Nonlinear dynamics in foreign exchange rates

This paper investigates whether the behavior of real and nominal foreign exchange rates as well as interest rates are governed by nonlinear dynamics; it also explores whether observed deviations from parity conditions exhibit nonlinear dependence. Standard statistical tests for randomness, such as autocorrelation tests, have low power against a large class of deterministic, nonlinear processes. Discerning nonrandomness of innovations in exchange rates is important for a variety of reasons. For example, many models of international asset pricing assume exchange rates to follow a random walk. Furthermore, nonlinear patterns in deviations from various exchange rate parities have implications for the existence of a time-varying foreign exchange risk premium. With the use of the BDS statistic and a correlation dimension analysis, this paper's primary findings are that (1) foreign exchange markets have become increasingly complex and therefore less amenable to forecasting over time; (2) although forward exchange risk premia are statistically significant and display a deterministic structure, this structure is complex and therefore not easily discernible; and (3) innovations in real exchange rates are consistent with a Purchasing Power Parity equilibrium.     

The cointegration relationships among G-7 foreign exchange rates

A search method is applied to foreign exchange rates of G-7 countries, in terms of the US dollar, to estimate cointegration relationships. The method searches numerically, by strictly following the definition of the cointegration, a particular linear combination of nonstationary series in order to make it a stationary series. The list of those exchange rates which are cointegrated from the new method is very different from those derived from the conventional maximum likelihood estimation or ordinary least squares methods. The new method also provides confidence intervals for cointegration coefficients. From the confidence intervals, it is determined that certain G-7 currencies expressed in terms of the mark or the pound become stationary.     

Identifying monetary policy in a small open economy under flexible exchange rates

Previous empirical study on the effects of monetary policy shocks in small open economies has generated puzzling dynamic responses in various macroeconomic variables. This paper argues that these puzzles derive from an identification of monetary policy that is inappropriate for such economies. To remedy this, it is proposed that a structural model be estimated to explicitly account for the features of the small open economy. Such a model is applied to Canada with tightly estimated results overall. The dynamic responses to the identified monetary policy shock are consistent with standard theory and highlight the exchange rate as a transmission mechanism.     

The impact of jump risks on nominal interest rates and foreign exchange rates

This article investigates the relationship between the nominal interest rate and inflation and also the forward exchange rate under a general specification of the underlying processes govering the foreign exchange rate. There are three distinct risks that affect the relation between the real rate of interest and the nominal rate namely, consumption risk, diffusion risk, and the existence of jump risks of inflation. Jump risks lower the nominal interest rate because of jump hedging of a nominal bond. The forward exchange rate depends on the expected depreciation of the domestic currency as well as these three risks. As the domestic jump risks increase, the domestic nominal interest rate decreases and the forward exchange rate decreases.     

R/S analysis of foreign exchange rates under two international monetary regimes

The purpose of this study is to examine empirically the behavior of foreign exchange markets during the most recent experiences with fixed and flexible rates. Specifically, this study explores the possibility that long-term dependence is present in the exchange rate series for the British pound, French franc, and German mark in terms of the U.S. dollar. Using R/S analysis, positive long-term dependence is uncovered for each exchange rate during the flexible regime but negative dependence is found in the fixed period.     

Intertemporal risk-return trade-off in foreign exchange rates

We investigate the intertemporal risk-return trade-off of foreign exchange (FX) rates for ten currencies quoted against the USD. For each currency, we use three risk measures simultaneously that pertain to that currency; its realized volatility, its realized skewness, and its value-at-risk. We apply monthly FX excess returns and risk measures calculated from daily observations. We find that there is a significant contemporaneous risk-return trade-off for the currencies under investigation. There is no evidence of noncontemporaneous risk-return trade-off. We pay special attention to the risk-return trade-off during the recent financial crisis.     

