Realized volatility forecasting and option pricing

A growing literature advocates the use of microstructure noise-contaminated high-frequency data for the purpose of volatility estimation. This paper evaluates and compares the quality of several recently-proposed estimators in the context of a relevant economic metric, i.e., profits from option pricing and trading. Using forecasts obtained by virtue of alternative volatility estimates, agents price short-term options on the S&P 500 index before trading with each other at average prices. The agents’ average profits and the Sharpe ratios of the profits constitute the criteria used to evaluate alternative volatility estimates and the corresponding forecasts. For our data, we find that estimators with superior finite sample Mean-squared-error properties generate higher average profits and higher Sharpe ratios, in general. We confirm that, even from a forecasting standpoint, there is scope for optimizing the finite sample properties of alternative volatility estimators as advocated by Bandi and Russell [Bandi, F.M., Russell, J.R., 2005. Market microstructure noise, integrated variance estimators, and the accuracy of asymptotic approximations. Working Paper; Bandi, F.M., Russell, J.R., 2008b. Microstructure noise, realized variance, and optimal sampling. Review of Economic Studies 75, 339–369] in recent work.     

Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data

We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be configured to possess an optimal convergence rate or to ensure positive semi-definite covariance matrix estimates. We also derive a noise-robust Hayashi–Yoshida estimator that can be implemented on the original data without prior alignment of prices. We uncover the finite sample properties of our estimators with simulations and illustrate their practical use on high-frequency equity data.     

Sieve estimation of panel data models with cross section dependence

In this paper we consider the problem of estimating semiparametric panel data models with cross section dependence, where the individual-specific regressors enter the model nonparametrically whereas the common factors enter the model linearly. We consider both heterogeneous and homogeneous regression relationships when both the time and cross-section dimensions are large. We propose sieve estimators for the nonparametric regression functions by extending Pesaran’s (2006) common correlated effect (CCE) estimator to our semiparametric framework. Asymptotic normal distributions for the proposed estimators are derived and asymptotic variance estimators are provided. Monte Carlo simulations indicate that our estimators perform well in finite samples.     

Asymptotic distributions of impulse response functions in short panel vector autoregressions

This paper establishes the asymptotic distributions of the impulse response functions in panel vector autoregressions with a fixed time dimension. It also proves the asymptotic validity of a bootstrap approximation to their sampling distributions. The autoregressive parameters are estimated using the GMM estimators based on the first differenced equations and the error variance is estimated using an extended analysis-of-variance type estimator. Contrary to the time series setting, we find that the GMM estimator of the autoregressive coefficients is not asymptotically independent of the error variance estimator. The asymptotic dependence calls for variance correction for the orthogonalized impulse response functions. Simulation results show that the variance correction improves the coverage accuracy of both the asymptotic confidence band and the studentized bootstrap confidence band for the orthogonalized impulse response functions.     

Likelihood estimation and inference in threshold regression

This paper studies likelihood-based estimation and inference in parametric discontinuous threshold regression models with i.i.d. data. The setup allows heteroskedasticity and threshold effects in both mean and variance. By interpreting the threshold point as a “middle” boundary of the threshold variable, we find that the Bayes estimator is asymptotically efficient among all estimators in the locally asymptotically minimax sense. In particular, the Bayes estimator of the threshold point is asymptotically strictly more efficient than the left-endpoint maximum likelihood estimator and the newly proposed middle-point maximum likelihood estimator. Algorithms are developed to calculate asymptotic distributions and risk for the estimators of the threshold point. The posterior interval is proved to be an asymptotically valid confidence interval and is attractive in both length and coverage in finite samples.     

A theory of robust long-run variance estimation

Long-run variance estimation can typically be viewed as the problem of estimating the scale of a limiting continuous time Gaussian process on the unit interval. A natural benchmark model is given by a sample that consists of equally spaced observations of this limiting process. The paper analyzes the asymptotic robustness of long-run variance estimators to contaminations of this benchmark model. It is shown that any equivariant long-run variance estimator that is consistent in the benchmark model is highly fragile: there always exists a sequence of contaminated models with the same limiting behavior as the benchmark model for which the estimator converges in probability to an arbitrary positive value. A class of robust inconsistent long-run variance estimators is derived that optimally trades off asymptotic variance in the benchmark model against the largest asymptotic bias in a specific set of contaminated models.     

