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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.

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.

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 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.

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.

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.

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.

This article proposes a new approach to detecting the presence of common cyclical features when several time series are sampled at different frequencies. We generalize the common-frequency approach introduced by Engle and Kozicki (1993) and Vahid and Engle (1993). We start with the mixed-frequency VAR representation investigated in Ghysels (2012) for stationary time series. For non-stationary time series in levels, we show that one has to account for the presence of two sets of long-run relationships. The first set is implied by identities stemming from the fact that the differences of the high-frequency I (1) regressors are stationary. The second set comes from possible additional long-run relationships between one of the high-frequency series and the low-frequency variables. Our transformed vector error-correction model (VECM) representations extend the results of Ghysels (2012) and are important for determining the correct set of variables to be used in a subsequent common cycle investigation. This fact has implications for the distribution of test statistics and for forecasting. Empirical analyses with quarterly real gross national product (GNP) and monthly industrial production indices for, respectively, the United States and Germany illustrate our new approach. We also conduct a Monte Carlo study which compares our proposed mixed-frequency models with models stemming from classical temporal aggregation methods.

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.