An Alternative Asymptotic Analysis of Residual-Based Statistics

This paper presents an alternative method to derive the limiting distribution of residual-based statistics. Our method does not impose an explicit assumption of (asymptotic) smoothness of the statistic of interest with respect to the model's parameters. and, thus, is especially useful in cases where such smoothness is difficult to establish. Instead, we use a locally uniform convergence in distribution condition, which is automatically satisfied by residual-based specification test statistics. To illustrate, we derive the limiting distribution of a new functional form specification test for discrete choice models, as well as a runs-based tests for conditional symmetry in dynamic volatility models.Le Cam's third lemma, Local Asymptotic Normality (LAN)

Semiparametrically point-optimal hybrid rank tests for unit roots

We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, that is, have the correct (asymptotic) size, irrespective of the true innovation density. For a correctly specified reference density, our test is point-optimal and nearly efficient. For arbitrary reference densities, we establish a Chernoff–Savage-type result, that is, our test performs as well as commonly used tests under Gaussian innovations but has improved power under other, for example, fat-tailed or skewed, innovation distributions. To avoid nonparametric estimation, we propose a simplified version of our test that exhibits the same asymptotic properties, except for the Chernoff–Savage result that we are only able to demonstrate by means of simulations

Causality effects in return volatility measures with random times

We provide a structural approach to identify instantaneous causality effects between durations and stock price volatility. So far, in the literature, instantaneous causality effects have either been excluded or cannot be identified separately from Granger type causality effects. By giving explicit moment conditions for observed returns over (random) duration intervals, we are able to identify an instantaneous causality effect. The documented causality effect has significant impact on inference for tick-by-tick data. We find that instantaneous volatility forecasts for, e.g., IBM stock returns must be decreased by as much as 40% when not having seen the next quote change before its (conditionally) median time. Also, instantaneous volatilities are found to be much higher than indicated by standard volatility assessment procedures using tick-by-tick data. For IBM, a naive assessment of spot volatility based on observed returns between quote changes would only account for 60% of the actual volatility. For less liquidly traded stocks at NYSE this effect is even stronger.Continuous time models Granger causality Instantaneous causality Durations Ultra-high frequency data Volatility per trade

Semiparametric Lower Bounds for Tail Index Estimation

We consider semiparametric estimation of the tail index parameter from i.i.d. observations in Pareto and Weibull type models, using a local and asymptotic approach. The slowly varying function describing the non-tail behavior of the distribution is considered as infinite dimensional nuisance parameter. Without further regularity conditions, we derive a Local Asymptotic Normality (LAN) result that describes essentially the least favorable submodel for the tail index parameter. From this result, we immediately obtain the optimal rate of convergence of tail index parameter estimators for more specific models previously studied. On top of the optimal rate of convergence, our LAN result also gives the minimal limiting variance of (regular) semiparametric estimators through the convolution theorem. We show that the Hill estimator is also semiparametrically efficient in the Pareto case in this much stronger sense. We also discuss the Weibull model in this respect

When Does Subagging Work?

We study the effectiveness of subagging, or subsample aggregating, on regression trees, apopular non-parametric method in machine learning. First, we give sufficient conditionsfor pointwise consistency of trees. We formalize that (i) the bias depends on the diameterof cells, hence trees with few splits tend to be biased, and (ii) the variance depends on thenumber of observations in cells, hence trees with many splits tend to have large variance.While these statements for bias and variance are known to hold globally in the covariatespace, we show that, under some constraints, they are also true locally. Second, we comparethe performance of subagging to that of trees across different numbers of splits. We findthat (1) for any given number of splits, subagging improves upon a single tree, and (2)this improvement is larger for many splits than it is for few splits. However, (3) a singletree grown at optimal size can outperform subagging if the size of its individual treesis not optimally chosen. This last result goes against common practice of growing largerandomized trees to eliminate bias and then averaging to reduce variance

Efficient estimation of integrated volatility and related processes

We derive nonparametric efficiency bounds for regular estimators of integrated smooth transformations of instantaneous variances, in particular, integrated power variance. We find that realized variance attains the efficiency bound for integrated variance under both regular and irregular sampling schemes. For estimating higher powers such as integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds, when observation times are equidistant. Moreover, the estimator in Jacod and Rosenbaum (2013), whose efficiency was documented for the submodel assuming constant volatility, is efficient also for nonconstant volatility paths. When the observation times are possibly random but predictable, we provide an estimator, similar to that of Kristensen (2010), which can get arbitrarily close to the nonparametric bound. Finally, parametric information about the functional form of volatility leads to a lower efficiency bound, unless the volatility process is piecewise constant

The dynamic mixed hitting-time model for multiple transaction prices and times

We propose a structural model for durations between events and (a vector of) associated marks, using a multivariate Brownian motion. Successive passage times of one latent Brownian component relative to random boundaries define durations. The other, correlated, Brownian components generate the marks. Our model embeds the class of stochastic conditional (SCD) and autoregressive conditional (ACD) duration models, which impose testable restrictions on the relation between the conditional expectation and conditional volatility of durations. We strongly reject the SCD and ACD specifications for both a very liquid and less liquid NYSE-traded stock, and characterize causality relations between volatilities and durations

Performance information dissemination in the mutual fund industry

This paper studies the dissemination of performance information in the mutual fund industry. We document a hump-shaped lag pattern for the reaction of mutual fund flows to past performance, i.e., we find that very recent performance is less important than performance several months ago. We attribute this pattern to the presence of less sophisticated investors that update performance information only infrequently. In the 1990s the effect is observed for all funds, but is especially pronounced for highly marketed funds. For the 2000s, we find a substantial increase in the overall probability of investors timely updating mutual fund performance information. As a result, the hump-shaped flow-performance lag pattern disappeared for all but the highly marketed funds.