robust tests for unit roots in the foreign exchange market abstract empirical studies that have tested for unit roots in foreign exchange rate data have assumed independent and identically distributed errors in order to apply dickey fuller test procedures this assumption ignores the temporal dependence of the error sequence present in many simple efficient market tests as discussed in hansen and hodrick 1980 as well as krasker 1980 in this paper we apply unit root test statistics that allow for heterogeneously distributed and mildly dependent error processes and thus provide superior tests of the unit root hypothesis in the case of foreign exchange rates

the market for lawyers and quality layers in legal services we study the functioning of the market for lawyers considering the strategic interaction among litigants lawyers and judges we investigate the value of legal representation and of systems of quality certification such as the queen s counsel system in our setting higher quality lawyers obtain better quality evidence and are better able to interpret it judges receive information from the lawyers and have reputational concerns we show that reputational concerns generate a decision bias in favor of certified lawyers and that this causes misallocation of lawyers at the market equilibrium as a result whereas a higher quality of lawyers increases welfare public information over quality may be welfare reducing

internal r d effort external imported technoloogy and economic value added empirical study of taiwan s electronic industry technology innovation is a significant resource in the contemporary knowledge based economy the main sources of technology innovation are internal r d effort and external imported technology two primary traditional production factors are physical capital and labour the theoretical basis for this study is an evolutionary cobb douglas production function explaining the effects of four resources internal r d effort imported technology physical capital and labour on a firm s sales and economic value added eva time series cross section panel data from 219 taiwan electronic manufacturers between 1990 and 2003 were employed for fixed effect model major empirical findings were observed in this study first internal r d effort can positively affect a firm s sales and eva conversely imported technology is found to have had no significant effect on sales and eva second although both physical capital and labour affect a firm s sales more than the effects of internal r d and external imported technolog

on the bad reputation of reputational concerns can reputational concerns do any good economists have shown how they lead agents to ignore valuable information to herd and to become overly risk averse we explore how they may be a social blessing an agent may exert effort to become informed about the uncertain benefits of a project a smart agent s efforts make him better informed a dumb agent s efforts are to no avail if an agent does not know his type reputational concerns are socially beneficial if an agent knows his type reputational concerns may be socially beneficial a dumb agent takes inefficient unconventional decisions to mimic a smart agent the latter exerts more effort in order not to be mistaken for a dumb this holds whether or not project rejection is a safe haven for the dumb

continuous time model of uncovered interest parity with regulated jump diffusion interest differential this study investigates to what extent can an exchange rate model built on uncovered interest parity uip match the empirical features of the exchange rate and the interest differential data this article presents a continuous time model of uip in which the interest differential evolves following regulated jump diffusion simulation experiments show that the model is capable of matching several important features of the data inclusion of jumps improves the model to capture persistent dynamics of interest differential and fat tails in exchange rate returns compared to simple diffusion processes

international travelling and trade further evidence for the case of spanish wine based on fractional vector autoregressive specifications this article deals with the relationship between international travelling and trade for this purpose we focus on a particular case study the connection between the spanish wine exports to germany and the german travellers to spain unlike previous studies we use a methodology based on fractional vector autoregressive var models which permits us to compute the impulse responses in a similar way as in the standard var case the results show that the orders of integration of the two series are constrained between 0 and 1 being higher for the arrivals series than for the exports the impulse response analysis reveals that an increase in travelling produces a positive initial impact on trade though it tends to disappear in the long run

foreign exchange market efficiency and common stochastic trends abstract in a recent paper baillie and bollerslev 1989 using daily data from 1980 to 1985 identified six common stochastic trends in a vector of seven nominal exchange rates implying the existence of one cointegrating vector cointegration implies that granger causality must run in at least one direction that is at least one of the exchange rates is predictable using current available information this result has been interpreted as foreign exchange market inefficiency by many another interpretation is suggested if the stationary linear combination of spot rates proxies for a time varying risk premium in some way then these results could be explained in a rational and risk averse market this possibility is eliminated if the time series properties of the risk premium are incompatible with those of the error correction term specifically it is demonstrated that the forward risk premium is non stationary for the exchange rates that comprise the exchange rate cointegration relationship in this paper the existence of common stochastic trends in a vector of nominal exchange rates is tested over the period 1974 to 1991 the efficiency of foreign exchange markets is then tested by examining the implications of stochastic trends in the forward premium and what this means for the time series properties of a time varying forward risk premium jel f31 g14

