arXiv subjects

Catherine S. Forbes

Publications and source records attributed to Catherine S. Forbes.

7 recordsLinked to original sources

arXiv2024

Familial inference: tests for hypotheses on a family of centres

Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular centre. This ambiguity leaves the possibility for a gap between scientific theory and statistical practice that can lead to rejection of a true null. In the face of replicability crises in many scientific disciplines, significant results of this kind are concerning. Rather than testing a single centre, this paper proposes testing a family of plausible centres, such as that induced by the Huber loss function (the Huber family). Each centre in the family generates a testing problem, and the resulting family of hypotheses constitutes a familial hypothesis. A Bayesian nonparametric procedure is devised to test familial hypotheses, enabled by a novel pathwise optimization routine to fit the Huber family. The favourable properties of the new test are demonstrated theoretically and experimentally. Two examples from psychology serve as real-world case studies.

stat.ME↗

arXiv2020

High-Frequency Jump Tests: Which Test Should We Use?

We conduct an extensive evaluation of price jump tests based on high-frequency financial data. After providing a concise review of multiple alternative tests, we document the size and power of all tests in a range of empirically relevant scenarios. Particular focus is given to the robustness of test performance to the presence of jumps in volatility and microstructure noise, and to the impact of sampling frequency. The paper concludes by providing guidelines for empirical researchers about which test to choose in any given setting.

q-fin.ST↗

arXiv2019

Forecasting observables with particle filters: Any filter will do!

We investigate the impact of filter choice on forecast accuracy in state space models. The filters are used both to estimate the posterior distribution of the parameters, via a particle marginal Metropolis-Hastings (PMMH) algorithm, and to produce draws from the filtered distribution of the final state. Multiple filters are entertained, including two new data-driven methods. Simulation exercises are used to document the performance of each PMMH algorithm, in terms of computation time and the efficiency of the chain. We then produce the forecast distributions for the one-step-ahead value of the observed variable, using a fixed number of particles and Markov chain draws. Despite distinct differences in efficiency, the filters yield virtually identical forecasting accuracy, with this result holding under both correct and incorrect specification of the model. This invariance of forecast performance to the specification of the filter also characterizes an empirical analysis of S&P500 daily returns.

stat.CO↗

arXiv2019

Updating Variational Bayes: Fast sequential posterior inference

Variational Bayesian (VB) methods produce posterior inference in a time frame considerably smaller than traditional Markov Chain Monte Carlo approaches. Although the VB posterior is an approximation, it has been shown to produce good parameter estimates and predicted values when a rich classes of approximating distributions are considered. In this paper we propose Updating VB (UVB), a recursive algorithm used to update a sequence of VB posterior approximations in an online setting, with the computation of each posterior update requiring only the data observed since the previous update. An extension to the proposed algorithm, named UVB-IS, allows the user to trade accuracy for a substantial increase in computational speed through the use of importance sampling. The two methods and their properties are detailed in two separate simulation studies. Two empirical illustrations of the proposed UVB methods are provided, including one where a Dirichlet Process Mixture model with a novel posterior dependence structure is repeatedly updated in the context of predicting the future behaviour of vehicles on a stretch of the US Highway 101.

stat.CO↗

arXiv2018

The determinants of bank loan recovery rates in good times and bad - new evidence

We find that factors explaining bank loan recovery rates vary depending on the state of the economic cycle. Our modeling approach incorporates a two-state Markov switching mechanism as a proxy for the latent credit cycle, helping to explain differences in observed recovery rates over time. We are able to demonstrate how the probability of default and certain loan-specific and other variables hold different explanatory power with respect to recovery rates over `good' and `bad' times in the credit cycle. That is, the relationship between recovery rates and certain loan characteristics, firm characteristics and the probability of default differs depending on underlying credit market conditions. This holds important implications for modelling capital retention, particularly in terms of countercyclicality.

q-fin.RM↗

arXiv2017

A Robust Bayesian Exponentially Tilted Empirical Likelihood Method

This paper proposes a new Bayesian approach for analysing moment condition models in the situation where the data may be contaminated by outliers. The approach builds upon the foundations developed by Schennach (2005) who proposed the Bayesian exponentially tilted empirical likelihood (BETEL) method, justified by the fact that an empirical likelihood (EL) can be interpreted as the nonparametric limit of a Bayesian procedure when the implied probabilities are obtained from maximizing entropy subject to some given moment constraints. Considering the impact that outliers are thought to have on the estimation of population moments, we develop a new robust BETEL (RBETEL) inferential methodology to deal with this potential problem. We show how the BETEL methods are linked to the recent work of Bissiri, Holmes and Walker (2016) who propose a general framework to update prior belief via a loss function. A controlled simulation experiment is conducted to investigate the performance of the RBETEL method. We find that the proposed methodology produces reliable posterior inference for the fundamental relationships that are embedded in the majority of the data, even when outliers are present. The method is also illustrated in an empirical study relating brain weight to body weight using a dataset containing sixty-five different land animal species.

stat.ME↗

arXiv2016

Inference on Self-Exciting Jumps in Prices and Volatility using High Frequency Measures

Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state space representation is used to link observed returns, plus nonparametric measures of integrated volatility and price jumps, to the specified model components; with Bayesian inference conducted using a Markov chain Monte Carlo algorithm. An evaluation of marginal likelihoods for the proposed model relative to a large number of alternative models, including some that have featured in the literature, is provided. An extensive empirical investigation is undertaken using data on the S&P500 market index over the 1996 to 2014 period, with substantial support for dynamic jump intensities - including in terms of predictive accuracy - documented.

stat.AP↗