Information criteria for impulse response function matching estimation of DSGE models

We propose new information criteria for impulse response function matching estimators (IRFMEs). These estimators yield sampling distributions of the structural parameters of dynamic stochastic general equilibrium (DSGE) models by minimizing the distance between sample and theoretical impulse responses. First, we propose an information criterion to select only the responses that produce consistent estimates of the true but unknown structural parameters: the Valid Impulse Response Selection Criterion (VIRSC). The criterion is especially useful for mis-specified models. Second, we propose a criterion to select the impulse responses that are most informative about DSGE model parameters: the Relevant Impulse Response Selection Criterion (RIRSC). These criteria can be used in combination to select the subset of valid impulse response functions with minimal dimension that yields asymptotically efficient estimators. The criteria are general enough to apply to impulse responses estimated by VARs, local projections, and simulation methods. We show that the use of our criteria significantly affects estimates and inference about key parameters of two well-known new Keynesian DSGE models. Monte Carlo evidence indicates that the criteria yield gains in terms of finite sample bias as well as offering tests statistics whose behavior is better approximated by the first order asymptotic theory. Thus, our criteria improve existing methods used to implement IRFMEs.     

Partial rank estimation of duration models with general forms of censoring

In this paper we propose estimators for the regression coefficients in censored duration models which are distribution free, impose no parametric specification on the baseline hazard function, and can accommodate general forms of censoring. The estimators are shown to have desirable asymptotic properties and Monte Carlo simulations demonstrate good finite sample performance. Among the data features the new estimators can accommodate are covariate-dependent censoring, double censoring, and fixed (individual or group specific) effects. We also examine the behavior of the estimator in an empirical illustration.     

Threshold estimation of Markov models with jumps and interest rate modeling

We reconstruct the level-dependent diffusion coefficient of a univariate semimartingale with jumps which is observed discretely. The consistency and asymptotic normality of our estimator are provided in the presence of both finite and infinite activity (finite variation) jumps. Our results rely on kernel estimation, using the properties of the local time of the data generating process, and the fact that it is possible to disentangle the discontinuous part of the state variable through those squared increments between observations not exceeding a suitable threshold function. We also reconstruct the drift and the jump intensity coefficients when they are level-dependent and jumps have finite activity, through consistent and asymptotically normal estimators. Simulated experiments show that the newly proposed estimators perform better in finite samples than alternative estimators, and this allows us to reexamine the estimation of a univariate model for the short term interest rate, for which we find fewer jumps and more variance due to the diffusion part than previous studies.     

Subsampling high frequency data

The main contribution of this paper is to propose a novel way of conducting inference for an important general class of estimators that includes many estimators of integrated volatility. A subsampling scheme is introduced that consistently estimates the asymptotic variance for an estimator, thereby facilitating inference and the construction of valid confidence intervals. The new method does not rely on the exact form of the asymptotic variance, which is useful when the latter is of complicated form. The method is applied to the volatility estimator of Aït-Sahalia et al. (2011) in the presence of autocorrelated and heteroscedastic market microstructure noise.     

Measuring correlations of integrated but not cointegrated variables: A semiparametric approach

Many macroeconomic and financial variables are integrated of order one (or I(1)) processes and are correlated with each other but not necessarily cointegrated. In this paper, we propose to use a semiparametric varying coefficient approach to model/capture such correlations. We propose two consistent estimators to study the dependence relationship among some integrated but not cointegrated time series variables. Simulations are used to examine the finite sample performances of the proposed estimators.     

Variance estimation in the change analysis of a linear regression model

We study a “direct test” of Chu and White (1992) proposed for detecting changes in the trend of a linear regression model. The power of this test strongly depends on a suitable estimation of the variance of the error variables involved. We discuss various types of variance estimators and derive their asymptotic properties under the null-hypothesis of “no change” as well as under the alternative of “a change in linear trend”. A small simulation study illustrates the estimators' finite sample behaviour.     

Jump-robust volatility estimation using nearest neighbor truncation

We propose two new jump-robust estimators of integrated variance that allow for an asymptotic limit theory in the presence of jumps. Specifically, our MedRV estimator has better efficiency properties than the tripower variation measure and displays better finite-sample robustness to jumps and small (“zero”) returns. We stress the benefits of local volatility measures using short return blocks, as this greatly alleviates the downward biases stemming from rapid fluctuations in volatility, including diurnal (intraday) U-shape patterns. An empirical investigation of the Dow Jones 30 stocks and extensive simulations corroborate the robustness and efficiency properties of our nearest neighbor truncation estimators.     

Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility

In this paper, we propose two estimators, an integral estimator and a discretized estimator, for the wavelet coefficient of regression functions in nonparametric regression models with heteroscedastic variance. These estimators can be used to test the jumps of the regression function. The model allows for lagged-dependent variables and other mixing regressors. The asymptotic distributions of the statistics are established, and the asymptotic critical values are analytically obtained from the asymptotic distribution. We also use the test to determine consistent estimators for the locations of change points. The jump sizes and locations of change points can be consistently estimated using wavelet coefficients, and the convergency rates of these estimators are derived. We perform some Monte Carlo simulations to check the powers and sizes of the test statistics. Finally, we give practical examples in finance and economics to detect changes in stock returns and short-term interest rates using the empirical wavelet method.     

