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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 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 paper's objectives are: to address the issue of cointegration (efficient market hypothesis) between Greek spot and futures markets over the period of the crisis, 1999‐2001; to investigate the short‐run and long‐run efficiency of the FTSE/ASE‐20 stock index futures contract and FTSE/ASE Mid 40 stock index futures contract traded on the Athens Derivatives Exchange (ADEX).

This paper examines efficiency of the Greek stock index futures market from 1999 to 2001. A variety of econometric models are employed to test for cointegration between prices. The paper uses daily data from the Athens Stock Exchanges (ASEs) and the ADEX. A more detailed discussion on the causal relationship between spot and futures price in ADEX is obtained by using the impulse response functions of the vector error‐correction model (to study the behaviour of series from real shocks).

The results show that the Greek futures and spot prices form a stable long‐run relationship. For both FTSE/ASE‐20 and FTSE/ASE Mid 40, futures markets play a price discovery role, implying that futures prices contain useful information about spot prices. Futures markets are informationally more efficient than underlying stock markets in Greece.

The results have important implications for both traders and speculators. The findings are strongly recommended to financial managers dealing with Greek stock index futures.

The contribution of this paper is to provide evidence using data from the early stage of the ADEX (started its official operation on 27 August 1999). It also investigates whether the hypotheses exist after the dramatic rise of ASE stock prices.

Cryptocurrency markets are notoriously noisy, but not all markets might behave in the exact same way. Therefore, the aim of this paper is to investigate which one of the cryptocurrency markets contributes the most to the common volatility component inherent in the market.

The paper extracts each of the cryptocurrency's markets' latent volatility using a stochastic volatility model and, subsequently, models their dynamics in a fractionally cointegrated vector autoregressive model. The authors use the refinement of Lien and Shrestha (2009, J. Futures Mark) to come up with unique Hasbrouck (1995, J. Finance) information shares.

The authors’ findings indicate that Bitfinex is the leading market for Bitcoin and Ripple, while Bitstamp dominates for Ethereum and Litecoin. Based on the dominant market for each cryptocurrency, the authors find that the volatility of Bitcoin explains most of the volatility among the different cryptocurrencies.

The authors’ findings are limited by the availability of the cryptocurrency data. Apart from Bitcoin, the data series for the other cryptocurrencies are not long enough to ensure the precision of the authors’ estimates.

To date, only price discovery in cryptocurrencies has been studied and identified. This paper extends the current literature into the realm of volatility discovery. In addition, the authors propose a discrete version for the evolution of a markets fundamental volatility, extending the work of Dias et al. (2018).

This paper aims to provide a reliable statistical model for time-series prices of short-stay accommodation and overnight stays in a eurozone country.

Exploiting the unit root feature, the cointegrated vector autoregressive model solves the problem of misspecification. Subsequently, variables are modelled for a long-run equilibrium with included deterministic variables.

The empirical results confirmed that overnight stays for foreign tourists were positively associated with the prices of short-stay accommodation.

The major limitation lies in the data vector and its time horizon; its extension could provide a more specific view.

Findings can assist practitioners and hotel executives by providing the information and rationale for adopting seasonal volatility pricing. Structural breaks in price time-series have practical implications for setting seasonal-pricing schemes. Tourists could benefit either from greater price stability or from differentiated seasonal prices, which are important in the promotion of the price attractiveness of the tourist destination.

The originality of the paper lies in the applied unit root econometrics for tourism price time-series modelling and the prediction of short-stay accommodation prices.

The purpose of this study is to explore the intricate relationship between oil prices, house prices in the UK and Norway, and the mediating role of gold and stock prices in both the short- and long-term, unraveling these complex linkages by employing an empirical approach.

This study benefits from a comprehensive set of econometric tools, including a multiequation vector autoregressive (VAR) system, Granger causality test, impulse response function, variance decomposition and a single-equation autoregressive distributed lag (ARDL) system. This rigorous approach enables to identify both short- and long-run dynamics to unravel the intricate linkages between Brent oil prices, housing prices, gold prices and stock prices in the UK and Norway over the period from 2005:Q1 to 2022:Q2.

The findings indicate that rising oil prices negatively impact house prices, whereas the positive influence of stock market performance on housing is more pronounced. A two-way causal relationship exists between stock market indices and house prices, whereas a one-way causal relationship exists from crude oil prices to house prices in both countries. The VAR model reveals that past housing prices, stock market indices in each country and Brent oil prices are the primary determinants of current housing prices. The single-equation ARDL results for housing prices demonstrate the existence of a long-run cointegrating relationship between real estate and stock prices. The variance decomposition analysis indicates that oil prices have a more pronounced impact on housing prices compared with stock prices. The findings reveal that shocks in stock markets have a greater influence on housing market prices than those in oil or gold prices. Consequently, house prices exhibit a stronger reaction to general financial market indicators than to commodity prices.

This study may have several limitations. First, the model does not include all relevant macroeconomic variables, such as interest rates, unemployment rates and gross domestic product growth. This omission may affect the accuracy of the model’s predictions and lead to inefficiencies in the real estate market. Second, this study does not consider alternative explanations for market inefficiencies, such as behavioral finance factors, information asymmetry or market microstructure effects. Third, the models have limitations in revealing how predictors react to positive and negative shocks. Therefore, the results of this study should be interpreted with caution.