maximum likelihood estimation of fractional cointegration with an application to u s and canadian bond rates we estimate a multivariate arfima model to illustrate a cointegration testing methodology based on joint estimates of the fractional orders of integration of a cointegrating vector and its parent series previous cointegration tests relied on a two step testing procedure and maintained the assumption in the second step that the parent series were known to have a unit root in our empirical example of fractional cointegration we illustrate how uncertainty regarding the order of integration of the parent series can be even more important than uncertainty regarding the order of integration of the cointegrating vector when testing for cointegration

multiscale behaviour of volatility autocorrelations in a financial market abstract we perform a scaling analysis on nyse daily returns we show that volatility correlations are power laws on a time range from one day to one year and more important that the exponent is not unique consistently with a multiscale behaviour

a theory of credibility this paper presents models in which one agent must decide whether to trust another whose motives are uncertain reliability can only be communicated through actions in this context it pays for people to build a reputation based on reliable behaviour someone becomes credible by consistently providing accurate and valuable information or by performing useful services the theory provides a justification for long term arrangements without binding contracts it also describes those situations where it pays an agent to cash in on his reputation many decisions depend on trusting someone consumers must decide whether to believe advertisements banks need to judge the reliability of loan applicants and employers must decide how much responsibility to delegate to their employees this paper attempts to model situations that arise when someone is uncertain about whether to trust the people he deals with in this context reputations for reliability are valuable an agent becomes credible by consistently providing accurate valuable information or by always acting responsibly i analyse a series of simple abstract models of information transmission in the basic model there are two agents the sender s and the receiver r who are to play the game a known finite number of times at each stage both players learn the value of a parameter measuring the importance of that period s play of the game that is the value of making a correct decision and s obtains payoff relevant information s then sends a signal to r who makes a decision that affects the welfare of both players after both players learn the consequences of r s decision the process repeats at each stage r must decide what action to take in order to do that he must assess the credibility of s the difficulty arises because r is uncertain about s s preferences when play begins i model this by assuming that with positive probability s has identical preferences to r s is a friend and with positive probability s has completely opposed preferences to r s is an enemy this uncertainty creates a trade off for enemy senders at each stage providing honest information enhances s s reputation but only at the expense of foregoing an opportunity for immediate gain by duping r the possibility that s is a friend lends credibility to what he says but this credibility may also be exploited by an enemy s the principal equilibrium has the following form in the basic model where s has no control over the importance of a given play s typically conveys accurate information for the first several periods r raises the probability he places on s being friendly after receiving accurate information if he believes that an enemy would have lied to him with positive probability the more important the information the more likely an enemy will attempt to deceive r an enemy will eventually take advantage of r by misleading him when this happens the sender loses all opportunities for deception in the future i

evidence on the extent and potential sources of long memory in u s treasury security returns and yields unlike equity returns many fixed income return measures appear to display long memory we show that the extent of long memory differs strongly for gross and excess holding period returns on u s treasury securities granger and others have argued that long memory may only reflect infrequent structural breaks we explore the impact of structural instability on tests for long memory and find only weak indications that it lies behind the long memory in our return series the evidence of long memory remains strong for yield and term premia series even after accounting for a series of potential underlying structural changes

long memory in foreign exchange rates using the geweke porter hudak test we find evidence of long memory in exchange rate data this implies that the empirical evidence of unit roots in exchange rates may not be robust to long memory alternatives fractionally integrated autoregressive moving average arfima models are estimated by both the time domain exact maximum likelihood ml method and the frequency domain approximate ml method impulse response functions and forecasts based on these estimated arfima models are evaluated to gain insight into the long memory characteristics of exchange rates some tentative explanations of the long memory found in the exchange rates are discussed

a model of expertise we study a model in which perfectly informed experts offer advice to a decision maker whose actions affect the welfare of all experts are biased and thus may wish to pull the decision maker in different directions and to different degrees when the decision maker consults only a single expert the expert withholds substantial information from the decision maker we ask whether this situation is improved by having the decision maker sequentially consult two experts we first show that there is no perfect bayesian equilibrium in which full revelation occurs when both experts are biased in the same direction it is never beneficial to consult both in contrast when experts are biased in opposite directions it is always beneficial to consult both indeed in this case full revelation may be induced in an extended debate by introducing the possibility of rebuttal

