Search

There is substantial uncertainty about the impact of quantitative easing on market liquidity. Identifying the impact is particularly challenging due to the potential for reverse causality, because liquidity considerations might affect quantitative easing purchases. We address this challenge by studying the Bank of England’s 2016–7 Corporate Bond Purchase Scheme. In particular, we use granular offer-level data from the Corporate Bond Purchase Scheme auctions to construct proxy measures for the Bank of England's demand for bonds and auction participants’ supply of bonds, allowing us to control for any reverse causality from liquidity to purchases. We find that Corporate Bond Purchase Scheme purchases improved the liquidity of purchased bonds.

We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise process based on high‐frequency data, where the noise process could be serially dependent, endogenous, and nonstationary. We characterize the limit distributions of the proposed estimators and construct confidence intervals under infill asymptotics. Our simulation and empirical studies show that the ReMeDI approach is very effective to measure the scale and the serial dependence of microstructure noise. Moreover, the estimators are quite robust to model specifications, sample sizes, and data frequencies.

Nonlinear dynamic modeling of spatio-temporal data is often a challenge, especially due to irregularly observed locations and location-wide nonstationarity. In this article we propose a semiparametric family of Dynamic Functional-coefficient Autoregressive Spatio-Temporal (DyFAST) models to address the difficulties. We specify the autoregressive smoothing coefficients depending dynamically on both a concerned regime and location so that the models can characterize not only the dynamic regime-switching nature but also the location-wide nonstationarity in real data. Different smoothing schemes are then proposed to model the dynamic neighboring-time interaction effects with irregular locations incorporated by (spatial) weight matrices. The first scheme popular in econometrics supposes that the weight matrix is pre-specified. We show that locally optimal bandwidths by a greedy idea popular in machine learning should be cautiously applied. Moreover, many weight matrices can be generated differently by data location features. Model selection is popular, but may suffer from loss of different candidate features. Our second scheme is thus to suggest a weight matrix fusion to let data combine or select the candidates with estimation done simultaneously. Both theoretical properties and Monte Carlo simulations are investigated. The empirical application to an EU energy market dataset further demonstrates the usefulness of our DyFAST models. Supplementary materials for this article are available online.

We provide an estimator of the lower regression function and provide large sample properties for inference. We also propose a test of the hypothesis of positive expectation dependence and derive its limiting distribution under the null hypothesis and provide consistent critical values. We apply our methodology to several empirical questions.

This paper studies a heterogeneous coefficient spatial factor model that separately addresses both common factor risks (strong cross-sectional dependence) and local dependency (weak cross-sectional dependence) in the equity returns. From the asset pricing perspective, we derive the theoretical implications of no asymptotic arbitrage for the heterogeneous spatial factor model. In empirical work, it is challenging to measure granular firm-to-firm connectivity for a high-dimensional panel of equity returns. We use extensive business news to construct firms’ links via which local shocks transmit, and we use those news-implied linkages as a proxy for the connectivity among firms. Empirically, we document a considerable degree of local dependency among S&P 500 stocks, and the spatial component does a great job in capturing the remaining correlations in the de-factored returns. We find that adding spatial interactions to factor models reduces mispricing and mean-squared errors. We also show that our news-implied linkages provide a comprehensive and integrated proxy for firm-to-firm connectivity, and it out-performs other existing networks in the literature.

We study a class of nonparametric regression models that includes deterministic time trends and both stationary and nonstationary stochastic processes (whose shocks are allowed to be mutually correlated). We propose a unified approach to estimation based on the weighted sieve method to tackle the issue of unbounded support of the covariates. This approach improves on the existing technology in terms of some key regularity conditions such as moment conditions and the α -mixing coefficients for the stationary process. We establish self-normalized central limit theorems for the sieve estimator and other related quantities. Monte Carlo simulation confirms the theoretical results. We use our methodology to study the effect of CO2 and solar irradiance on global sea level rise.

