A fractional cointegration var analysis of exchange rate dynamics

In their seminal work, Baillie and Bollerslev (1994) carried out an analysis of deviations from the cointegrating relationship of seven important exchange rates. They suggested that the exchange rate series possess long memory and therefore such processes could be well described as fractionally integrated processes. Hence, the influence of shocks to the equilibrium exchange rates may only vanish at very long horizons. In this work we analyze the cointegrating structure of five exchange rates to the US dollar, namely the British pound, the Euro, the Swedish Krona, the Canadian Dollar and the Swiss Franc. The series possess long memory and we show that they can be modeled through fractional integration. In fact, standard cointegration is rejected with the more traditional Johansen CVAR methodology. By using the recently introduced Fractionally Cointegrated VAR by Johansen and Nielsen (2012) we provide a cointegrating relationship taking into account fractional integration.     

A model of fractional cointegration, and tests for cointegration using the bootstrap

The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simulate the null hypothesis of non-cointegration in a vector autoregressive modelling framework. The simulations are used to estimate p-values for alternative regression-based test statistics, including the F goodness-of-fit statistic, the Durbin–Watson statistic and estimates of the residual d. The bootstrap distributions are economical to compute, being conditioned on the actual sample values of all but the dependent variable in the regression. The procedures are easily adapted to test stronger null hypotheses, such as statistical independence. The tests are not in general asymptotically pivotal, but implemented by the bootstrap, are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals. As an example, the tests are applied to the series for UK consumption and disposable income. The power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data. The F test performs better in these experiments than the residual-based tests, although the Durbin–Watson in turn dominates the test based on the residual d.     

Unit root and cointegration tests on the efficiency and biasedness of forward exchange rates

This paper analyzes the stationarity of spot and forward exchange rates by testing for the presence of unit roots in the autoregressive process of the exchange rate time series. The results of the unit root and cointegration tests for forward exchange rates of six major currencies are inconsistent with earlier studies by others that found the existence of unit roots but the absence of cointegration. Our results show that realized spot rates are cointegrated with past forward rates. Both Dickey-Fuller and Augmented Dickey-Fuller tests affirm the unbiased forward rate hypothesis for 30- and 90-day forward rates. The Augmented Dickey-Fuller tests on the longer term forward rate, however, reveal the existence of cointegration that leads to the rejection of the hypothesis.     

Bilateral trade flows and exchange rate sensitivity: Evidence from likelihood-based panel cointegration

This paper estimates price and income elasticities for bilateral trade equations between Sweden and her eight major trading partners for the period 1960–2001. The methodology used here is the likelihood-based panel cointegration recently developed in the literature. Evidence is found that depreciation of the SEK is expected to improve the Swedish export sector towards six of her eight major trading partners. Regarding Swedish imports, only in four of the eight cases, the price elasticity indicates that depreciation of the SEK decreases Swedish imports. Considering the Marshall–Lerner condition, this is fulfilled for two of the eight countries in the sample. The income elasticities are found to be positive for all countries in the sample. The policy implications of our results are discussed.     

Multilateral adjustment,regime switching and real exchange rate dynamics

The purpose of this paper is to examine the role of multilateral adjustment to U.S. external imbalances in driving bilateral real exchange rate movements by developing a new regime-switching model that consists of a Markov-switching model with a time-varying transition matrix that depends on a threshold variable. Consequently, the dynamics of the real exchange rate can be modeled in the context of two regimes: one in which multilateral adjustment to large U.S. external imbalances is an important factor driving movements in the real exchange rate and the second in which the real exchange rate is driven mainly by country-specific macroeconomic fundamentals. We apply this model to the bilateral real Canada–U.S. dollar exchange rate and compare its performance to several other alternative models. All of the models are estimated using a Bayesian approach. Our findings suggest that during periods of large U.S. imbalances, an exchange rate model for the real Canada–U.S. dollar exchange rate should allow for multilateral adjustment effects.     