Forecasting foreign exchange rates using idiosyncratic volatility

Average idiosyncratic stock volatility forecasts the bilateral exchange rates of the US dollar against major foreign currencies in and out of sample. The US dollar tends to appreciate after an increase in US idiosyncratic volatility. Similarly, ceteris paribus, German and Japanese idiosyncratic volatilities positively and significantly correlate with future US dollar prices of the Deutsche mark and the Japanese yen, respectively. Our results suggest that exchange rates are predictable.     

A study of diffusion processes for foreign exchange rates

The nature of the stochastic process generating the time path of foreign exchange rates plays an important role in dynamic theories of international financial economics. An important consideration in this stochastic process is the relationship between currency return variances and exchange rate levels. Using five years of daily data separated into quarterly intervals, this study demonstrates that currency return variances depend on exchange rate levels and the dependency is unstable intertemporally. Thus, these empirical results contradict the assumption of stable log-normal distribution and the more general assumption of constant elasticities of variances. For elasticity coefficients ordinary least squares estimates are compared to maximum likelihood estimates; the maximum likelihood estimator clearly is superior. Implications of these results for models of foreign exchange rates are discussed.     

Forward exchange rates as predictors of future spot rates and the efficiency of the foreign exchange market

The theory of informationally efficient markets (EMIT) is applied to the foreign exchange market and some of its operational implications are illustrated. The EMIT is joined with alternative models of the equilibrium return on the foreign exchange market: the Pure Expectations Hypothesis, the Modern Theory and tentative formulations of return as a function of risk. The alternative joint Hypotheses are rejected by the data but this does not necessarily imply the rejection of EMIT. The rejection may be due to the inadequacies of the equilibrium return models used, notwithstanding the fact that the risk premium has been captured, to a certain extent, in the empirical tests and the evidence against the EMIT weakened.     

The capitalization of income streams and the effects of open-market policy under fixed exchange rates

This paper investigates the long- and short-run neutrality of open-market monetary policy in a world of fixed exchange rates and imperfect substitutability between bonds denominated in different currencies. Using an illustrative portfolio-balance model, it shows that when the public discounts the future tax liabilities associated with the national debt and the central bank supports the exchange rate by trading non-interest-bearing foreign assets, open-market policy has a short-run effect, but no long-run effect, on the domestic price level and interest rate. When the foreign-exchange intervention assets earn interest that is rebated to and capitalized by the public, open-market policy loses even its short-run efficacy — the capital-account offset to monetary policy is complete.     

Pricing of foreign exchange options under the MPT stochastic volatility model and the CIR interest rates

We consider an extension of the model proposed by Moretto, Pasquali, and Trivellato [2010. “Derivative Evaluation Using Recombining Trees under Stochastic Volatility.” Advances and Applications in Statistical Sciences 1 (2): 453–480] (referred to as the MPT model) for pricing foreign exchange (FX) options to the case of stochastic domestic and foreign interest rates driven by the Cox, Ingersoll, and Ross dynamics introduced in Cox, Ingersoll, and Ross [1985. “A Theory of Term Structure of Interest Rates.” Econometrica 53(2): 385–408]. The advantage of the MPT model is that it retains some crucial features of Heston's stochastic volatility model but, as demonstrated in Moretto, Pasquali, and Trivellato [2010. “Derivative Evaluation Using Recombining Trees under Stochastic Volatility.” Advances and Applications in Statistical Sciences 1 (2): 453–480], it is better suited for discretization through recombining lattices, and thus it can also be used to value and hedge exotic FX products. In the model examined in this paper, the instantaneous volatility is correlated with the exchange rate dynamics, but the domestic and foreign short-term rates are assumed to be mutually independent and independent of the dynamics of the exchange rate. The main result furnishes a semi-analytical formula for the price of the FX European call option, which hinges on explicit expressions for conditional characteristic functions.     

Monetary policy under dual exchange rates

This paper finds that the introduction of dual exchange rates gives the monetary authority greater independence from external constraints than it would otherwise enjoy. The monetary authority is able to influence the level of aggregate demand in the short run and to sterilize the effects of temporary foreign disturbances. In addition, the paper finds that dual rates insulate the domestic economy fully from foreign interest rate changes but do not provide insulation from speculative disturbances.     

