variance portfolio exercise. The dataset is tick-by-tick data comprising 437 U.S. equities over the sample period 2006–2011. We show that our estimator is able to outperform its competitors, while the associated trading costs are competitive. [ABSTRACT FROM PUBLISHER]

This article develops a general multivariate additive noise model for synchronized asset prices and provides a multivariate extension of the generalized flat-top realized kernel estimators, analyzed earlier by Varneskov (2014), to estimate its quadratic covariation. The additive noise model allows for α-mixing dependent exogenous noise, random sampling, and an endogenous noise component that encompasses synchronization errors, lead-lag relations, and diurnal heteroscedasticity. The various components may exhibit polynomially decaying autocovariances. In this setting, the class of estimators considered is consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence,n1/4. A simple finite sample correction based on projections of symmetric matrices ensures positive definiteness without altering the asymptotic properties of the estimators. It, thereby, guarantees the existence of nonlinear transformations of the estimated covariance matrix such as correlations and realized betas, which inherit the asymptotic properties from the flat-top realized kernel estimators. An empirically motivated simulation study assesses the choice of sampling scheme and projection rule, and it shows that flat-top realized kernels have a desirable combination of robustness and efficiency relative to competing estimators. Last, an empirical analysis of signal detection and out-of-sample predictions for a portfolio of six stocks of varying size and liquidity illustrates the use and properties of the new estimators. [ABSTRACT FROM PUBLISHER]

This article proposes a novel Pearson-type quasi-maximum likelihood estimator (QMLE) of GARCH(p, q) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not just the heavy-tailed but also the skewed innovations. Under strict stationarity and some weak moment conditions, the strong consistency and asymptotic normality of the PQMLE are obtained. With no further efforts, the PQMLE can be applied to other conditionally heteroscedastic models. A simulation study is carried out to assess the performance of the PQMLE. Two applications to four major stock indexes and two exchange rates further highlight the importance of our new method. Heavy-tailed and skewed innovations are often observed together in practice, and the PQMLE now gives us a systematic way to capture these two coexisting features. [ABSTRACT FROM AUTHOR]

In this article, we propose a nonparametric procedure to estimate the integrated volatility of an Itô semimartingale in the presence of jumps and microstructure noise. The estimator is based on a combination of the preaveraging method and threshold technique, which serves to remove microstructure noise and jumps, respectively. The estimator is shown to work for both finite and infinite activity jumps. Furthermore, asymptotic properties of the proposed estimator, such as consistency and a central limit theorem, are established. Simulations results are given to evaluate the performance of the proposed method in comparison with other alternative methods. [ABSTRACT FROM AUTHOR]

The authors discuss aspects of the Gaussian pseudo-maximum likelihood (PML) estimators for factors of univariate generalized autoregressive conditional heteroscedasticity (GARCH) models. They mention their zero conditional mean which is irrespective to asymmetry degree and kurtosis of the variable's distribution. An overview of their maximum likelihood (ML) procedures is also presented.