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Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

This study proposed an optimal model to examine the relationship between the Bitcoin price and six macroeconomic variables – the Bitcoin price, Standard and Poor's 500 volatility index, US treasury 10-year yield, US consumer price index, gold price and dollar index. It also examined the effectiveness of the vector error correction model (VECM) in analyzing the interrelationship among these variables. The authors employed the following approach: first, the authors sampled the period August 2010–February 2022. This is because Bitcoin achieved a market capitalization of more than US$1 tn over this period, gaining market attention and acceptance from retail, corporate and institutional investors. Second, the authors employed a VECM with the six macroeconomic variables. Finally, the authors expanded the long-run equilibrium relationship (time-invariant cointegration)-based VECM to develop a time-varying cointegration (TVC) VECM. The authors estimated the TVC VECM using the Chebyshev polynomial specification based on various information criteria. The results showed that the Bitcoin price can be modeled with the VECM (p = 1, r = 1). The TVC approach generated more explanatory power for Bitcoin pricing, indicating the effectiveness of the approach for modeling the long-run relationship between Bitcoin price and macroeconomic variables.

The existing literature on the Black-Litterman (BL) model does not offer adequate guidance on how to generate investors’ views in an objective manner. Therefore, the purpose of this paper is to establish a generalized multivariate Vector Error Correction Model (VECM)/Vector Auto-Regressive (VAR)-Dynamic Conditional Correlation (DCC)/Asymmetric DCC (ADCC) framework, and applies it to generate objective views to improve the practicality of the BL model.

This paper establishes a generalized VECM/VAR-DCC/ADCC framework that can be utilized to model multivariate financial time series in general, and produce objective views as inputs to the BL model in particular. To test the VECM/VAR-DCC/ADCC preconditioned BL model’s practical utility, it is applied to a six-asset China portfolio (including one risk-free asset).

With dynamically optimized view confidence parameters, the VECM/VAR-DCC/ADCC preconditioned BL model offers clear advantage over the standard mean-variance method, and provides an automated portfolio optimization alternative to the classic BL approach.

The VECM/VAR-DCC/ADCC framework and its application in the BL model proposed by this paper provide an alternative approach to the classic BL method. Since all the view parameters, including estimated mean return vectors, conditional covariance matrices and pick matrices, are generated in the VECM/VAR and DCC/ADCC preconditioning stage, the model improves the objectiveness of the inputs to the BL stage. In conclusion, the proposed model offers a practical choice for automated portfolio balancing and optimization in a China context.

Conventional methods to test for long-term PPP based on the theory of cointegration are typically undertaken in the framework of vector error correction models (VECM). The standard approach in the use of VECMs is to employ a model of full-order, which assumes nonzero entries in all the coefficient matrices. But, the use of full-order VECM models may lead to incorrect inferences if zero entries are required in the coefficient matrices. Specifically, if we wish to test for indirect causality, instantaneous causality, or Granger non-causality, and employ “overparameterised” full-order VECM models that ignore entries assigned a priori to be zero, then the power of statistical inference is weakened and the resultant specifications can produce different conclusions concerning the cointegrating relationships among the variables. In this paper, an approach is presented that incorporates zero entries in the VECM analysis. This approach is a more straightforward and effective means of testing for causality and cointegrating relations. The paper extends prior work on PPP through an investigation of causality between the U.S. Dollar and the Japanese Yen. The results demonstrate the inconsistencies that can arise in the area and show that bi-directional feedback exists between prices, interest rates and the exchange rate such that adjustment mechanisms are complete within the context of PPP.

Establishing the strength of a novel variable–mortgage debt as a fraction of US gross domestic product (GDP)–on forecasting capitalisation rates in both the US office and multifamily sectors.

The authors specify a vector error correction model (VECM) to the data. VECM are used to address the nonstationarity issues of financial variables while maintaining the information embedded in the levels of the data, as opposed to their differences. The cap rate series used are from Green Street Advisors and represent transaction cap rates which avoids the problem of artificial smoothness found in appraisal-based cap rates.

Using a VECM specified with the novel variable, unemployment and past cap rates contains enough information to produce more robust forecasts than the traditional variables (return expectations and risk premiums). The method is robust both in and out of sample.

This has direct implications for governmental policy, offering a path to real estate price stability and growth through mortgage access–functions largely influenced by the Fed and the quasi-federal agencies Fannie Mae and Freddie Mac. It also offers a timely alternative to interest rate-based forecasting models, which are likely to be less useful as interest rates are to be held low for the foreseeable future.

This study offers a new and highly explanatory variable to the literature while being among the only to model either (1) transactional cap rates (versus appraisal) (2) out-of-sample data (versus in-sample) (3) without the use of the traditional variables thought to be integral to cap rate modelling (return expectations and risk premiums).

The purpose of this paper is to provide an extensive review of the monetary model of exchange rate determination which is the main theoretical framework on analyzing exchange rate behavior over the last 40 years. Furthermore, we test the flexible price monetarist variant and the sticky price Keynesian variant of the monetary model. We conduct our analysis employing a sample of 14 advanced economies using annual data spanning the period 1880–2012.