comparing structural decomposition analysis and index to analyze and understand historical changes in economic environmental employment or other socio economic indicators it is useful to assess the driving forces or determinants that underlie these changes two techniques for decomposing indicator changes at the sector level are structural decomposition analysis sda and index decomposition analysis ida for example sda and ida have been used to analyze changes in indicators such as energy use co2 emissions labor demand and value added the changes in these variables are decomposed into determinants such as technological demand and structural effects sda uses information from input output tables while ida uses aggregate data at the sector level the two methods have developed quite independently which has resulted in each method being characterized by specific unique techniques and approaches this paper has three aims first the similarities and differences between the two approaches are summarized second the possibility of transferring specific techniques and indices is explored finally a numerical example is used to illustrate differences between the two approaches

convergence to the long run equilibrium the case of natural gas markets abstract intuitively the persistence of a shock may last longer in futures contracts with a longer maturity estimation of the speed with which different contract lengths converges to the long run equilibrium following a shock provides a means for comparing the informational efficiency of the contracts standard empirical investigation of the response of a market to a shock utilizes impulse response analysis however this analysis is problematic since there is not a unique variance covariance decomposition pesaran and shin pesaran m h shin y 1996 cointegration and speed of convergence to equilibrium j econ 71 117 143 introduced an alternative to the standard impulse response analysis the persistence profile by estimating the one step ahead forecast error for the entire system the persistence profile provides a unique measure of the effect of the shock this paper empirically estimates persistence profiles for the natural gas futures market the findings indicate that the persistence of a shock does increase with the contract length

cointegration and forward and spot exchange rate regressions abstract we investigate the relationship between cointegration models of the current spot exchange rate s t and the current forward rate f t and cointegration models of the future spot rate s t 1 and f t and the implications of this relationship for tests of the forward rate unbiasedness hypothesis fruh we show that simple models of cointegration between s t and f t imply complicated models of cointegration between s t 1 and f t consequently standard methods are often inappropriate for modeling the cointegrated behavior of s t 1 f t and we show that the use of such methods can lead to erroneous inferences regarding the fruh

fractional integration in agricultural futures price volatilities this article tests whether the volatility of agricultural futures prices exhibits fractional integration volatility series were constructed for fourteen agricultural futures price series with over 5 300 observations per series the volatility series exhibit strong long term dependence which is an indicator of fractional integration a fractional integration model figarch 1 d 1 performs significantly better than a traditional volatility model garch 1 1 in modeling agricultural futures price volatility

long memory and persistence in aggregate output abstract we examine persistence in u s aggregate output by estimating fractionally integrated arima models these models provide better low frequency approximations to the wold representation than previous stochastic specifications and earlier results on the importance of a permanent component emerge as special cases we find evidence of long memory which induces persistence though this long memory need not be associated with a unit root our point estimates indicate that macroeconomic shocks while persistent are distinctly less persistent than many earlier studies suggest however confidence intervals associated with the long run response are quite wide

fractional cointegration low frequency dynamics and long run purchasing power parity an analysis of the australian dollar over its recent float a relatively new but generalized concept of fractional cointegration is applied to shed some light on the validity of purchasing power parity ppp as a long run equilibrium condition by examining the long run relationship between quarterly consumer price indices and bilateral exchange rates of the australian dollar and seven major oecd trading partners over australia s recent float the paper demonstrates that relaxing the condition that the residual from the cointegration equation must be a i 0 process provides a wide range of cases of parity reversion with processes that are ci 1 d with 0 d 1 findings tend to suggest that while standard tests of cointegration fail to support cointegration between nominal exchange rates domestic and foreign prices and thus the empirical favour for ppp as a long run phenomenon the fractional cointegration analysis permits deviations from equilibrium to follow a fractionally integrated process and hence captures a much wider class of parity or mean reversion

news management and the value of firms the literature on asymmetric information has been concerned mainly with the problem of the informed party lying to the uninformed parties however in many cases the informed party will stop short of lying but will seek to gain from private information by managing the disclosure of news this article examines the pricing of a firm when there is such manipulation of news i model this situation as a variant of the persuasion game of milgrom and roberts 1986 in which i can parameterize the notion of the degree of credence placed by the market on the disclosures of the informed party an empirical hypothesis thrown up by the theory is that for otherwise identical firms a low price earnings ratio will be associated with a greater degree of positive skewness of the disclosure strategy