Temporal aggregation and unit roots in nominal foreign exchange rates

Extant empirical evidence on the logarithm of the daily and weekly spot exchange rates indicates the presence of unit roots. At a lower frequency, however, there is evidence that monthly spot rates do not have a unit root, although the autocorrelation coefficient may be close to one in absolute value. Unlike earlier studies, the present article applies various tests to data with different frequencies and reports evidence suggesting that exchange rates may not have unit roots. Absence of nonstationarity in the observations implies that econometric models may not have to apply any differencing.The authors gratefully acknowledge Hashem Dezhbakhsh for helpful suggestions. Comments are welcome.     

Deep networks for predicting direction of change in foreign exchange rates

Trillions of dollars are traded daily on the foreign exchange (forex) market, making it the largest financial market in the world. Accurate forecasting of forex rates is a necessary element in any effective hedging or speculation strategy in the forex market. Time series models and shallow neural networks provide acceptable point estimates for future rates but are poor at predicting the direction of change and, hence, are not very useful for supporting profitable trading strategies. Machine learning classifiers trained on input features crafted based on domain knowledge produce marginally better results. The recent success of deep networks is partially attributable to their ability to learn abstract features from raw data. This motivates us to investigate the ability of deep convolution neural networks to predict the direction of change in forex rates. Exchange rates for the currency pairs EUR/USD, GBP/USD and JPY/USD are used in experiments. Results demonstrate that trained deep networks achieve satisfactory out‐of‐sample prediction accuracy.     

Fixed versus flexible exchange rates in an equilibrium business cycle model

This essay re-examines the question of which exchange rate regime is preferable, using a rational expectations model that explicitly incorporates wealth, and emphasizing the information-signalling role of prices. Previous authors have stressed the argument that floating rates provide agents with an additional source of information, which improves forecasting accuracy, leading to more efficient allocations. This paper adds the counterweighing argument that they also have the effect, in contrast to fixed rates, of introducing an additional source of (monetary) disturbances in the determination of real variables. Another issue addressed is the nature of exchange rate adjustments to monetary disturbances.     

Real exchange rates under alternative nominal exchange-rate systems

The paper develops an equilibrium model of the determination of exchange rates, the relative price of nontraded goods, and the current account. The focus is on the effects of various real and nominal disturbances and the conditions under which the nominal exchange-rate system is neutral with respect to real variables in the economy. The model demonstrates an assymetry in the roles of trade and nontraded goods in affecting exchange rates. An econometric investigation of the raltion between the exchange-rate system and the variability of real exchange rates provides some evidence against the neutrality hypothesis.     

Forecasting exchange rates under parameter and model uncertainty

We introduce a forecasting method that closely matches the econometric properties required by exchange rate theory. Our approach formally models (i) when (and if) predictor variables enter or leave a regression model, (ii) the degree of parameter instability, (iii) the (potentially) rapidly changing relevance of regressors, and (iv) the appropriate shrinkage intensity over time. We consider (short-term) forecasting of six major US dollar exchange rates using a standard set of macro fundamentals. Our results indicate the importance of shrinkage and flexible model selection/averaging criteria to avoid poor forecasting results.     

Bandwagon effects and run patterns in exchange rates

I analyze the monthly exchange rates of the US dollar against the pound sterling, the Japanese yen, and the Swiss franc. All three exchange rates show bandwagon patterns, changes in one direction tend to be followed by changes in the same direction. This regularity points towards the importance of momentum traders on foreign exchange markets. A recent experimental analysis suggests the following hypothesis regarding the dynamics of bandwagon effects: if there is a repetition of similar occurrences many agents expect this run to continue but reduce the perceived chances of further repetitions when they actually occur. For exchange rates this implies that a continuation of a change in one direction should become weaker if an exchange rate has shown repeated changes in the same direction in the immediate past. This conjecture is supported by the findings of this study.