Donald and Hsu (2014) studied the estimation and inference for the counterfactual distribution and quantile functions in a binary treatment model. We extend their work to the continuous treatment model. Specifically, we propose a weighted regression estimator for the counterfactual distribution but we estimate the weighting function from a covariate balancing equation by maximizing a globally concave criterion function. We estimate the quantile function by inverting the estimated counterfactual distribution. To test the distributional effect, we consider the (uniform) confidence bands, the sup and L 2 distance, and the Mann–Whitney test. We also consider the stochastic dominance test for the distributional effect and the L 2 test for constant quantiles. A simulation study reveals that our tests exhibit a satisfactory finite-sample performance, and an application shows their practical value.

This paper proposes five pointwise consistent and asymptotic normal estimators of the asymptotic variance function of the Nadaraya-Watson kernel estimator for nonparametric regression. The proposed...

In this paper, we propose three new predictive models: the multi-step nonparametric predictive regression model and the multi-step additive predictive regression model, in which the predictive variables are locally stationary time series; and the multi-step time-varying coefficient predictive regression model, in which the predictive variables are stochastically nonstationary. We also establish the estimation theory and asymptotic properties for these models in the short horizon and long horizon case. To evaluate the effectiveness of these models, we investigate their capability of stock return prediction. The empirical results show that all of these models can substantially outperform the traditional linear predictive regression model in terms of both in-sample and out-of-sample performance. In addition, we find that these models can always beat the historical mean model in terms of in-sample fitting, and also for some cases in terms of the out-of-sample forecasting.

We develop a novel estimation methodology for an additive nonparametric panel model that is suitable for capturing the pricing of coupon-paying government bonds followed over many time periods. We use our model to estimate the discount function and yield curve of nominally riskless government bonds. The novelty of our approach is the combination of two different techniques: cross-sectional nonparametric methods and kernel estimation for time varying dynamics in the time series context. The resulting estimator is used for predicting individual bond prices given the full schedule of their future payments. In addition, it is able to capture the yield curve shapes and dynamics commonly observed in the fixed income markets. We establish the consistency, the rate of convergence, and the asymptotic normality of the proposed estimator. A Monte Carlo exercise illustrates the good performance of the method under different scenarios. We apply our methodology to the daily CRSP bond market dataset, and compare ours with the popular Diebold and Li (2006) method.

This paper studies a model with both a parametric global trend and a nonparametric local trend. This model may be of interest in a number of applications in economics, finance, ecology, and geology. The model nests the parametric global trend model considered in Phillips (2007) and Robinson (2012), and the nonparametric local trend model. We first propose two hypothesis tests to detect whether either of the special cases are appropriate. For the case where both null hypotheses are rejected, we propose an estimation method to capture both aspects of the time trend. We establish consistency and some distribution theory in the presence of a large sample. Moreover, we examine the proposed hypothesis tests and estimation methods through both simulated and real data examples. Finally, we discuss some potential extensions and issues when modelling time effects.

We consider approximating a multivariate regression function by an affine combination of one-dimensional conditional component regression functions. The weight parameters involved in the approximation are estimated by least squares on the first-stage nonparametric kernel estimates. We establish asymptotic normality for the estimated weights and the regression function in two cases: the number of the covariates is finite, and the number of the covariates is diverging. As the observations are assumed to be stationary and near epoch dependent, the approach in this paper is applicable to estimation and forecasting issues in time series analysis. Furthermore, the methods and results are augmented by a simulation study and illustrated by application in the analysis of the Australian annual mean temperature anomaly series. We also apply our methods to high frequency volatility forecasting, where we obtain superior results to parametric methods.

Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

This paper considers nonparametric additive models that have deterministic time trend and both stationary and integrated variables as components. The diverse nature of the regressors caters for applications in a variety of settings. In addition, we extend the analysis to allow the stationary regressor to be instead locally stationary, and we allow the models to include a linear form of the integrated variable. Heteroscedasticity is allowed for in all models. We propose an estimation strategy based on orthogonal series expansion that takes account of the different type of stationarity/nonstationarity possessed by each covariate. We establish the large sample distribution theory for all the estimated functions we consider. In spite of the entanglement of different kinds of regressors, we can separate out the distribution theory for each estimator. We provide Monte Carlo simulations that establish the favourable properties of our procedures in moderate sized samples. Finally, we apply our techniques to the study of a pairs trading strategy.

This paper develops a two-step semiparametric methodology for portfolio weight selection for characteristics- based factor-tilt and factor-timing investment strategies. We build upon the expected utility maximization framework of Brandt (1999) and Ait-sahalia and Brandt (2001). We assume that asset returns obey a characteristics- based factor model with time-varying factor risk premia as in Li and Linton (2020). We prove under our return- generating assumptions that in a market with a large number of assets, an approximately optimal portfolio can be established using a two-step procedure. The first step finds optimal factor-mimicking sub-portfolios using a quadratic objective function over linear combinations of characteristics-based factor loadings. The second step dynamically combines these factor-mimicking sub-portfolios based on a time-varying signal, using the investor’s expected utility as the objective function. We develop and implement a two-stage semiparametric estimator. We apply it to CRSP (Center for Research in Security Prices) and FRED (Federal Reserve Economic Data) data and find excellent in-sample and out-sample performance consistent with investors’ risk aversion levels.

We propose a general framework for the specification testing of continuous treatment effect models. We assume a general residual function, which includes the average and quantile treatment effect models as special cases. The null models are identified under the confoundedness condition and contain a nonparametric weighting function. We propose a test statistic for the null model in which the weighting function is estimated by solving an expanding set of moment equations. We establish the asymptotic distributions of our test statistic under the null hypothesis and under fixed and local alternatives. The proposed test statistic is shown to be more efficient than that constructed from the true weighting function and can detect local alternatives deviated from the null models at the rate of Op (N-1/2). A simulation method is provided to approximate the null distribution of the test statistic. Monte-Carlo simulations show that our test exhibits a satisfactory finite-sample performance, and an application shows its practical value.

We carry out some analysis of the daily data on the number of new cases and the number of new deaths by (191) countries as reported to the European Centre for Disease Prevention and Control (ECDC). Our benchmark model is a quadratic time trend model applied to the log of new cases for each country. We use our model to predict when the peak of the epidemic will arise in terms of new cases or new deaths in each country and the peak level. We also predict how long the number of new daily cases in each country will fall by an order of magnitude. Finally, we also forecast the total number of cases and deaths for each country. We consider two models that link the joint evolution of new cases and new deaths.

We devise a new high-frequency covariance matrix estimator based on price durations which is guaranteed to be positive-definite. Both non-parametric and parametric versions are proposed. A comprehensive Monte Carlo simulation shows that this class of estimators are less biased, more efficient, and generate lower RMSE as well as QLIKE errors. Empirically, we apply both estimators to a global minimum variance portfolio allocation problem and find they can generate comparably low portfolio variance, higher Sharpe ratios, but with considerably lower portfolio turnovers. This matrix estimator is also shown empirically to be more well-conditioned.

We study the problem of jump detection for ultra-high-frequency tick-by-tick data. We propose a novel easy-to-implement procedure that can separate the contribution of microstructure noise and that of finite activity price jumps from the price process, which may have interesting implications on asset pricing and forecasting problems. We provide theoretical grounds of our approach, and suggests practical guidelines for determining the tuning parameter. Making a comparison with the “star performers” in a recent comprehensive review for jump detection methods by Maneesoonthorn et al. (2020) as well as a test based on Christensen et al. (2014) on tick data, we show that our method performs admirably well via extensive simulation and rich empirical illustration.