These findings hold significant implications for formulating dynamic policies aimed at stabilizing the housing markets of these two oil-producing nations. The practical implications of this study extend to academics, investors and policymakers, particularly in light of the volatility characterizing both housing and commodity markets. The findings reveal that shocks in stock markets have a more profound impact on housing market prices compared with those in oil or gold prices. Consequently, house prices exhibit a stronger reaction to general financial market indicators than to commodity prices.

These findings could also serve as valuable insights for future research endeavors aimed at constructing models that link real estate market dynamics to macroeconomic indicators.

Using a variety of econometric approaches, this paper presents an innovative empirical analysis of the intricate relationship between euro property prices, stock prices, gold prices and oil prices in the UK and Norway from 2005:Q1 to 2022:Q2. Expanding upon the existing literature on housing market price determinants, this study delves into the role of gold and oil prices, considering their impact on industrial production and overall economic growth. This paper provides valuable policy insights for effectively managing the impact of oil price shocks on the housing market.

The authors aim to report empirical linkages between the US and Brazil, Russia, India and China (BRIC) financial stress indices catalyzing catalyzing dependent economic policy initiatives (an extended version of Singh and Singh, 2017a).

Initially, the study develops financial stress indices for the respective BRIC financial markets. Later, it captures linkages among the said US-BRIC indices by using Johansen cointegration, vector autoregression/vector error correction models (VECM), generalized impulse response functions, Toda–Yamamoto Granger causality, variance decomposition analyses and bivariate generalized autoregressive conditional heteroskedasticity (GARCH) model under constant conditional correlation framework, in general. Markov regime switching and efficient causality tests proposed by Hill (2007) are also used.

Overall, there are both short-run and long-run dynamic interactions observed between the US and Indian financial stress indices. For rest of the markets, only short-run interactions are found to be in existence. The time-varying co-movement coefficients report financial contagion impact of the US financial crisis on Russian and Indian financial systems only. Contrary to this, Brazilian and Chinese financial systems are largely exhibiting interdependence with the US financial system. Efficient causality tests report indirect impact of the Russian financial system on Brazilian via auxiliary Indian financial system.

The present study is the first of its kind capturing linkages among the US-BRIC financial stress indices by using diverse econometric models. The results support different market participants and policymakers in understanding effectiveness and implementation of economic policies while considering their cross-market interactions as well.

Investment in Australia’s property market, whether directly or indirectly through Australian real estate investment trusts (A-REITs), grew remarkably since the 1990s. The degree of segregation between the property market and other financial assets, such as shares and bonds, can influence the diversification benefits within multi-asset portfolios. This raises the question of whether direct and indirect property investments are substitutable. Establishing how information transmits between asset classes and impacts the predictability of returns is of interest to investors. The paper aims to discuss these issues.

The authors study the linkages between direct and indirect Australian property sectors from 1985 to 2013, with shares and bonds. This paper employs an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process to de-smooth a valuation-based direct property index. The authors establish directional lead-lag relationships between markets using bi-variate Granger causality tests. Johansen cointegration tests are carried out to examine how direct and indirect property markets adjust to an equilibrium long-term relationship and short-term deviations from such a relationship with other asset classes.

The authors find the use of appraisal-based property data creates a smoothing bias which masks the extent of how information is transmitted between the indirect property sector, stock and bond markets, and influences returns. The authors demonstrate that an ARFIMA process accounting for a smoothing bias up to lags of four quarters can overcome the overstatement of the smoothing bias from traditional AR models, after individually appraised constituent properties are aggregated into an overall index. The results show that direct property adjusts to information transmitted from market-traded A-REITs and stocks.

The study shows direct property investments and A-REITs are substitutible in a multi-asset portfolio in the long and short term.

The authors apply an ARFIMA(p,d,q) model to de-smooth Australian property returns, as proposed by Bond and Hwang (2007). The authors expect the findings will contribute to the discussion on whether direct property and REITs are substitutes in a multi-asset portfolio.

This research aims to ascertain the extent to which the coronavirus disease 2019 (COVID-19) epidemic affected the relationship between inflation and real estate investment trusts (REITs) returns in South Africa.

This research used the Johansen cointegration test and effective test in establishing if there is a long-run cointegrating equation between the variables. To ascertain if COVID-19 resulted in a different relationship regime between inflation and REITs returns, the sequential Bai–Perron method was used.

Between December 2013 and July 2022, there was no evidence of a long-run relationship between inflation and REITs returns, and a restricted vector autoregressive (VAR) model with a period lag for each variable best describing the relationship. Using the sequential Bai–Perron method, for one break, the results show February 2020 as a structural break in the relationship. A cointegrating equation is also found for the period before the structural break and another after the break. Interestingly, the relationship is negative before the break and a new positive relationship (regime) is confirmed after the noted break.

This research helps REITs stakeholders to position themselves in light of any changes to macroeconomic activity within South Africa.

This is one of the first studies to test inflation relationship with REITs returns in South Africa and the effects of COVID-19 thereof. This research helps REITs stakeholders to position themselves in light of any changes to macroeconomic activity within South Africa.