Local Lead–Lag Relationships and Nonlinear Granger Causality: An Empirical Analysis

The Granger causality test is essential for detecting lead–lag relationships between time series. Traditionally, one uses a linear version of the test, essentially based on a linear time series regression, itself being based on autocorrelations and cross-correlations of the series. In the present paper, we employ a local Gaussian approach in an empirical investigation of lead–lag and causality relations. The study is carried out for monthly recorded financial indices for ten countries in Europe, North America, Asia and Australia. The local Gaussian approach makes it possible to examine lead–lag relations locally and separately in the tails and in the center of the return distributions of the series. It is shown that this results in a new and much more detailed picture of these relationships. Typically, the dependence is much stronger in the tails than in the center of the return distributions. It is shown that the ensuing nonlinear Granger causality tests may detect causality where traditional linear tests fail.publishedVersio

Recognizing and visualizing copulas : an approach using local Gaussian approximation

Copulas are much used to model nonlinear and non-Gaussian dependence between stochastic variables. Their functional form is determined by a few parameters, but unlike a dependence measure like the correlation, these parameters do not have a clear interpretation in terms of the dependence structure they create. In this paper we examine the relationship between a newly developed local dependence measure, the local Gaussian Correlation, and standard copula theory. We are able to describe characteristics of the dependence structure in different copula models in terms of the local Gaussian correlation. In turn, these characteristics can be effectively visualized. More formally, the characteristic dependence structure can be used to construct a goodness-of-fit test for bivariate copula models by comparing the theoretical local Gaussian correlation for a specific copula and the estimated local Gaussian correlation. A Monte Carlo study reveals that the test performs very well compared to a commonly used alternative test. We also propose two types of diagnostic plots which can be used to investigate the cause of a rejected null. Finally, our methods are used on a ”classic” insurance data set

Introducing localgauss, an R Package for Estimating and Visualizing Local Gaussian Correlation

Quantifying non-linear dependence structures between two random variables is a challenging task. There exist several bona-fide dependence measures able to capture the strength of the non-linear association, but they typically give little information about how the variables are associated. This problem has been recognized by several authors and has given rise to the concept of local measures of dependence. A local measure of dependence is able to capture the “local” dependence structure in a particular region. The idea is that the global dependence structure is better described by a portfolio of local measures of dependence computed in different regions than a one-number measure of dependence. This paper introduces the R package localgauss which estimates and visualizes a measure of local dependence called local Gaussian correlation. The package provides a function for estimation, a function for local independence testing and corresponding functions for visualization purposes, which are all demonstrated with examples

Modelling clusters of corporate defaults: Regime-switching models significantly reduce the contagion source

In this paper, we report robust evidence that the process of corporate defaults is time-dependent and can be modelled by extending an autoregressive count time series model class via the introduction of regime-switching. That is, some of the parameters of the model depend on the regime of an unobserved Markov chain, capturing the model changes during clusters observed for count time series in corporate defaults. Thus, the process of corporate defaults is more dynamic than previously believed. Moreover, the contagion effect—that current defaults affect the probability of other firms defaulting in the future—is reduced compared to models without regime-switching, and is only present in one regime. A two-regime model drives the counts of monthly corporate defaults in the United States. To estimate the model, we introduce a novel quasi-maximum likelihood estimator by adapting the extended Hamilton–Gray algorithm for the Poisson autoregressive model.publishedVersio

A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using Template Model Builder

A very common way to estimate the parameters of a hidden Markov model (HMM) is the relatively straightforward computation of maximum likelihood (ML) estimates. For this task, most users rely on user-friendly implementation of the estimation routines via an interpreted programming language such as the statistical software environment R. Such an approach can easily require time-consuming computations, in particular for longer sequences of observations. In addition, selecting a suitable approach for deriving confidence intervals for the estimated parameters is not entirely obvious, and often the computationally intensive bootstrap methods have to be applied. In this tutorial, we illustrate how to speed up the computation of ML estimates significantly via the R package TMB. Moreover, this approach permits simple retrieval of standard errors at the same time. We illustrate the performance of our routines using different data sets: first, two smaller samples from a mobile application for tinnitus patients and a well-known data set of fetal lamb movements with 87 and 240 data points, respectively. Second, we rely on larger data sets of simulated data of sizes 2000 and 5000 for further analysis. This tutorial is accompanied by a collection of scripts, which are all available in the Supporting Information. These scripts allow any user with moderate programming experience to benefit quickly from the computational advantages of TMB.publishedVersio

Taking MT evaluation metrics to extremes : beyond correlation with human judgments

