Time-varying Dependence Structure Research Articles

Regression analysis of multivariate recurrent event data allowing time-varying dependence with application to stroke registry data.

In multivariate recurrent event data, each patient may repeatedly experience more than one type of event. Analysis of such data gets further complicated by the time-varying dependence structure among different types of recurrent events. The available literature regarding the joint modeling of multivariate recurrent events assumes a constant dependency over time, which is strict and often violated in practice. To close the knowledge gap, we propose a class of flexible shared random effects models for multivariate recurrent event data that allow for time-varying dependence to adequately capture complex correlation structures among different types of recurrent events. We developed an expectation-maximization algorithm for stable and efficient model fitting. Extensive simulation studies demonstrated that the estimators of the proposed approach have satisfactory finite sample performance. We applied the proposed model and the estimating method to data from a cohort of stroke patients identified in the University of Texas Houston Stroke Registry and evaluated the effects of risk factors and the dependence structure of different types of post-stroke readmission events.

Changes in seasonal compound floods in Vietnam revealed by a time-varying dependence structure of extreme rainfall and high surge

Compound floods due to intense rainfall and storm surges in coastal areas have shown an increasing trend in some parts of the world, and many studies suggested a strong link with climate change. Yet, such link has not been fully explored and quantitively assessed. In this paper, we demonstrate the development and application of a nonstationary framework to determining different compound scenarios, where individual drivers and their interactions have altered under climate change. The framework has been applied to one of the most flood-prone areas: the Ho Chi Minh City of Vietnam, to help analyze the present and future compound flood risks in both the dry and wet seasons driven by the joint effect from heavy inland rainfall and high skew surge. Over the period of 1980–2017, the two drivers are found to be significantly correlated in March and April, corresponding to the transition from dry-to-wet seasons. We also find that the commonly-used traditional multivariate statistical models underestimate the flood magnitudes for both the current (represented by 2020) and future (represented by 2050) scenarios, when compared with the results produced by the nonstationary methods. In addition, the results reveal that the dry season is expected to receive more floods triggered by the increased intensity and frequency of rainfall extremes, with the magnitude reaching a similar level to that of the wet season. This is in line with the climate projections under RCP4.5 and 8.5 scenarios although the duration of dry spells is expected to increase and the total annual rainfall to decrease in Vietnam. The simulated flood inundations indicate remarkable increases in flood magnitude and extension, especially at the locations identified as low risk by the stationary models.

Asymmetric time-varying dependence and variable structure dependence measurement and analysis of EUA and CER

Abstract This paper analyzed the time-varying dependence and structural dependence between EU allowances (EUAs) and certified emission reductions (CERs) by using price fluctuation data from 2008 to 2021 on EU ETS. It was found that (1) there was a strong nonlinear spillover relationship between EUAs and CERs. From 14 March 2008 to 16 March 2012, the time-varying dependence values of EUAs and CERs were mostly between 0.6 and 1 and the mean coefficient of dependence was 0.86, showing a strong interdependence. From 17 March 2012 to 2 January 2017, the correlation between them was mostly below 0.6 and the mean coefficient of dependence fell to 0.25. This indicates that the dependency between EUA futures and CER futures was very low at this stage. However, in general, the mean value of dependence was above 0.55, that is, there was a dependency between them. (2) From 14 March 2008 to 2 January 2017, there were 12 structural mutation points in EUA and CER yield sequences. After four mutation points, the dependence coefficient increased and the structural dependence enhanced. Meanwhile, after eight mutation points, the dependence coefficient decreased and the structural dependence weakened. The overall level remained above 0.6, showing the existence of structural dependence. (3) Abrupt changes in EUA and CER prices were closely related to the promulgation of major policies and unpredictable emergencies. The former caused carbon prices to fluctuate slightly. When the period of change was short and the recovery was rapid, it caused sharp fluctuations in carbon prices. When the duration of change was long, and the recovery was slow, it yielded impacts that extend far beyond the publication of important information.