Goodness-of-fit tests for long memory moving average marginal density

This paper addresses the problem of fitting a known density to the marginal error density of a stationary long memory moving average process when its mean is known and unknown. In the case of unknown mean, when mean is estimated by the sample mean, the first order difference between the residual empirical and null distribution functions is known to be asymptotically degenerate at zero, and hence can not be used to fit a distribution up to an unknown mean. In this paper we show that by using a suitable class of estimators of the mean, this first order degeneracy does not occur. We also investigate the large sample behavior of tests based on an integrated square difference between kernel type error density estimators and the expected value of the error density estimator based on errors. The asymptotic null distributions of suitably standardized test statistics are shown to be chi-square with one degree of freedom in both cases of the known and unknown mean. In addition, we discuss the consistency and asymptotic power against local alternatives of the density estimator based test in the case of known mean. A finite sample simulation study of the test based on residual empirical process is also included.     

Panel cointegration tests of the Fisher effect

Most empirical evidence suggests that the Fisher effect, stating that inflation and nominal interest rates should cointegrate with a unit slope on inflation, does not hold, a finding at odds with many theoretical models. This paper argues that these results can be attributed in part to the low power of univariate tests, and that the use of panel data can generate more powerful tests. For this purpose, we propose two new panel cointegration tests that can be applied under very general conditions, and that are shown by simulation to be more powerful than other existing tests. These tests are applied to a panel of quarterly data covering 20 OECD countries between 1980 and 2004. The evidence suggest that the Fisher effect cannot be rejected once the panel evidence on cointegration has been taken into account. Copyright © 2007 John Wiley & Sons, Ltd.     

Value at risk and return in Chinese and the US stock markets: Double long memory and fractional cointegration

Given that the United States is an engine of global stock market while China is the largest emerging market with a cornucopia of anomalies in particular, it is vital to investigate the risk-return relationship in the two markets. This paper brings new insights not only into risk-return tradeoff, but also to the leverage effect, with the application of the fractionally co-integrated vector auto-regression (FCVAR) model capturing the fractional cointegrated relationship and long memory property. Results show that China stock markets own the property of double long memory but the US markets don’t. Most of all, in the US market, a positive risk-return tradeoff exists for the whole sample while after the crisis, even we find the negative relation, it’s not a volatility feedback effect but low risk and high returns. However, there is only a volatility feedback effect in China stock markets. Besides, there is a leverage effect in the US market, while Chinese market exhibits a reverse one, another anomaly, indicating significant difference in the two markets again.     

The exchange rate and macroeconomic determinants: Time-varying transitional dynamics

In this paper, I consider modeling the effects of the macroeconomic determinants on the nominal exchange rate to be channeled through the transition probabilities in a Markovian process. The model posits that the deviation of the exchange rate from its fundamental value alters the market's belief in the probability of the process staying in certain regime next period. This paper further takes into account the ARCH effects of the volatility of the exchange rate. Empirical results generally confirm that fundamentals can affect the evolution of the dynamics of the exchange rate in a nonlinear way through the transition probabilities. In addition, I find that the volatility of the exchange rate is associated with significant ARCH effects which are subject to regime changes.     

Tariff-tax reform and exchange rate dynamics in a monetary economy

Using a dynamic monetary model, this paper analyzes the short- and long-run impacts of a tariff-tax reform on the economy, with attention being paid to short-run fluctuations in exchange rates. When a policy reform is announced and if the public believe that it will decrease excess demand, the domestic currency depreciates now to reflect its future depreciation. On the contrary, the domestic currency immediately appreciates if the public believe that it will increase excess demand. However, if there is a relatively small increase in excess demand, the public may mis-react in the exchange rate market by observing currency depreciation first and then appreciation toward the steady-state rate.     

Numerical distribution functions for unit root and cointegration tests

This paper employs response surface regressions based on simulation experiments to calculate distribution functions for some well-known unit root and cointegration test statistics. The principal contributions of the paper are a set of data files that contain estimated response surface coefficients and a computer program for utilizing them. This program, which is freely available via the Internet, can easily be used to calculate both asymptotic and finite-sample critical values and P-values for any of the tests. Graphs of some of the tabulated distribution functions are provided. An empirical example deals with interest rates and inflation rates in Canada.     

