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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 “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.

It is widely documented that while contemporaneous spot and forward financial prices trace each other extremely closely, their difference is often highly persistent and the conventional cointegration tests may suggest lack of cointegration. This chapter studies the possibility of having cointegrated errors that are characterized simultaneously by high persistence (near-unit root behavior) and very small (near zero) variance. The proposed dual parameterization induces the cointegration error process to be stochastically bounded which prevents the variables in the cointegrating system from drifting apart over a reasonably long horizon. More specifically, this chapter develops the appropriate asymptotic theory (rate of convergence and asymptotic distribution) for the estimators in unconditional and conditional vector error correction models (VECM) when the error correction term is parameterized as a dampened near-unit root process (local-to-unity process with local-to-zero variance). The important differences in the limiting behavior of the estimators and their implications for empirical analysis are discussed. Simulation results and an empirical analysis of the forward premium regressions are also provided.

The Factor-augmented Error-Correction Model (FECM) generalizes the factor-augmented VAR (FAVAR) and the Error-Correction Model (ECM), combining error-correction, cointegration and dynamic factor models. It uses a larger set of variables compared to the ECM and incorporates the long-run information lacking from the FAVAR because of the latter’s specification in differences. In this paper, we review the specification and estimation of the FECM, and illustrate its use for forecasting and structural analysis by means of empirical applications based on Euro Area and US data.

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.

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 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.

This chapter advances a panel vector autoregressive/vector error correction model (PVAR/PVECM) framework for purposes of examining the sources and determinants of cross-country variations in macroeconomic performance using large cross-country data sets. Besides capturing the simultaneity of the potential determinants of cross-country variations in macroeconomic performance and carefully separating short- from long-run dynamics, the PVAR/PVECM framework advanced allows to capture a variety of other features typically present in cross-country macroeconomic data, including model heterogeneity and cross-sectional dependence. We use the PVAR/PVECM framework we advance to reexamine the dynamic interrelation between investment in physical capital and output growth. The empirical findings for an unbalanced panel of 90 countries over the time period from at most 1950 to 2000 suggest for most regions of the world surprisingly strong support for a long-run relationship between output and investment in physical capital that is in line with neoclassical growth theory. At the same time, the notion that there would be even a long-run (let alone short-run) causal relation between investment in physical capital and output (or vice versa) is strongly refuted. However, the size of the feedback from output growth to investment growth is estimated to strongly dominate the size of the feedback from investment growth to output growth.

Purpose – The purpose of this chapter is to present an investigation on the dynamic linkages between global macro hedge funds and traditional financial assets of developed and emerging markets.

Methodology/approach – To explore relationships among these price indices, we analyse Granger causality and vector autoregression (VAR) dynamics through impulse response functions. Besides, multivariate cointegration is used to know long-term relationships between assets and allows risk-averse investors to reduce uncertainty. Finally, a vector error correction model (VECM) provides active asset managers the opportunity to anticipate short-term price movements.

Findings – Our results show that in a Granger causality sense, we observe long- and short-term relationships between global macro hedge funds and traditional financial assets for Canada, France and Germany. This implies that opportunities for international portfolio diversification are significantly lower for countries having relationships between assets. For Canada, France and Germany, the risk-averse investors can reduce their long-term volatility by investing according to the cointegrating vector, whereas active managers can benefit from the knowledge of short-term asset price movements. The VEC Pairwise Granger causality in the short term confirms our analysis of causality according to VAR models.

Originality/value of paper – These results are original because they help the investor to understand the dynamics of the relationship between global macro hedge funds and traditional financial assets.