Sovereign contagion risk measure across financial markets in the eurozone: a bivariate copulas and Markov Regime Switching ARMA based approaches

This paper analyzes sovereign risk contagion across financial markets in the eurozone during and after the European debt crisis. A particular focus is made on the causal impact of pre-Brexit and Covid-19 pandemic on the dependence between European markets. We use data set from 28 February 2008 to 11 March 2021 and combine copulas and MRS-ARMA techniques to measure dependence across financial markets and assessing asymmetric dependence structure and regime switching process. We develop a dynamic Kendall’s tau correlation and provide evidence of time-varying dependence structure between several pairwise markets. The dependence structure shows a sharp rise on 23 June 2016, day of the referendum on Brexit. Results indicates that Covid-19 pandemic has intensified dependence and sovereign risk spillovers between sovereign CDS European markets. Significant time-varying characteristics of dynamic dependence structures suggests that fund managers and investors should consider in their investment strategies to manage systemic risk and high-risk investment. The identification of dependence structure regime between global financial markets would enhance response to major crises by investors and policy makers.

Smooth-Transition Regression Models for Non-Stationary Extremes

Abstract We introduce a smooth-transition generalized Pareto (GP) regression model to study the time-varying dependence structure between extreme losses and a set of economic factors. In this model, the distribution of the loss size is approximated by a GP distribution, and its parameters are related to explanatory variables through regression functions, which themselves depend on a time-varying predictor of structural changes. We use this approach to study the dynamics in the monthly severity distribution of operational losses at a major European bank. Using the VIX as a transition variable, our analysis reveals that when the uncertainty is high, a high number of losses in a recent past are indicative of less extreme losses in the future, consistent with a self-inhibition hypothesis. On the contrary, in times of low uncertainty, only the growth rate of the economy seems to be a relevant predictor of the likelihood of extreme losses.

Time-varying dependence structure between oil and agricultural commodity markets: A dependence-switching CoVaR copula approach

We examine the energy-food nexus using the dependence-switching copula model. Specifically, we look at the dependence for four distinct market states, such as, increasing oil–increasing commodity, declining oil–declining commodity, increasing oil–declining commodity, as well as declining oil–increasing commodity markets. Our results support the argument that the crash of oil markets and agricultural commodities happen at the same time, especially during crisis period. However, the same is not true during times of normal economic conditions, implying that investors cannot make excess profits in both agricultural and oil markets at once. Furthermore, our analysis suggests that the return chasing effect dominates for all commodities on maximum occasions. The CoVaR and ΔCoVaR results indicate important risk spillover from oil to agricultural markets, especially around the financial crisis.

Co-Movement between Tourist Arrivals of Inbound Tourism Markets in South Korea: Applying the Dynamic Copula Method Using Secondary Time Series Data

Tourism demand is severely affected by unpredicted events, which has prompted scholars to examine ways of predicting the effects of positive and negative shocks on tourism, to ensure a sustainable tourism industry. The purpose of this study was to investigate if non-linear dependence structures exist between tourist flows into South Korea from five major source countries, as South Korea has undergone fluctuations in tourist arrivals due to diverse circumstances and has complex relations with tourism source countries. Additionally, the study examines the structures of extreme tail dependence, which is indicated in the case of unexpected events, and identifies how co-movements vary over time through dynamic copula–GARCH (generalized autoregressive conditional heteroskedasticity) tests. The secondary time series data for the 2005–2019 period of tourist arrivals to Korea were derived from the Korea Tourism Knowledge and Information System for testing the copula models. The copula estimations indicate significant dependencies among all market pairs as well as the strongest dependence between China and Taiwan. Moreover, extreme tail dependence structures show co-movements for four pairs of tourism markets in only negative shocks, for five pairs in both positive and negative conditions, but no co-movement in the China–Taiwan pair. Finally, the dynamic dependence structures reveal that the China–Taiwan dependence is higher than the other time-varying dependence structures, implying that the two markets complement each other.