modeling long run behavior with the fractional arima model abstract when modeling long run behavior fractional arima models can give insights unobtainable with the nonfractional arima models as an application the deterministic trend and unit root with drift models are nested in the fractional arima model this allows testing between the two models based on estimated parameter values this test is applied to postwar us quarterly real gnp the test concludes that gnp is consistent with both models the estimated fractional parameter is significantly smaller than reported in diebold and rudebusch 1989 the difference is explained by bias in the previous estimates relationships with the cumulative impulse response and spectral density at frequency zero are noted

foreign exchange market efficiency revisited abstract the cointegration of spot rates is neither a necessary nor a sufficient condition to account for the lack of foreign exchange market efficiency instead crowder crowder w 1994 1996 j int money finance 13 551 564 15 661 664 and engel engel c 1996 j int money finance 15 557 560 claimed that the stationarity of the forward premium is crucial to the hypothesis of market efficiency in this paper we employ the panel unit root test of im et al to examine the stationarity of forward premia and interest differentials among nine oecd countries we reject the unit root null for both the time series of the forward premium and interest differential which in turn supports the hypothesis of foreign exchange market efficiency

a fractional cointegration analysis of the long run relationship between black and official foreign exchange rates the case of the brazilian cruzeiro this paper applies a relatively new but generalized concept of fractional cointegration to shed some light on the validity of a long run relationship between monthly black and official us dollar rates of the brazilian cruzeiro an investigation of the stochastic properties of these rates reveals that while the relationship is not cointegrated in their logs they appear to be fractionally cointegrated if we allow for mean reverting processes that are ci 1 d with 0 d 1 the paper demonstrates that relaxing the condition that the residual from the cointegration equation must be a i 0 process captures a much wider class of mean reversion behaviour furthermore an analysis of the short run dynamics propelling the long run relationship tends to imply that although the official rate influences the changes in the black rate this is purely over the short run in the longer term the black rate is found to be the initial receptor of any exogenous shock to the equilibrium and it is the official exchange

long memory and structural changes in the forward discount an empirical investigation abstract we analyze the evidence for long memory and structural changes in the five g7 countries forward discount we establish evidence for long memory by estimating the long memory parameter without allowing for structural breaks we also document evidence for multiple structural breaks in the mean of the forward discount we then adjust for structural changes in the forward discount rate and re estimate the long memory parameter after removing the breaks we still find evidence of stationary long memory in each country s forward discount

on the power of dickey fuller tests against fractional alternatives abstract we examine the properties of dickey fuller unit root tests under fractionally integrated alternatives and find that these tests have quite low power

the drivers of export value added in china s provinces a multi regional input output model it is vital to calculate chinese provinces exports in domestic and global value chains from the perspective of value added to address the problem of double counting in this study we calculated t

a theory of yes men this paper illustrates an incentive for workers to conform to the opinion of their supervisors when firms use subjective performance evaluation this desire to conform arises endogenously from the firm s need to induce the worker to exert effort the author shows that firms may optimally eschew the use of incentive contracts to retain workers incentives for honesty the author illustrates that the incentive to conform implies inefficiencies even when workers are risk neutral and is likely to lead to more centralized decision making than in the absence of the desire to conform copyright 1993 by american economic association

information aggregation in debate who should speak first abstract privately informed individuals speak openly in front of other members of a committee about the desirability of a public decision each individual wishes to appear well informed for any given order of speech committee members may herd by suppressing their true information with individuals of heterogeneous expertise optimizing over the order of speech can improve the extraction of information but not perfectly so it is not always optimal to use the common anti seniority rule whereby experts speak in order of increasing expertise a committee with more able experts may be afflicted by greater herding problems yielding a worse outcome

waves and persistence in merger and acquisition activity abstract markov regime switching and sine wave models have been used to capture the apparent wave like behavior in aggregate u s merger and acquisition m and a activity in this paper we offer an alternative characterization of the dynamic structure in m and a activity as a strongly dependent or long memory process

cointegration and predictability of asset prices abstract this article argues that whatever concerns one might have about the identification of a cointegrating relationship with market inefficiency cointegration tests can still be usefully employed to investigate the predictability of asset prices we examine the case of n dimensional systems and show that the standard assumption made in the literature that cointegration implies predictability of all n asset prices is not valid in the presence of r cointegrating vectors only r prices are predictable and standard wald or lm tests carried out within johansen s maximum likelihood ml framework can be used to establish for which prices unpredictability does not hold similarly one can distinguish between joint unpredictability in the short and long run when asset prices are driven by fundamentals

