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This survey focuses on two families of nonlinear vector time series models, the family of vector threshold regression (VTR) models and that of vector smooth transition regression (VSTR) models. These two model classes contain incomplete models in the sense that strongly exogeneous variables are allowed in the equations. The emphasis is on stationary models, but the considerations also include nonstationary VTR and VSTR models with cointegrated variables. Model specification, estimation and evaluation is considered, and the use of the models illustrated by macroeconomic examples from the literature.

The authors propose a semiparametric approach for testing independence between two infinite-order cointegrated vector autoregressive series (IVAR(∞)). The procedures considered can be viewed as extensions of classical methods proposed by Haugh (1976, JASA) and Hong (1996b, Biometrika) for testing independence between stationary univariate time series. The tests are based on the residuals of long autoregressions, hence allowing for computational simplicity, weak assumptions on the form of the underlying process, and a direct interpretation of the results in terms of innovations (or shocks). The test statistics are standardized versions of the sum of weighted squares of residual cross-correlation matrices. The weights depend on a kernel function and a truncation parameter. Multivariate portmanteau statistics can be viewed as a special case of our procedure based on the truncated uniform kernel. The asymptotic distributions of the test statistics under the null hypothesis are derived, and consistency is established against fixed alternatives of serial cross-correlation of unknown form. A simulation study is presented which indicates that the proposed tests have good size and power properties in finite samples.

For this discussion, assume there are n sample observations of the dependent variable y at unique locations. In spatial samples, often each observation is uniquely associated with a particular location or region, so that observations and regions are equivalent. Spatial dependence arises when an observation at one location, say y i is dependent on “neighboring” observations y j, y j∈ϒi. We use ϒi to denote the set of observations that are “neighboring” to observation i, where some metric is used to define the set of observations that are spatially connected to observation i. For general definitions of the sets ϒi,i=1,…,n, typically at least one observation exhibits simultaneous dependence, so that an observation y j, also depends on y i. That is, the set ϒj contains the observation y i, creating simultaneous dependence among observations. This situation constitutes a difference between time series analysis and spatial analysis. In time series, temporal dependence relations could be such that a “one-period-behind relation” exists, ruling out simultaneous dependence among observations. The time series one-observation-behind relation could arise if spatial observations were located along a line and the dependence of each observation were strictly on the observation located to the left. However, this is not in general true of spatial samples, requiring construction of estimation and inference methods that accommodate the more plausible case of simultaneous dependence among observations.

The life insurance industry has been exposed to high levels of longevity risk born from the mismatch between realized mortality trends and anticipated forecast. Annuity providers are exposed to extended periods of annuity payments. There are no immediate instruments in the market to counter the risk directly. This paper aims to develop appropriate instruments for hedging longevity risk and providing an insight on how existing products can be tailor-made to effectively immunize portfolios consisting of life insurance using a cointegration vector error correction model with regime-switching (RS-VECM), which enables both short-term fluctuations, through the autoregressive structure [AR(1)] and long-run equilibria using a cointegration relationship. The authors also develop synthetic products that can be used to effectively hedge longevity risk faced by life insurance and annuity providers who actively hold portfolios of life insurance products. Models are derived using South African data. The authors also derive closed-form expressions for hedge ratios associated with synthetic products written on life insurance contracts as this will provide a natural way of immunizing the associated portfolios. The authors further show how to address the current liquidity challenges in the longevity market by devising longevity swaps and develop pricing and hedging algorithms for longevity-linked securities. The use of a cointergrating relationship improves the model fitting process, as all the VECMs and RS-VECMs yield greater criteria values than their vector autoregressive model (VAR) and regime-switching vector autoregressive model (RS-VAR) counterpart’s, even though there are accruing parameters involved.