Dependence Structure between Tourist Arrivals of Inbound Tourism Markets inSouth Korea

Tourism demand is severely affected by unpredicted events. The purpose of this study was to investigate if non-linear dependence structures exist between tourist flows into South Korea from five major source countries, as South Korea has undergone fluctuations in tourist arrivals due to diverse circumstances and has complex relations with tourism source countries. Additionally, the study examines the structures of extreme tail dependence, which is indicated in the case of unexpected events, and identifies how co-movements vary over time through dynamic copula-GARCH (Generalized Autoregressive Conditional Heteroskedasticity) tests. The copula estimations indicate significant dependencies among all market pairs as well as the strongest dependence between China and Taiwan. Moreover, extreme tail dependence structures show co-movements for four pairs of tourism markets in only negative shocks, for five pairs in both positive and negative conditions, but no co-movement in the China-Taiwan pair. Finally, the dynamic dependence structures reveal that the China-Taiwan dependence is higher than the other time-varying dependence structures, implying that the two markets complement each other.

Bivariate frequency analysis of seasonal runoff series under future climate change

ABSTRACT Climate change will not only affect a single hydrological series but also may affect the dependence structure. However, traditional hydrological approaches often fail to analyse the multiple characteristics of runoff within a bivariate framework under climate change. This study explores the influence of future climate change (2031 − 2080) on the runoff volume series in spring, summer and autumn as well as their dependence structures in the Luanhe River Basin, China. The results indicate that the time-varying dependence structure between spring and summer runoff series, as well as that between the summer and autumn runoff series, are mainly related to the summer precipitation. The differences between copula models with constant dependence parameters and those with time-varying dependence parameters are presented under different cases. This study incorporates the impacts of climate change on the bivariate frequency analysis of seasonal runoff series, which may provide important guidance for water resource management under climate change.

Portfolio stress testing applied to commodity futures

In this article, we construct a portfolio of commodity futures which mimics the Dow Jones Commodity Index and perform an extensive stress testing exercise with a focus on hybrid scenarios. The increased volume of investments in commodities as financial instruments over the last decades underline the importance of a more thorough framework for stress testing of related portfolios. Our study is the first to show comparatively the marginal impact of the model choice for portfolio components versus the marginal role of tail dependence on the portfolio profit and loss in stress testing exercises. We model the distribution of returns of portfolio components with an asymmetric AR-GARCH model combined with Extreme Value Theory for extreme tails, and employ multivariate copula functions to model the time-varying joint dependence structure. Our study reveals that indeed, for a realistic stress test, a special attention should be given to the tail risk in individual commodity returns as well as to tail correlations. We also draw conclusions about parameter risk persistent in stress testing exercises. Finally yet importantly, in line with Basel IIIb, the study highlights the importance of using forward-looking hybrid and hypothetical scenarios over historical scenarios.

Smooth Transition Regression Models for Non-Stationary Extremes

We introduce a smooth transition Generalized Pareto (GP) regression model to study the link between extreme losses and the economic context. The advantage of our approach consists in specifying a time-varying dependence structure between financial factors and the severity distribution of the losses. To do so, the parameters of the GP distribution are related to explanatory variables through regression functions which themselves depend on a time-varying predictor of structural changes. We use this technique to study the dynamics in the monthly severity distribution of losses at UniCredit. Using the VIX as transition variable, our analysis reveals that when the uncertainty is high, a high number of losses in a recent past is indicative of less extreme losses in the future, consistent with a self-inhibition hypothesis. On the contrary, in times of low uncertainty, only the economy’s growth rate seems to be a relevant predictor of the likelihood of extreme losses

A TVM-Copula-MIDAS-GARCH model with applications to VaR-based portfolio selection