the roles of reputation and transparency on the behavior of biased experts we analyze situations in which an expert is biased toward some decision but cares also about his reputation in the market for experts the information the expert reveals decreases as his bias moves toward stronger preference for the status quo we show that it is optimal to publicly disclose both the expert s contribution and his identity surprisingly revealing the intensity of the expert s bias doesn t always improve the information he reveals in equilibrium the presence of a second expert raises the first expert s incentives to report truthfully when reports are public but reduces them when they are secret in particular having an option to call another expert may be detrimental in terms of information production if reports are not public finally sequential consultation of experts reduces the information obtained when reports are public but raises it when they are secret

real exchange rates under the gold standard purchasing power parity is one of the most important equilibrium conditions in international macroeconomics empirically it is also one of the most hotly contested numerous recent studies for example have sought to determine the validity of purchasing power parity using data from the post bretton woods float and have reached different conclusions we assert that most such studies are flawed for two reasons first the post 1973 data contain by definition only a very limited amount of the low frequency information relevant for examination of long run parity second the dynamic econometric techniques used to model deviations from parity are typically quite crude with respect to admissible low frequency dynamics both deficiencies are rectified in the present paper with dramatic results we construct a new data set of 16 real exchange rates covering more than a century of the classic gold standard period and we study deviations from parity using long memory models that allow for subtle forms of mean

information transmission when the sender s preferences are uncertain abstract in deciding on the magnitude of a certain action say investment a decision maker relies on the report of an informed and interested expert who can suppress favorable information the main departure from the related literature is that the decision maker is uncertain as to whether the expert is of a type that wants to minimize the magnitude of the action or to maximize it the unique equilibrium outcome is fully characterized by a threshold level of favorable information if the information is more favorable than that threshold level and if the expert is of the type that wants to maximize the magnitude of the action the information is fully revealed in all other cases the expert report less favorable information and the equilibrium inference is that in expectation the actual information is just as favorable as the threshold level

the nature of the relationship between international tourism and international trade the case of german imports of spanish wine this article deals with the relationship between international trade and tourism we focus on the effect that german tourism to spain has on german imports of spanish wine due to the different stochastic properties of the series under analysis which display different orders of integration a methodology is used based on long memory regression models where tourism is supposed to be exogenous the period covered is january 1998 to november 2004 the results show that tourism has an effect on wine imports that lasts between 2 and 9 months disaggregating the imports across the different types of wine it is observed that only for red wines from navarra penedus and valdepenas and to a certain extent for sparkling wine tourism produces an effect on future import demand from a policy making perspective our results imply that the impact of tourism on the host economy is not only direct and short term but also oblique and delayed thus reinforcing the case for tourism as a means for economic development

rethinking an old empirical puzzle econometric evidence on the forward discount anomaly using both semiparametric and parametric estimation methods this paper corroborates earlier findings of fractionally integrated behaviour in the forward premium two new explanations are also proposed to help reconcile earlier conflicting empirical evidence on the time series properties of the forward premium traditional regression approaches used to test the forward rate unbiasedness hypothesis are then evaluated including regression in levels in returns fama s 1984 regression and in error correction format interesting statistical and or interpretive implications are found in all three cases for example the predictions of the appropriate nonstandard limit theory are consistent with many of the standard empirical results reported from fama s regression including the commonly occurring yet puzzling negative correlations between spot returns and the forward premium it is suggested that the principal failure of unbiasedness may be due instead to the difference in persistence between these two series copyright 2001 john wiley sons ltd

cointegration fractional cointegration and exchange rate dynamics multivariate tests due to johansen 1988 1991 as implemented by baillie and bollerslev 1989a and diebold gardeazabal and yilmaz 1994 reveal mixed evidence on whether a group of exchange rates are cointegrated further analysis of the deviations from the cointegrating relationship suggests that it possesses long memory and may possibly be well described as a fractionally integrated process hence the influence of shocks to the equilibrium exchange rates may only vanish at very long horizons in the article by baillie and bollerslev 1989a it is argued that seven different nominal spot and forward exchange rates all contain unit roots in their univariate time series representations at the same time however the spot exchange rates appear to be tied together in the long run through a cointegration type relationship the latter finding of baillie and bollerslev has attracted particular interest and several studies such as those by hakkio and rush 1991 and sephton and larsen 1991 have already addressed this issue using the same data as the baillie and bollerslev article sephton and larsen 1991 describe the evidence for the presence of cointegration as being fragile and note that mixed conclusions are reached by truncating the baillie and bollerslev sample at different points in time diebold gardeazabal and yilmaz 1994 henceforth diebold et al provide interesting evidence that application of the johansen 1988 1991 tests with and without an intercept will result in different inferences on the baillie and bollerslev data set furthermore diebold et al carry out an ex ante forecasting experiment and find that the addition of an error correction term to the martingale model as implied by the standard cointegration paradigm fails to reduce the prediction mean square error when compared to a simple martingale model this therefore leads diebold et al to conclude that there exists substantial uncertainty regarding the existence of cointegration relationships among nominal dollar exchange rates this article provides some additional evidence on the existence of such a long run relationship among the same seven nominal spot exchange rates after further analysis it appears that a form of cointegration does exist between the exchange rates so that they do not drift apart in the long run we argue that this form of cointegration is