Trending time-varying coefficient time series models with serially correlated errors

This paper studies a time-varying coefficient time series model with a time trend function and serially correlated errors to characterize the nonlinearity, nonstationarity, and trending phenomenon. A local linear approach is developed to estimate the time trend and coefficient functions. The asymptotic properties of the proposed estimators, coupled with their comparisons with other methods, are established under the α$\alpha$-mixing conditions and without specifying the error distribution. Further, the asymptotic behaviors of the estimators at the boundaries are examined. The practical problem of implementation is also addressed. In particular, a simple nonparametric version of a bootstrap test is adapted for testing misspecification and stationarity, together with a data-driven method for selecting the bandwidth and a consistent estimate of the standard errors. Finally, results of two Monte Carlo experiments are presented to examine the finite sample performances of the proposed procedures and an empirical example is discussed.     

Asymptotics of the principal components estimator of large factor models with weakly influential factors

This paper introduces a drifting-parameter asymptotic framework to derive accurate approximations to the finite sample distribution of the principal components (PC) estimator in situations when the factors’ explanatory power does not strongly dominate the explanatory power of the cross-sectionally and temporally correlated idiosyncratic terms. Under our asymptotics, the PC estimator is inconsistent. We find explicit formulae for the amount of the inconsistency, and propose an estimator of the number of factors for which the PC estimator works reasonably well. For the special case when the idiosyncratic terms are cross-sectionally but not temporally correlated (or vice versa), we show that the coefficients in the OLS regressions of the PC estimates of factors (loadings) on the true factors (true loadings) are asymptotically normal, and find explicit formulae for the corresponding asymptotic covariance matrix. We explain how to estimate the parameters of the derived asymptotic distributions. Our Monte Carlo analysis suggests that our asymptotic formulae and estimators work well even for relatively small n$n$ and T$T$. We apply our theoretical results to test a hypothesis about the factor content of the US stock return data.     

On Maximum Likelihood Estimation of Dynamic Panel Data Models

We analyse the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider transformed maximum likelihood (TML) and random effects maximum likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first‐order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual‐specific effects. We consider different approaches taking into account the non‐negativity restriction for the variance. We show that these approaches may lead to a solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this issue is non‐negligible for small values of T and that different approaches might lead to different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log‐likelihood function. We illustrate these issues modelling US state level unemployment dynamics.     

Residual‐based IV estimation of dynamic panel data models with fixed effects

In dynamic panel regression, when the variance ratio of individual effects to disturbance is large, the system‐GMM estimator will have large asymptotic variance and poor finite sample performance. To deal with this variance ratio problem, we propose a residual‐based instrumental variables (RIV) estimator, which uses the residual from regressing Δy_i,t?1 on as the instrument for the level equation. The RIV estimator proposed is consistent and asymptotically normal under general assumptions. More importantly, its asymptotic variance is almost unaffected by the variance ratio of individual effects to disturbance. Monte Carlo simulations show that the RIV estimator has better finite sample performance compared to alternative estimators. The RIV estimator generates less finite sample bias than difference‐GMM, system‐GMM, collapsing‐GMM and Level‐IV estimators in most cases. Under RIV estimation, the variance ratio problem is well controlled, and the empirical distribution of its t‐statistic is similar to the standard normal distribution for moderate sample sizes.     

Panel data models with spatially correlated error components

In this paper we consider a panel data model with error components that are both spatially and time-wise correlated. The model blends specifications typically considered in the spatial literature with those considered in the error components literature. We introduce generalizations of the generalized moments estimators suggested in Kelejian and Prucha (1999. A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509–533) for estimating the spatial autoregressive parameter and the variance components of the disturbance process. We then use those estimators to define a feasible generalized least squares procedure for the regression parameters. We give formal large sample results for the proposed estimators. We emphasize that our estimators remain computationally feasible even in large samples.     

Nonparametric dynamic panel data models: Kernel estimation and specification testing

Motivated by the first-differencing method for linear panel data models, we propose a class of iterative local polynomial estimators for nonparametric dynamic panel data models with or without exogenous regressors. The estimators utilize the additive structure of the first-differenced model—the fact that the two additive components have the same functional form, and the unknown function of interest is implicitly defined as a solution of a Fredholm integral equation of the second kind. We establish the uniform consistency and asymptotic normality of the estimators. We also propose a consistent test for the correct specification of linearity in typical dynamic panel data models based on the _L2$L_2$ distance of our nonparametric estimates and the parametric estimates under the linear restriction. We derive the asymptotic distributions of the test statistic under the null hypothesis and a sequence of Pitman local alternatives, and prove its consistency against global alternatives. Simulations suggest that the proposed estimators and tests perform well for finite samples. We apply our new method to study the relationships among economic growth, the initial economic condition and capital accumulation, and find a significant nonlinear relation between economic growth and the initial economic condition.