The theoretical background of the paper relies on the monetary model to the exchange rate determination. We provide a thorough econometric analysis using a battery of unit root and cointegration testing techniques. We test the price-flexible monetarist version and the sticky-price version of the model using annual data from 1880 to 2012 for a group of industrialized countries.

We provide strong evidence of the existence of a nonlinear relationship between exchange rates and fundamentals. Therefore, we model the time-varying nature of this relationship by allowing for Markov regime switches for the exchange rate regimes. Modeling exchange rates within this context can be motivated by the fact that the change in regime should be considered as a random event and not predictable. These results show that linearity is rejected in favor of an MS-VECM specification which forms statistically an adequate representation of the data. Two regimes are implied by the model; the one of the estimated regimes describes the monetary model whereas the other matches in most cases the constant coefficient model with wrong signs. Furthermore it is shown that depending on the nominal exchange rate regime in operation, the adjustment to the long run implied by the monetary model of the exchange rate determination came either from the exchange rate or from the monetary fundamentals. Moreover, based on a Regime Classification Measure, we showed that our chosen Markov-switching specification performed well in distinguishing between the two regimes for all cases. Finally, it is shown that fundamentals are not only significant within each regime but are also significant for the switches between the two regimes.

The results are of interest to practitioners and policy makers since understanding the evolution and determination of exchange rates is of crucial importance. Furthermore, our results are linked to forecasting performance of exchange rate models.

The present analysis extends previous analyses on exchange rate determination and it provides further support in favor of the monetary model as a long-run framework to understand the evolution of exchange rates.

The purpose of this paper is to measure the effectiveness of the hedging with futures currency contracts. Measuring the effectiveness of hedging has become mandatory for Indian companies as the new Indian accounting standards, Ind-AS, specify that the effectiveness of hedges taken by the companies should be evaluated using quantitative methods but leaves it to the company to choose a method of evaluation.

The paper compares three models for evaluating the effectiveness of hedge – ordinary least square (OLS), vector error correction model (VECM) and dynamic conditional correlation multivariate GARCH (DCC-MGARCH) model. The OLS and VECM are the static models, whereas DCC-MGARCH is a dynamic model.

The overall results of the study show that dynamic model (DCC-MGARCH) is a better model for calculating the hedge effectiveness as it outperforms OLS and VECM models.

The new Indian accounting standards (Ind-AS) mandates the calculation of hedge effectiveness. The results of this study are useful for the treasurers in identifying appropriate method for evaluation of hedge effectiveness. Similarly, policymakers and auditors are benefitted as the study provides clarity on different methods of evaluation of hedging effectiveness.

Many previous studies have evaluated the efficiency of the Indian currency futures market, but with rising importance of hedging in the Indian companies, Reserve Bank of India’s initiatives and encouragement for the use of futures for hedging the currency risk and now the mandatory accounting requirement for measuring hedging effectiveness, it has become more relevant to evaluate the effectiveness of hedge. To the authors’ best knowledge, this is one of the first few papers which evaluate the effectiveness of the currency future hedging.

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 “Fed Model” postulates a cointegrating relationship between the equity yield on the S&P 500 and the bond yield. We evaluate the Fed Model as a vector error correction forecasting model for stock prices and for bond yields. We compare out-of-sample forecasts of each of these two variables from a univariate model and various versions of the Fed Model including both linear and nonlinear vector error correction models. We find that for stock prices the Fed Model improves on the univariate model for longer-horizon forecasts, and the nonlinear vector error correction model performs even better than its linear version.

Primarily based on Alonso’s bid-rent model, the purpose of this paper is to examine the dynamics of the Singapore’s overall retail rental market by adopting a vector error correction model (VECM) estimation.

This paper uses the proxy for the overall retail rental value, which is indicated by a combination of the shop rent index from 2004 to 2013 and the retail rent index (RRI) in 2014, maintained by the Urban Redevelopment Authority (URA). The independent factors are the real gross domestic product (GDP), monthly earnings of individuals and vacancy rates (VR).

Such a behavioral model examines the dynamic structures that overshoot and/or diverge from equilibrium.

The variables LOGGDP and VR are co-integrated of order one, I(1), while variables LOGME and LOGSRI are co-integrated of order two, I(2), to enable them to be employed in the VECM model.

The VECM model shows a good fit that allows the error correction term (ecm) together with the economic, financial and rental variables to jointly explain about 79.2 percent of the variation in the overall RRI. With a positive CoinEq1 coefficient that is positive and statistically significant at 5 percent level, it would take a long time for the system to return to its equilibrium once it has been shocked. Another variable that shows significant explanatory relationships includes past rents (index points) in the second order lags [D(LOGSRI(−2))]. The variable [D(LOGGDP(−3))], with a significant t-statistic value at 2.916, also helps to explain the changes in the overall rents.

This paper highlights the importance of the first and third differences of the lagged macroeconomic variables of the monthly earnings of individuals is moderately significant. The VR in the first and second differences is significant in accounting for the variation in changes of overall retail rents with their t-statistics values being above 3.0. It is thus meaningful for policy makers to so enhance their in-depth understanding.

This paper fulfills an identified need to study how the results from the ex post forecasting estimates from the VECM for overall retail rents in Singapore can be enabled.