SummaryMultilateral comparison of outcomes drawn from multiple groups pervade the social sciences and measurement of their variability, usually involving functions of respective group location and scale parameters, is of intrinsic interest. However, such approaches frequently mask more fundamental differences that more comprehensive examination of relative group distributional structures reveal. Indeed, in categorical data contexts, location- and scale-based techniques are no longer feasible without artificial and questionable cardinalisation of categories. Here, Gini’s transvariation measure is extended and employed in providing quantitative and visual multilateral comparison tools in discrete, continuous, categorical, univariate, or multivariate settings which are particularly useful in paradigms where cardinal measure is absent. Two applications, one analysing Eurozone cohesion in terms of the convergence or divergence of constituent nations income distributions, the other, drawn from a study of ageing, health, and income inequality in China, exemplify their use in a continuous and categorical data environment.

We consider a semiparametric quantile factor panel model that allows observed stock-specific characteristics to affect stock returns in a nonlinear time-varying way, extending Connor, Hagmann, and Linton (2012) to the quantile restriction case. We propose a sieve-based estimation methodology that is easy to implement. We provide tools for inference that are robust to the existence of moments and to the form of weak cross-sectional dependence in the idiosyncratic error term. We apply our method to daily stock return data where we find significant evidence of nonlinearity in many of the characteristic exposure curves.

We propose an asset pricing factor model constructed with semiparametric characteristics-based mispricing and factor loading functions. We approximate the unknown functions by B-splines sieve where the number of B-splines coefficients is diverging. We estimate this model and test the existence of the mispricing function by a power enhanced hypothesis test. The enhanced test solves the low power problem caused by diverging B-splines coefficients, with the strengthened power approaching one asymptotically. We also investigate the structure of mispricing components through Hierarchical K-means Clusterings. We apply our methodology to CRSP (Center for Research in Security Prices) and Compustat data for the US stock market with one-year rolling windows during 1967-2017. This empirical study shows the presence of mispricing functions in certain time blocks. We also find that distinct clusters of the same characteristics lead to similar arbitrage returns, forming a ���peer group��� of arbitrage characteristics.

This paper studies nonparametric estimation of the infinite order regression E ( Y t k | F t − 1 ) , k ∈ Z with stationary and weakly dependent data. We propose a Nadaraya–Watson type estimator that operates with an infinite number of conditioning variables. We propose a bandwidth sequence that shrinks the effects of long lags, so the influence of all conditioning information is modelled in a natural and flexible way, and the issues of omitted information bias and specification error are effectively handled. We establish the asymptotic properties of the estimator under a wide range of static and dynamic regressions frameworks, thereby allowing various kinds of conditioning variables to be used. We establish pointwise/uniform consistency and CLTs. We show that the convergence rates are at best logarithmic, and depend on the smoothness of the regression, the distribution of the marginal regressors and their dependence structure in a non-trivial way via the Lambert W function. We apply our methodology to examine the intertemporal risk-return relation for the aggregate stock market, and some new empirical evidence is reported. For the S&P 500 daily data from 1950 to 2017 using our estimator we report an overall positive risk-return relation. We also find evidence of strong time variation and counter-cyclical behaviour in risk aversion. These conclusions are possibly attributable to the allowance of further flexibility and the inclusion of otherwise neglected information in our method.

We propose a test of the hypothesis of conditional stochastic dominance in the presence of many conditioning variables (whose dimension may grow to infinity as the sample size diverges). Our approach builds on a semiparametric location scale model in the sense that the conditional distribution of the outcome given the covariates is characterized by a nonparametric mean function and a nonparametric skedastic function with an independent innovation whose distribution is unknown. We propose to estimate the nonparametric mean and skedastic regression functions by the l₁-penalized nonparametric series estimation with thresholding. Under the sparsity assumption, where the number of truly relevant series terms are relatively small (but their identities are unknown), we develop the estimation error bounds for the regression functions and series coefficients estimates allowing for the time series dependence. We derive the asymptotic distribution of the test statistic, which is not pivotal asymptotically, and introduce the smooth stationary bootstrap to approximate its sample distribution. We investigate the finite sample performance of the bootstrap critical values by a set of Monte Carlo simulations. Finally, our method is illustrated by an application to stochastic dominance among portfolio returns given all the past information.

