Subsampling the distribution of diverging statistics with applications to finance

In this paper we propose a subsampling estimator for the distribution of statistics diverging at either known or unknown rates when the underlying time series is strictly stationary and strong mixing. Based on our results we provide a detailed discussion of how to estimate extreme order statistics with dependent data and present two applications to assessing financial market risk. Our method performs well in estimating Value at Risk and provides a superior alternative to Hill's estimator in operationalizing Safety First portfolio selection.     

Unit root testing via the stationary bootstrap

A nonparametric, residual-based stationary bootstrap procedure is proposed for unit root testing in a time series. The procedure generates a pseudoseries which mimics the original, but ensures the presence of a unit root. Unlike many others in the literature, the proposed test is valid for a wide class of weakly dependent processes and is not based on parametric assumptions on the data-generating process. Large sample theory is developed and asymptotic validity is shown via a bootstrap functional central limit theorem. The case of a least squares statistic is discussed in detail, including simulations to investigate the procedure's finite sample performance.     

Role and impact of the environment on entrepreneurial learning

Abstract

This article is presenting an overview of the literature devoted to entrepreneurial learning and, more specifically, those research bringing environmental elements into the study of the entrepreneurial learning process. Then, it shows how each of the four Special Issue selected research papers contribute to enhancing our knowledge of the complexity of the learning process vis-à-vis entrepreneurial processes placed in context. By doing this, it makes an attempt to explain the specific context behind each contribution as well as presenting the wider context. Finally, the article is suggesting a set of key challenges and research pathways that might be explored in the future.     

Career motives and entrepreneurial decision-making: examining preferences for causal and effectual logics in the early stage of new ventures

The influence of entrepreneurs’ career motives is examined on two alternative modes of decision-making logic; causation and effectuation. Based on Sarasvathy’s (Acad Manage Rev 26(2):243–288, 2001) seminal study, causation is defined as a decision-making process that focuses on what ought to be done given predetermined goals and possible means, and effectuation as a decision-making process emphasizing the question of what can be done given possible means and imagined ends. Analysis suggests that entrepreneurs who identify themselves with linear or expert career motives have a higher preference for causal decision-making logic. Entrepreneurs who identify themselves with spiral or transitory career motives have a higher preference for effectual decision-making logic. In addition, indications that prior start-up experience moderates the relationship between career motives and effectual decision-making logic for spiral-minded entrepreneurs is found. The overall results give ample support for the assumption that entrepreneurs’ career motives influence their decision-making.     

Semiparametric Estimation for Non-Ruin Probabilities

We consider the classical risk model with unknown claim size distribution F and unknown Poisson arrival rate u . Given a sample of claims from F and a sample of interarrival times for these claims, we construct an estimator for the function Z ( u ), which gives the probability of non-ruin in that model for initial surplus u . We obtain strong consistency and asymptotic normality for that estimator for a large class of claim distributions F . Confidence bounds for Z ( u ) based on the bootstrap are also given and illustrated by some numerical examples.     

Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics

This paper studies taper-based estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework, and makes several theoretical contributions: (i) we treat multiple frequencies jointly, (ii) we allow for long-range dependence or anti-persistence at differing frequencies, (iii) we allow for tapers that are only piecewise smooth or discontinuous, including flat-top and truncation tapers, (iv) we study higher-order accuracy through the limit distribution’s Laplace Transform, (v) we develop a taper-based estimation theory for the spectral distribution, and show how confidence bands can be constructed. Simulation results produce quantiles and document the finite-sample size properties of the estimators, and a few empirical applications demonstrate the utility of the new methods.     

Subsampling Inference with K Populations and a Non‐standard Behrens–Fisher Problem

We revisit the methodology and historical development of subsampling, and then explore in detail its use in hypothesis testing, an area which has received surprisingly modest attention. In particular, the general set‐up of a possibly high‐dimensional parameter with data from K populations is explored. The role of centring the subsampling distribution is highlighted, and it is shown that hypothesis testing with a data‐centred subsampling distribution is more powerful. In addition we demonstrate subsampling’s ability to handle a non‐standard Behrens–Fisher problem, i.e., a comparison of the means of two or more populations which may possess not only different and possibly infinite variances, but may also possess different distributions. However, our formulation is general, permitting even functional data and/or statistics. Finally, we provide theory for K ‐ sample U ‐ statistics that helps establish the asymptotic validity of subsampling confidence intervals and tests in this very general setting.     

Model-free versus Model-based Volatility Prediction

The well-known ARCH/GARCH models for financial time series havebeen criticized of late for their poor performance in volatilityprediction, that is, prediction of squared returns.¹ Focusingon three representative data series, namely a foreign exchangeseries (Yen vs. Dollar), a stock index series (the S&P500index), and a stock price series (IBM), the case is made thatfinancial returns may not possess a finite fourth moment. Takingthis into account, we show how and why ARCH/GARCH models—whenproperly applied and evaluated—actually do have nontrivialpredictive validity for volatility. Furthermore, we show howa simple model-free variation on the ARCH theme can performeven better in that respect. The model-free approach is basedon a novel normalizing and variance–stabilizing transformation(NoVaS, for short) that can be seen as an alternative to parametricmodeling. Properties of this transformation are discussed, andpractical algorithms for optimizing it are given.     

Local block bootstrap inference for trending time series

Resampling for stationary sequences has been well studied in the last couple of decades. In the paper at hand, we focus on nonstationary time series data where the nonstationarity is due to a slowly-changing deterministic trend. We show that the local block bootstrap methodology is appropriate for inference under this locally stationary setting without the need of detrending the data. We prove the asymptotic consistency of the local block bootstrap in the smooth trend model, and complement the theoretical results by a finite-sample simulation.