This paper develops a novel time-varying multivariate Copula-MIDAS-GARCH (TVM-Copula-MIDAS-GARCH) model with exogenous explanatory variables to model the joint distribution of returns. The model accounts for mixed frequency factors that affect the time-varying dependence structure of financial assets. Furthermore, we examine the effectiveness of the proposed model in VaR-based portfolio selection. We conduct an empirical analysis on estimating the 90%, 95%, 99% VaRs of the portfolio constituted of the Shanghai Composite Index, Shanghai SE Fund Index, and Shanghai SE Treasury Bond Index. The empirical results show that the proposed TVM-Copula-MIDAS-GARCH model is effective to investigate the nonlinear time-varying dependence among those three indices and performs better in portfolio selection.

A Time Varying Approach to the Stock Return–Inflation Puzzle

Summary In the large literature on the stock return–inflation puzzle, existing works have used constant coefficient linear regression models or change point analysis with abrupt change points. Motivated by the time varying stock return–inflation relationship and the drawbacks of change point analysis, we propose to use the recently emerged locally stationary models to model stock return and inflation. Although the model exhibits non-parametric time varying dependence structure over a long time span, it has local stationarity within each small time interval. Detailed empirical analysis is conducted and comparisons are made between various approaches. We find that the stock return–inflation correlation is negative during early sample periods and turns positive during late sample periods, but the turning time point is different for the total inflation rate and core inflation rate.

Resource optimization of product development projects with time-varying dependency structure

Project managers are continuously under pressure to shorten product development durations. One practical approach for reducing the project duration is lessening dependencies between different development components and teams. However, most of the resource allocation strategies for lessening dependencies place the implicit and simplistic assumption that the dependency structure between components is static (i.e., does not change over time). This assumption, however, does not necessarily hold true in all product development projects. In this paper, we present an analytical framework for optimally allocating resources to shorten the lead-time of product development projects having a time-varying dependency structure. We build our theoretical framework on a linear system model of product development processes, in which system integration and local development teams exchange information asynchronously and aperiodically. By utilizing a convexity result from the matrix theory, we show that the optimal resource allocation can be efficiently found by solving a convex optimization problem. We provide illustrative examples to demonstrate the proposed framework. We also present boundary analyses based on major graph models to provide managerial guidelines for improving empirical PD processes.

Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice

Abstract. Multivariate hydrologic design under stationary conditions is traditionally performed through the use of the design criterion of the return period, which is theoretically equal to the average inter-arrival time of flood events divided by the exceedance probability of the design flood event. Under nonstationary conditions, the exceedance probability of a given multivariate flood event varies over time. This suggests that the traditional return-period concept cannot apply to engineering practice under nonstationary conditions, since by such a definition, a given multivariate flood event would correspond to a time-varying return period. In this paper, average annual reliability (AAR) was employed as the criterion for multivariate design rather than the return period to ensure that a given multivariate flood event corresponded to a unique design level under nonstationary conditions. The multivariate hydrologic design conditioned on the given AAR was estimated from the nonstationary multivariate flood distribution constructed by a dynamic C-vine copula, allowing for time-varying marginal distributions and a time-varying dependence structure. Both the most-likely design event and confidence interval for the multivariate hydrologic design conditioned on the given AAR were identified to provide supporting information for designers. The multivariate flood series from the Xijiang River, China, were chosen as a case study. The results indicated that both the marginal distributions and dependence structure of the multivariate flood series were nonstationary due to the driving forces of urbanization and reservoir regulation. The nonstationarities of both the marginal distributions and dependence structure were found to affect the outcome of the multivariate hydrologic design.