We propose an asset pricing factor model constructed with semi-parametric characteristics-based mispricing and factor loading functions. We approximate the unknown functions by B-splines sieve where the number of B-splines coefficients is diverging. We estimate this model and test the existence of the mispricing function by a power enhanced hypothesis test. The enhanced test solves the low power problem caused by diverging B-spline coefficients, with the strengthened power approaches to one asymptotically. We also investigate the structure of mispricing components through Hierarchical K-means Clusterings. We apply our methodology to CRSP (Center for Research in Security Prices) and FRED (Federal Reserve Economic Data) data for the US stock market with one-year rolling windows during 1967-2017. This empirical study shows the presence of mispricing functions in certain time blocks. We also find that distinct clusters of the same characteristics lead to similar arbitrage returns, forming a “peer group” of arbitrage characteristics.

This paper proposes efficient estimation of risk measures by fully exploring the first and second moment information in a GARCH framework. We propose a quantile estimator based on inverting an empirical likelihood weighted distribution estimator. It is found that the new quantile estimator is uniformly more efficient than the simple empirical quantile and a quantile estimator based on normalized residuals. We show that the same conclusion applies to the estimation of conditional Expected Shortfall. We find that these proposed estimators for conditional Value-at-Risk and expected shortfall are asymptotically mixed normal. Simulation evidence provided.

High-frequency trading (HFT) has grown substantially in recent years due to fast-paced technological developments and their rapid uptake, particularly in equity markets. This review investigates how HFT could evolve and, by developing a robust understanding of its effects, identifies potential risks and opportunities that HFT could present in terms of financial stability and other market outcomes such as volatility, liquidity, price efficiency, and price discovery. Despite commonly held negative perceptions, the available evidence indicates that HFT and algorithmic trading may have several beneficial effects on markets. However, these types of trading may cause instabilities in financial markets in specific circumstances. Carefully chosen regulatory measures are needed to address concerns in the shorter term. However, further work is needed to inform policies in the longer term, particularly in view of likely uncertainties and lack of data. This work will be vital in supporting evidence-based regulation in this controversial and rapidly evolving field.

This paper provides new identification results for the bid–ask spread and the nonparametric distribution of the latent fundamental price increments ( e t ) from the observed transaction prices alone. The results are established via the characteristic function approach, and hence allow for discrete or continuous e t and the observed price increments do not need to have any finite moments. Constructive identification (and overidentification) results are established first in the basic Roll (1984) model, and then in various extended Roll models, including general unbalanced order flow, serially dependent latent trade direction indicators, adverse selection, random spread and a multivariate Roll model.

Following the work of Gini, Dagum and Tukey, this paper extends Gini’s Transvariation measure for comparing two distributions to the simultaneous comparison of many distributions. In so doing, it develops measures of absolute and relative similarity, dissimilarity and exceptionality together with techniques for assessing particular aspects of variations across those distributions. These techniques are exemplified in a study of differences between the income distributions of males and females drawn from Metis, Inuit, North American Indian and Non-Aboriginal constituencies in Canada in the first decade of the twenty-first century. While the distributions were becoming increasingly similar (interpreted as improving equality of opportunity), this was occurring primarily at the center of the distribution. At the extremes, the distributions were diverging, suggesting that such improvements in equality of opportunity were not for all.

We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension n is large relative to the sample size T). In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided ${\log }^3n/T\to 0$ . We obtain the limiting distributions of the Lagrange multiplier and Wald tests under both the null and local alternatives concerning the mean vector $\mu $ . Testing linear restrictions of $\mu $ is also investigated. Finally, our methodology is shown to perform well in finite sample situations both when the Kronecker product model is true and when it is not true.