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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.

This paper proposes an efficient test designed to have power against alternatives where the error correction term follows a Markov switching dynamics. The adjustment to long run equilibrium is different in different regimes characterised by the hidden state Markov chain process. Using a general nonlinear MS-ECM framework, we propose an optimal test for the null of no cointegration against an alternative of a globally stationary MS cointegration. The Monte Carlo studies demonstrate that our proposed tests display superior powers compared to the linear tests. In an application to price-dividend relationships, our test is able to find cointegration while linear based tests fail to do so.

Purpose – This chapter aims to investigate the stock market comovements between Mexico and the world capital market using nonlinear modeling tools.

Methodology/approach – We apply recent nonlinear cointegration and nonlinear error correction models (NECMs) to investigate the comovements between stock prices over the recent period.

Findings – While the previous literature only highlights some evidence of time-varying comovements, our chapter aims to specify the mechanism characterizing the comovement process through the comparison of two nonlinear error correction models (NECMs). It shows a nonlinear relationship between stock prices that are activated per regime.

Originality – Studying the integration hypothesis between stock markets over the recent financial crisis, our findings highlight strong evidence of significant comovements that explain the global collapse of stock markets in 2008–2009.

This chapter develops an asymptotic theory for a general transformation model with a time trend, stationary regressors, and unit root nonstationary regressors. This model extends that of Han (1987) to incorporate time trend and nonstationary regressors. When the transformation is specified as an identity function, the model reduces to the conventional cointegrating regression, possibly with a time trend and other stationary regressors, which has been studied in Phillips and Durlauf (1986) and Park and Phillips (1988, 1989). The limiting distributions of the extremum estimator of the transformation parameter and the plug-in estimators of other model parameters are found to critically depend upon the transformation function and the order of the time trend. Simulations demonstrate that the estimators perform well in finite samples.

During the global financial crisis of 2008–2009, most developed and emerging economies and financial markets have recorded important financial losses. Those economies have experienced momentous corrections, and their assets were significantly devaluated, implying many losses and bankruptcies for banks, investors, and firms. Overall, despite continuing efforts made by governments and central banks to support their financial systems, most financial markets (stock markets, derivative markets, monetary markets, and currency markets) have been strongly affected by this crisis. Furthermore, the rapid transmission of the US subprime crisis to several European and Asian developed and emerging countries and the transformation into a global financial and economic crisis have revealed a high level of financial integration and linkage with the US market. The financial shocks have also induced negative feedbacks to macroeconomic indicators, suggesting significant relationships between financial markets and macroeconomies.

In this chapter the author studies the capital market efficiency hypothesis and checks whether the stock price adjustment dynamics is instantaneous, continuous, and linear or not. In particular, the author proposes to analyze the stock price evolution while taking into account the presence of transaction costs, the coexistence of heterogeneous investors, and the interdependence between stock markets. On the one hand, he provides strong evidence to suggest that the efficiency hypothesis is rejected. On the other hand, he proves that the stock index adjustment is rather discontinuous, asymmetrical, and nonlinear. Using threshold cointegration techniques, he proposes a new nonlinear modeling to reproduce the CAC40 adjustment dynamics that not only replicates the French market adjustment dynamics in the presence of market frictions but also captures the interdependence between the French and American stock markets, highlighting the reaction of French shareholders in relation to the changes in the behaviour of American speculators.

This paper proposes a Bayesian procedure to investigate the purchasing power parity (PPP) utilizing an exponential smooth transition vector error correction model (VECM). Employing a simple Gibbs sampler, we jointly estimate the cointegrating relationship along with the nonlinearities caused by the departures from the long-run equilibrium. By allowing for nonlinear regime changes, we provide strong evidence that PPP holds between the US and each of the remaining G7 countries. The model we employed implies that the dynamics of the PPP deviations can be rather complex, which is attested to by the impulse response analysis.