The market model adopted from Ngai and Sherris (2011) is a cointegration RS-VECM for this enables both short-term fluctuations, through the AR(1) and long-run equilibria using a cointegration relationship (Johansen, 1988, 1995a, 1995b), with a heteroskedasticity through the use of regime-switching. The RS-VECM is seen to have the best fit for Australian data under various model selection criteria by Sherris and Zhang (2009). Harris (1997) (Sajjad et al., 2008) also fits a regime-switching VAR model using Australian (UK and US) data to four key macroeconomic variables (market stock indices), showing that regime-switching is a significant improvement over autoregressive conditional heteroscedasticity (ARCH) and generalised autoregressive conditional heteroscedasticity (GARCH) processes in the account for volatility, evidence similar to that of Sherris and Zhang (2009) in the case of Exponential Regressive Conditional Heteroscedasticity (ERCH). Ngai and Sherris (2011) and Sherris and Zhang (2009) also fit a VAR model to Australian data with simultaneous regime-switching across many economic and financial series.

The authors develop a longevity swap using nighttime data instead of usual income measures as it yields statistically accurate results. The authors also develop longevity derivatives and annuities including variable annuities with guaranteed lifetime withdrawal benefit (GLWB) and inflation-indexed annuities. Improved market and mortality models are developed and estimated using South African data to model the underlying risks. Macroeconomic variables dependence is modeled using a cointegrating VECM as used in Ngai and Sherris (2011), which enables both short-run dependence and long-run equilibrium. Longevity swaps provide protection against longevity risk and benefit the most from hedging longevity risk. Longevity bonds are also effective as a hedging instrument in life annuities. The cost of hedging, as reflected in the price of longevity risk, has a statistically significant effect on the effectiveness of hedging options.

This study relied on secondary data partly reported by independent institutions and the government, which may be biased because of smoothening, interpolation or extrapolation processes.

An examination of South Africa’s mortality based on industry experience in comparison to population mortality would demand confirmation of the analysis in this paper based on Belgian data as well as other less developed economies. This study shows that to provide inflation-indexed life annuities, there is a need for an active market for hedging inflation in South Africa. This would demand the South African Government through the help of Actuarial Society of South Africa (ASSA) to issue inflation-indexed securities which will help annuities and insurance providers immunize their portfolios from longevity risk.

In South Africa, there is an infant market for inflation hedging and no market for longevity swaps. The effect of not being able to hedge inflation is guaranteed, and longevity swaps in annuity products is revealed to be useful and significant, particularly using developing or emerging economies as a laboratory. This study has shown that government issuance or allowing issuance, of longevity swaps, can enable insurers to manage longevity risk. If the South African Government, through ASSA, is to develop a projected mortality reference index for South Africa, this would allow the development of mortality-linked securities and longevity swaps which ultimately maximize the social welfare of life assurance policy holders.

The paper proposes longevity swaps and static hedging because they are simple, less costly and practical with feasible applications to the South African market, an economy of over 50 million people. As the market for MLS develops further, dynamic hedging should become possible.

The present article aims to estimate an autoregressive vector model covering the period of 1990–2021 to analyze the effect of public spending and monetary supply increases in economic activity in Morocco.

A literature review on the policy of recovery with fiscal and monetary tools and its theoretical foundations was established. Then, an empirical study on the Moroccan context was executed to study the effectiveness of these instruments in Morocco from 1990 to 2021, using autoregressive vector modeling.

The results present a state of a positive relationship and statistical significance of public spending, money supply and economic growth. The impulse response function analysis and the forecast error variance decomposition showed that public spending does not have a large impact on gross domestic product, while the money supply has a real power to stimulate the growth of economic activity in Morocco.

This study aims to demonstrate the positive effect of the coordination of public spending and monetary supply increases on gross domestic product in Morocco. Additionally, the analysis using vector autoregressive modeling, impulse response functions, variance decomposition techniques and causality tests, provides crucial insights to guide researchers, practitioners and policymakers in developing more effective and resilient economic strategies. The findings from this study not only illuminate immediate recovery strategies but also contribute to strengthening the resilience of economies against potential future shocks.