the long memory of the forward premium abstract the estimation of arfima models by approximate maximum likelihood estimation methods reveals the forward premia for the currencies of canada germany and the uk vis a vis the us dollar to be well described by a fractionally integrated process these models imply that all the forward premia are mean reverting although their autocorrelations are quite persistent this degree of persistence has led other studies to erroneously conclude that the forward premia contains a unit root jel c22 e31

disclosures and asset returns public information in financial markets often arrives through the disclosures of interested parties who have a material interest in the reactions of the market to the new information when the strategic interaction between the sender and the receiver is formalized as a disclosure game with verifiable reports equilibrium prices can be given a simple characterization in terms of the concatenation of binomial pricing trees there are a number of empirical implications the theory predicts that the return variance following a poor disclosed outcome is higher than it would have been if the disclosed outcome were good also when investors are risk averse this leads to negative serial correlation of asset returns other points of contact with the empirical literature are discussed

relying on the information of interested parties we investigate the conventional wisdom that competition among interested parties attempting to influence a decisionmaker by providing verifiable information elicits all relevant information we find that if the decisionmaker is strategically sophisticated and well informed about the relevant variables and about the preferences of the interested party or parties competition may be unnecessary to achieve this result if the decisionmaker is unsophisticated or not well informed competition is not generally sufficient if the interested parties interests are sufficiently opposed however or if the decisionmaker is seeking to advance the parties welfare then competition can reduce or even eliminate the decisionmaker s need for prior knowledge about the relevant variables and for strategic sophistication in other settings only the combination of competition among information providers and a sophisticated skepticism is sufficient to allow effective decisionmaking

stationary time varying risk premia in forward foreign exchange rates abstract there is mounting evidence that forward foreign exchange rates contain time varying risk premia however this evidence is from tests for which statistical inference is based on asymptotic distribution theory furthermore it is uncertain whether risk premia evolve as stationary or nonstationary processes this paper applies two exact small sample pointwise most powerful invariant statistical tests to determine 1 whether forward exchange rates contain time varying risk premia and 2 whether the time varying risk premia are stationary or nonstationary these tests finds strong evidence that forward exchange rates contain stationary time varying risk premia during the recent float evidence from the interwar float is mixed

common stochastic trends in a system of exchange rates univariate tests reveal strong evidence for the presence of a unit root in the univariate time series representation for seven daily spot and forward exchange rate series furthermore all seven spot and forward rates appear to be cointegrated that is the forward premiums are stationary and one common unit root or stochastic trend is detectable in the multivariate time series models for the seven spot and forward rates respectively this is consistent with the hypothesis that the seven exchange rates possess one longrun relationship and that the disequilibrium error around that relationship partly accounts for subsequent movements in the exchange rates a general consensus has emerged in recent years that many macroeconomic time series such as gnp consumption expenditures disposable income etc can be characterized by a stochastic trend model in particular nelson and plosser 22 described this property as one of being difference stationary so that the first difference of a time series is stationary an alternative trend stationary model where a stationary component is added to a deterministic trend term has generally been found to be less appropriate 1 similarly it has long been recognized that many financial time series such as foreign exchange rates are nonstationary e g in meese and singleton 21 the issue of nonstationary is not merely a statistical curiosity but has several important implications for the modeling of exchange rates for instance many models of exchange rate determination under rational expectations require stationarity assumptions when solving out the expected future values of the fundamentals further there has been some controversy over the appropriate transformations to use when conducting tests of whether the forward rate is an unbiased and efficient predictor of the future spot exchange rate 2 some authors e g frenkel 11 12 have conducted tests in levels while geweke and feige 14