Point optimal tests of the null hypothesis of cointegration

This paper obtains an asymptotic Gaussian power envelope for tests of the null hypothesis of cointegration. In addition, the paper proposes a feasible point optimal cointegration test whose local asymptotic power function is found to be close to the asymptotic Gaussian power envelope.     

Numerical distribution functions of likelihood ratio tests for cointegration

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith ( 1997 ) that allow for the possibility of exogenous variables integrated of order one. The paper calculates critical values that are very much more accurate than those available previously. The principal contributions of the paper are a set of data files that contain estimated asymptotic quantiles obtained from response surface estimation and a computer program for utilizing them. This program, which is freely available via the Internet, can be used to calculate both asymptotic critical values and P-values. Copyright © 1999 John Wiley & Sons, Ltd.     

Generalized empirical likelihood tests in time series models with potential identification failure

We introduce test statistics based on generalized empirical likelihood methods that can be used to test simple hypotheses involving the unknown parameter vector in moment condition time series models. The test statistics generalize those in Guggenberger and Smith [2005. Generalized empirical likelihood estimators and tests under partial, weak and strong identification. Econometric Theory 21 (4), 667–709] from the i.i.d. to the time series context and are alternatives to those in Kleibergen [2005a. Testing parameters in GMM without assuming that they are identified. Econometrica 73 (4), 1103–1123] and Otsu [2006. Generalized empirical likelihood inference for nonlinear and time series models under weak identification. Econometric Theory 22 (3), 513–527]. The main feature of these tests is that their empirical null rejection probabilities are not affected much by the strength or weakness of identification. More precisely, we show that the statistics are asymptotically distributed as chi-square under both classical asymptotic theory and weak instrument asymptotics of Stock and Wright [2000. GMM with weak identification. Econometrica 68 (5), 1055–1096]. We also introduce a modification to Otsu's (2006) statistic that is computationally more attractive. A Monte Carlo study reveals that the finite-sample performance of the suggested tests is very competitive.     

Real exchange rate,stationarity, and economic fundamentals

Using monthly data for the US/UK real exchange rate over the period 1921–2002, we find evidence that the mean reverting tendency of the real exchange rate is stochastic, and regime-dependent. There is one regime over which PPP holds as a long-run equilibrium relation, i.e. a stationary PPP regime, and another regime over which PPP does not hold, i.e. a non-stationary PPP regime. The transition from the non-stationary to the stationary regime is found to be affected by the real interest rate differential, and by the volatility of the nominal exchange rate. The real output differential does not appear to affect the transition probability.     

Balance sheets, exchange rate policy, and welfare

We evaluate the welfare implications of fixed and flexible exchange rate regimes in a small open-economy model that incorporates the financial accelerator coupled with liability dollarization. We solve the model up to a second-order approximation which allows us to rigorously address the relationship between uncertainty and welfare. We identify leverage and debt-to-GDP ratios above which an exchange rate peg is welfare superior to a flexible exchange rate regime. The results indicate that emerging market countries with even moderate levels of foreign currency-denominated debt may find it beneficial to stabilize their exchange rates.     

Market efficiency and cointegration: Some evidence in Pacific-Basin black exchange markets

This paper investigates the efficiency of the black exchange markets in Indonesia, Malaysia, the Philippines, South Korea, Taiwan, and Thailand. The study applies unit root and cointegration tests to examine black exchange market efficiency of Pacific-Basin countries. The generating process of black exchange rates appears to be a random walk. This is consistent with Gupta (1981) and other foreign exchange rate unit root test studies. Johansen cointegration tests are performed for these black exchange markets together with Japan and Singapore. The results suggest that there is at least one unit root among the black market exchange rates. Hence, black exchange markets are not collectively efficient.     

Stable processes of exchange

In this paper we address a long standing gap in economic theory—the gap between claims for the dynamic efficiency of trading in markets, and the findings of formal economic theory, which justify those claims only under restrictive assumptions. We use agent-based methods to study the dynamics of exchange with trading agents who are characterized by several different preference relations. We see that outcomes converge with high probability to Pareto optima in the cases studied, including the well-known example due to Scarf.