Research

We propose using a permutation test to detect discontinuities in an underlying economic model at a known cutoff point. Relative to the existing literature, we show that this test is well suited for event studies based on time-series data. The test statistic measures the distance between the empirical distribution functions of observed data in two local subsamples on the two sides of the cutoff. Critical values are computed via a standard permutation algorithm. Under a high-level condition that the observed data can be coupled by a collection of conditionally independent variables, we establish the asymptotic validity of the permutation test, allowing the sizes of the local subsamples to be either be fixed or grow to infinity. In the latter case, we also establish that the permutation test is consistent. We demonstrate that our high-level condition can be verified in a broad range of problems in the infill asymptotic time-series setting, which justifies using the permutation test to detect jumps in economic variables such as volatility, trading activity, and liquidity. These potential applications are illustrated in an empirical case study for selected FOMC announcements during the ongoing COVID-19 pandemic.

For VAR models with common explosive root, the OLS estimator of the autoregressive coefficient matrix is inconsistent (refer to Nielsen, 2009 and Phillips and Magdalinos, 2013). Although Phillips & Magdalinos (2013) proposed using the future observations as the instrumental variable for removing the endogeneity from VAR models, type I error occurs when testing for a common explosive root from the distinct explosive roots before the implementation of IV estimation. Such error creates bias and variance in the estimate and further causes incorrect inference in the structural analysis such as forecast error decomposition (FEVD). Hence, we propose using of seemingly unrelated regression (SUR) estimation for VAR models with explosive roots. Our SUR estimator is consistent in the case of both distinct explosive roots and common explosive root. We also consider models with drift in the system for generalization. Simulations show that the SUR estimate performs better than OLS and IV estimate in the case of both a common explosive root and distinct explosive roots case. In structural FEVD analysis, simulations show that SUR yields a different result from OLS and IV. We demonstrate the use of SUR in FEVD for agricultural commodity markets between 3 July 2010, and 29 January 2011.

We present a general framework for optimal nonparametric spot volatility estimation based on intraday range data, comprised of the first, highest, lowest, and last price over a given time-interval. We rely on a decision-theoretic approach together with a coupling-type argument to directly tailor the form of the nonparametric estimator to the specific volatility measure of interest and relevant loss function. The resulting new optimal estimators offer substantial efficiency gains compared to existing commonly used range-based procedures.

This paper introduces a novel nonparametric high-frequency jump test for discretely observed Itô semimartingales. Based on observations sampled recursively at first exit times from a symmetric double barrier, our method distinguishes between threshold exceedances caused by the Brownian component and jumps, which enables the construction of a feasible, noiserobust statistical test. Simulation results demonstrate superior finite-sample performance of our test compared to existing methods. An empirical analysis of NYSE-traded stocks provides clear statistical evidence for jumps, with the results highly robust to spurious detections.

We contribute to the growing literature on high-frequency spot volatility estimation by deriving a new integral representation for the recently introduced asymptotic minimum risk equivariant (AMRE) candlestickbased class of estimators. Our new theoretical representation enables the practical numerical computation of the hitherto impractical to compute optimal estimators based on multiple adjacent candlesticks. We also propose a new exact sampling scheme for high-frequency candlestick data, which facilitates straightforward calculation of the asymptotic risk and confidence intervals for the estimators. The resulting critical values for the highest-density intervals highlight the substantial efficiency gains from incorporating more than one candlestick in the estimation process. We showcase the practical value of the new techniques in elucidating the behavior of financial market volatility around the time of important news announcements.

We address the uniform inference problem for high-frequency data that includes prices, volumes, and trading flows. Such data is modeled with a general state-space framework, where latent state process is the corresponding risk indicators, e.g., volatility, price jump, average order size, and arrival of events. The functional estimators are formed as the collection of localized estimates across different time points. Although the proposed estimators do not admit a functional central limit theorem, a Gaussian strong approximation, or coupling, is established under in-fill asymptotics to facilitate feasible inference. We apply the proposed methodology to distinguish the informative part from the Federal Open Market Committee speeches, and to analyze the impact of social media activities on cryptocurrency market.

This paper studies a semiparametric inference procedure for a finite-dimensional parameter in a continuous-time regression model involving high-frequency data in a large cross-section. The model concerns the relationship between a noisy dependent process and a possibly nonlinear transform of stochastic volatility over a fixed time span, with its coefficients allowed to depend on a set of firm-specific characteristics. The construction of the estimator involves two steps: the nonparametric recovery of stochastic volatility processes, followed by a parametric second stage that uses the volatility estimates. We show that the estimator admits a central limit theorem and provide a consistent estimator of the asymptotic conditional variance based on a factor-analytic method. The finite sample performance of the inference procedure is satisfactory in a realistically calibrated Monte Carlo setting. In a novel empirical application, we study the relationship between bid-ask spread and the spot standard deviation of asset price. The slope coefficient estimate, which measures the heterogeneous level of information asymmetry, is closely related to firm characteristics such as size, algorithmic trading proxies, and institutional ownership.