Automatic Machine Translation (MT) evaluation is an active field of research, with a handful of new metrics devised every year. Evaluation metrics are generally benchmarked against manual assessment of translation quality, with performance measured in terms of overall correlation with human scores. Much work has been dedicated to the improvement of evaluation metrics to achieve a higher correlation with human judgments. However, little insight has been provided regarding the weaknesses and strengths of existing approaches and their behavior in different settings. In this work we conduct a broad meta-evaluation study of the performance of a wide range of evaluation metrics focusing on three major aspects. First, we analyze the performance of the metrics when faced with different levels of translation quality, proposing a local dependency measure as an alternative to the standard, global correlation coefficient. We show that metric performance varies significantly across different levels of MT quality: Metrics perform poorly when faced with low-quality translations and are not able to capture nuanced quality distinctions. Interestingly, we show that evaluating low-quality translations is also more challenging for humans. Second, we show that metrics are more reliable when evaluating neural MT than the traditional statistical MT systems. Finally, we show that the difference in the evaluation accuracy for different metrics is maintained even if the gold standard scores are based on different criteria

Analysis of left truncated data with an application to insurance data

This thesis discusses different ways of analysing left truncated data when the lower bound itself is a stochastic variable. We will consider the possible dependence between the variable of interest and the truncating variable, and how the dependency structure between these variables influence estimation of the underlying distribution

Modelling clusters of corporate defaults: Regime-switching models significantly reduce the contagion source

In this paper, we report robust evidence that the process of corporate defaults is time-dependent and can be modelled by extending an autoregressive count time series model class via the introduction of regime-switching. That is, some of the parameters of the model depend on the regime of an unobserved Markov chain, capturing the model changes during clusters observed for count time series in corporate defaults. Thus, the process of corporate defaults is more dynamic than previously believed. Moreover, the contagion effect—that current defaults affect the probability of other firms defaulting in the future—is reduced compared to models without regime-switching, and is only present in one regime. A two-regime model drives the counts of monthly corporate defaults in the United States. To estimate the model, we introduce a novel quasi-maximum likelihood estimator by adapting the extended Hamilton–Gray algorithm for the Poisson autoregressive model

Computational issues in parameter estimation for hidden Markov models with template model builder

A popular way to estimate the parameters of a hidden Markov model (HMM) is direct numerical maximization (DNM) of the (log-)likelihood function. The advantages of employing the TMB [Kristensen K, Nielsen A, Berg C, et al. TMB: automatic differentiation and Laplace approximation. J Stat Softw Articles. 2016;70(5):1–21] framework in R for this purpose were illustrated recently [Bacri T, Berentsen GD, Bulla J, et al. A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using template model builder. Biom J. 2022 Oct;64(7):1260–1288]. In this paper, we present extensions of these results in two directions. First, we present a practical way to obtain uncertainty estimates in form of confidence intervals (CIs) for the so-called smoothing probabilities at moderate computational and programming effort via TMB. Our approach thus permits to avoid computer-intensive bootstrap methods. By means of several examples, we illustrate patterns present for the derived CIs. Secondly, we investigate the performance of popular optimizers available in R when estimating HMMs via DNM. Hereby, our focus lies on the potential benefits of employing TMB. Investigated criteria via a number of simulation studies are convergence speed, accuracy, and the impact of (poor) initial values. Our findings suggest that all optimizers considered benefit in terms of speed from using the gradient supplied by TMB. When supplying both gradient and Hessian from TMB, the number of iterations reduces, suggesting a more efficient convergence to the maximum of the log-likelihood. Last, we briefly point out potential advantages of a hybrid approach.publishedVersio

A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using Template Model Builder

A very common way to estimate the parameters of a hidden Markov model (HMM) is the relatively straightforward computation of maximum likelihood (ML) estimates. For this task, most users rely on user-friendly implementation of the estimation routines via an interpreted programming language such as the statistical software environment R. Such an approach can easily require time-consuming computations, in particular for longer sequences of observations. In addition, selecting a suitable approach for deriving confidence intervals for the estimated parameters is not entirely obvious, and often the computationally intensive bootstrap methods have to be applied. In this tutorial, we illustrate how to speed up the computation of ML estimates significantly via the R package TMB. Moreover, this approach permits simple retrieval of standard errors at the same time. We illustrate the performance of our routines using different data sets: first, two smaller samples from a mobile application for tinnitus patients and a well-known data set of fetal lamb movements with 87 and 240 data points, respectively. Second, we rely on larger data sets of simulated data of sizes 2000 and 5000 for further analysis. This tutorial is accompanied by a collection of scripts, which are all available in the Supporting Information. These scripts allow any user with moderate programming experience to benefit quickly from the computational advantages of TMB