A copula-GARCH approach for analyzing dynamic conditional dependency structure between liquefied petroleum gas freight rate, product price arbitrage and crude oil price

Global liquefied petroleum gas (LPG) trade shows an increasing trend but is under-researched. This paper focuses on the LPG market and aims to model the dependence dynamics among LPG freight rates, crude oil price and propane location arbitrage. Conditional copula-GARCH model is applied to estimate dependencies. Different types of copulas with both time-invariant and time-varying dependence structures are fitted and their suitability has been compared. The findings suggest that firstly, Baltic LPG (BLPG) freight rate and the arbitrage between propane Far East and Middle East prices have conditional time-varying dependence and the dependence is higher in market downturns. Furthermore, BLPG and the arbitrage between Far East and US propane prices, have symmetric dependence and such a relationship has strengthened since 2013. Secondly, Middle East propane price is found to have the strongest correlation with crude oil prices compared to Far East and US propane prices, indicating higher sensitivity to crude oil price changes. Last but not least, the relationship between crude oil and BLPG is relatively weak and mostly positive.

Generalized Additive Models for Pair-Copula Constructions

ABSTRACTPair-copula constructions are flexible dependence models that use bivariate copulas as building blocks. In this article, we extend them with generalized additive models to allow covariates effects. Borrowing ideas from a traditionally univariate context, we let each pair-copula parameter depend directly on the covariates in a parametric, semiparametric, or nonparametric way. We propose a sequential estimation method that we study by simulation, and apply it to investigate the time-varying dependence structure between the intraday returns on four major foreign exchange rates. An R package, scripts reproducing the results in this article, and additional simulation results are provided as supplementary material.

Determinants of dependence structures of sovereign credit default swap spreads between G7 and BRICS countries

We investigate the time-varying dependence structures between G7 and BRICS countries' sovereign credit default swap (CDS) spreads for different timescales by combining wavelet analysis and the copula approach. First, by employing wavelet analysis, we find increasing dependence between the G7 and BRICS's CDS spreads with a decreasing significance level as the timescale increases. Second, the CDS spread dependence across most timescales is better described by the time-varying, than the time-invariant, copulas. Third, gold served as a risk-haven asset may play a good indicator to measure the sovereign credit risk, as well as its dependence. Additionally, the CDS spreads for both G7 and BRICS countries behave simultaneously when the economy is prosperous, but not for the economic depression period. Finally, from the regression of the wavelet components, we find no significant results for the short-term wavelets, whereas significant results are present for both the middle- and long-term scales.

Sovereign bond market dependencies and crisis transmission around the eurozone debt crisis: a dynamic copula approach

ABSTRACTWe examine the dependency between the European government bond markets around the recent sovereign debt crisis. A dynamic copula approach is used to model the time-varying dependence structure of those government bond markets, evaluate the nature and strength of their dependencies over time, and gauge the transmission of the crisis shocks. Our results can be summarized as follows: i) the eurozone sovereign bond markets under consideration have a significant and positive dependence with the Greek and the EMU benchmark sovereign bond markets; ii) the dynamic-BB7 copula function best describes the dependence structure between these sovereign bond markets and provides evidence of asymmetric tail dependence; iii) the conditional probability of crisis transmission from Greece to other eurozone countries is higher than the other way around; and iv) Greece is the most vulnerable country when the eurozone entered into the sovereign debt crisis.

Dynamic dependence structure between energy markets and the Italian stock index

The dependence structure between the main energy markets (such as crude oil, natural gas, and coal) and the main stock index plays a crucial role in the economy of a given country. As the dependence structure between these series is dramatically complex and it appears to change over time, time-varying dependence structure given by a class of dynamic copulas is taken into account.To this end, each pair of time series returns with a dynamic t-Student copula is modelled, which takes as input the time-varying correlation. The correlation evolves with the DCC(1,1) equation developed by Engle.The model is tested through a simulation by employing empirical data issued from the Italian Stock Market and the main connected energy markets. The author considers empirical distributions for each marginal series returns in order to focus on the dependence structure. The model’s parameters are estimated by maximization of the log-likelihood. Also evidence is found that the proposed model fits correctly, for each pair of series, the left tail dependence coefficient and it is then compared with a static copula dependence structure which clearly underperforms the number of joint extreme values at a given confidence level.