The Russian invasion of Ukraine generated unprecedented panic in the European financial system. As expected, the European Union (EU) felt most of the negative effects of the war due to geographical proximity to Ukraine and energy dependence on Russia. This study aims to investigate the influence of Brent crude oil (BCO), Dutch Title Transfer Facility Natural Gas, and CBOE Volatility Index (VIX) on Deutscher Aktien Index (DAX), Austrian Traded Index (ATX) and Milano Indice di Borsa (FTSEMIB). The German, Austrian and Italian equity indexes were chosen due to the heavy dependence of these countries on Russian gas and oil.

The data cover the period from November 24, 2021, to June 24, 2022, including five months of the Russia–Ukraine war. To generate the intended results, vector autoregressive, structural vector autoregressive, vector error correction model, Johansen test and Granger causality test were used.

The results highlight that natural gas and the VIX carried negative effects on DAX, ATX and FTSEMIB. The BCO was expected to have influenced three selected equity indexes, while the results suggest that it was priced only in ATX.

This research provides modest evidence for the policymakers on the systemic risk that Russian gas has for the EU equity markets. From a managerial perspective, changes in oil and gas prices are a permanently integral part of portfolio risk analysis.

The aim of this chapter is to assess the real exchange rate misalignments. A smooth transition autoregressive model (STAR) is used for Tunisian exchange market. This model allows us to see whether these differences are temporary or persistent over the period 1975–2012. We start by defining the exchange rate’s fundamental determinants to provide the equilibrium exchange rate value. Then, we study the observed exchange rate adjustment toward its equilibrium level. Vector autoregressive model and vector error correction model are applied to characterize the joint dynamics of variables in the long run. The results indicate a long-run relationship between variables. In order to consider the nonlinearity for better results, we will move to nonlinear smooth transition model. We found there is a high degree of exchange rate misalignment. We recognized that this difference decreases in the long run and disappears at the end.

Predicting commodity futures trading volumes represents an important matter to policymakers and a wide spectrum of market participants. The purpose of this study is to concentrate on the energy sector and explore the trading volume prediction issue for the thermal coal futures traded in Zhengzhou Commodity Exchange in China with daily data spanning January 2016–December 2020.

The nonlinear autoregressive neural network is adopted for this purpose and prediction performance is examined based upon a variety of settings over algorithms for model estimations, numbers of hidden neurons and delays and ratios for splitting the trading volume series into training, validation and testing phases.

A relatively simple model setting is arrived at that leads to predictions of good accuracy and stabilities and maintains small prediction errors up to the 99.273th quantile of the observed trading volume.

The results could, on one hand, serve as standalone technical trading volume predictions. They could, on the other hand, be combined with different (fundamental) prediction results for forming perspectives of trading trends and carrying out policy analysis.

This research paper uses a novel methodological approach to investigate the spillover effects among the key sectors of the US economy.

The paper links the US sectors via a node theoretic scheme based on a general equilibrium framework, whereas it estimates the general equilibrium equation as a Global Vector Autoregressive process, taking into consideration the potential existence of dominant units.

Based on our findings, the dominant sector in the US economy, for the period 1992–2015, is the sector of information technology, finance and communications, a fact that gives credence to the view that the US economy is a service-driven economy. In addition, the US economy seems to benefit by the increased labour mobility across knowledge-intensive sectors, thus avoiding the ‘employment trap’ which in turn enabled the US economy to overcome the financial crisis of 2007.

Firstly, the paper models by means of a network approach which is based on a general equilibrium framework, the linkages between the US sectors while treating the sector of information, technology, communications and finance as dominant, as dictated by its degree of centrality in the network structure. Secondly, the paper offers a robustness analysis regarding both the existence and the identification of dominant sectors (nodes) in the US economy. Thirdly, the paper studies a wide period, namely 1992–2015, fully capturing the recent global recession, while acknowledging the impact of the global crisis through the introduction of the relevant exogenous dummy variables; Lastly and most importantly, it is the first study to apply the GVAR approach in a network general equilibrium framework at the sectoral level.