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It is well known that stationary geometrically ergodic Markov chains are $\beta$-mixing (absolutely regular) with geometrically decaying mixing coefficients. Furthermore, for initial distributions other than the stationary one, geometric ergodicity implies $\beta$-mixing under suitable moment assumptions. In this note we show that similar results hold also for subgeometrically ergodic Markov chains. In particular, for both stationary and other initial distributions, subgeometric ergodicity implies $\beta$-mixing with subgeometrically decaying mixing coefficients. Although this result is simple it should prove very useful in obtaining rates of mixing in situations where geometric ergodicity can not be established. To illustrate our results we derive new subgeometric ergodicity and $\beta$-mixing results for the self-exciting threshold autoregressive model., Comment: v2 updated reference to Meitz and Saikkonen (2019)

Theories often make predictions about the signs of the effects of economic shocks on observable variables, thus implying inequality constraints on the parameters of a structural vector autoregression (SVAR). We introduce a new Bayesian procedure to evaluate the probabilities of such constraints, and, hence, to validate the theoretically implied economic shocks. We first estimate a SVAR, where the shocks are identified by statistical properties of the data, and subsequently label these statistically identified shocks by the Bayes factors calculated from their probabilities of satisfying given inequality constraints. In contrast to the related sign restriction approach that also makes use of theoretically implied inequality constraints, no restrictions are imposed. Hence, it is possible that only a subset or none of the theoretically implied shocks can be labelled. In the latter case, we conclude that the data do not lend support to the theory implying the signs of the effects in question. We illustrate the method by empirical applications to the crude oil market, and U.S. monetary policy.

Testing for regime switching when the regime switching probabilities are specified either as constants ('mixture models') or are governed by a finite-state Markov chain ('Markov switching models') are long-standing problems that have also attracted recent interest. This paper considers testing for regime switching when the regime switching probabilities are time-varying and depend on observed data ('observation-dependent regime switching'). Specifically, we consider the likelihood ratio test for observation-dependent regime switching in mixture autoregressive models. The testing problem is highly nonstandard, involving unidentified nuisance parameters under the null, parameters on the boundary, singular information matrices, and higher-order approximations of the log-likelihood. We derive the asymptotic null distribution of the likelihood ratio test statistic in a general mixture autoregressive setting using high-level conditions that allow for various forms of dependence of the regime switching probabilities on past observations, and we illustrate the theory using two particular mixture autoregressive models. The likelihood ratio test has a nonstandard asymptotic distribution that can easily be simulated, and Monte Carlo studies show the test to have good finite sample size and power properties. (C) 2020 The Authors. Published by Elsevier B.V.

A correction: The Econometrics Journal, Volume 24, Issue 1, January 2021, Page 198, https://doi.org/10.1093/ectj/utaa015 Tests for identification through heteroskedasticity in structural vector autoregressive analysis are developed for models with two volatility states where the time point of volatility change is known. The tests are Wald-type tests for which only the unrestricted model, including the covariance matrices of the two volatility states, has to be estimated. The residuals of the model are assumed to be from the class of elliptical distributions, which includes Gaussian models. The asymptotic null distributions of the test statistics are derived, and simulations are used to explore their small-sample properties. Two empirical examples illustrate the usefulness of the tests in applied work.

Did sovereign default risk affect macroeconomic activity through firms' access to credit during the European sovereign debt crisis? We investigate this question by a estimating a structural panel vector autoregressive model for Italy, Spain, Portugal, and Ireland, where the sovereign risk shock is identified using sign restrictions. The results suggest that decline in the creditworthiness of the sovereign contributed to a fall in private lending and economic activity in several euro-area countries by reducing the value of banks' assets and crowding out private lending., Comment: 24 pages

This article characterises the dimension of indeterminacy of linear rational expectations (LRE) models and derives their full set of solutions. It extends the analysis of indeterminate equilibria in Lubik and Schorfheide (2003) where some equilibria are incorrectly classified as indeterminate even though they entail the same observable outcome.

Conventional structural vector autoregressive (SVAR) models with Gaussian errors are not identified, and additional identifying restrictions are needed in applied work. We show that the Gaussian case is an exception in that a SVAR model whose error vector consists of independent non-Gaussian components is, without any additional restrictions, identified and leads to essentially unique impulse responses. Building upon this result, we introduce an identification scheme under which the maximum likelihood estimator of the parameters of the non-Gaussian SVAR model is consistent and asymptotically normally distributed. As a consequence, additional economic identifying restrictions can be tested. In an empirical application, we find a negative impact of a contractionary monetary policy shock on financial markets, and clearly reject the commonly employed recursive identifying restrictions.

In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary measure at a rate slower than geometric. Specifically, we consider suitably defined higher-order nonlinear autoregressions that behave similarly to a unit root process for large values of the observed series but we place almost no restrictions on their dynamics for moderate values of the observed series. Results on the subgeometric ergodicity of nonlinear autoregressions have previously appeared only in the first-order case. We provide an extension to the higher-order case and show that the autoregressions we consider are, under appropriate conditions, subgeometrically ergodic. As useful implications we also obtain stationarity and $\beta$-mixing with subgeometrically decaying mixing coefficients., Comment: Feb 2020: Major revision (most significant changes in Section 5)

Viimeisten vuosikymmenien aikana kansainvälisessä ekonometrisessa tutkimuskirjallisuudessa on esitetty useita makrotaloudellista tilaa kuvaavien muuttujien informaatiota yhdistäviä lyhyen aikavälin mallinnus- ja ennustemenetelmiä. Näitä ns. nowcasting-menetelmiä on myös onnistuneesti hyödynnetty ja sovellettu Suomen talouden seurantaan. Tässä artikkelissa esittelemme katsauksen monella taholla tehtyyn kehitystyöhön ja näiden hankkeiden yhteydessä saatuihin tuloksiin Suomen aineiston tapauksessa. Suomen taloutta koskevien suhdanneindeksien hyödyntämisen myötä suhdanteiden käännepisteiden määrittäminen on tarkempaa ja käännepisteiden tuottamia taantumajaksoja voidaan vastaavasti ennustaa binäärivastemalleja käyttäen. Suomen Pankin nowcasting-malli mahdollistaa puolestaan uusien tilastojulkistusten uutisarvon analyysin. Tilastokeskuksessa ja Etlassa on vastaavasti hyödynnetty moderneja koneoppimisen menetelmiä, jotta puutteellisesta mikroaineistosta kyetään tuottamaan bruttokansantuotteen pikaestimaatteja aiempaa lyhyemmällä viiveellä. ETLAnowprojektissa hyödynnetään puolestaan mm. uusia Google-hakutilastoja työttömyyden ennustamisessa. peerReviewed

Could macroeconomic factors such as income inequality be the real root cause of financial crises? We explore a broad variety of financial and macroeconomic variables and employ a general-to-specific model selection process to find the most reliable predictors of financial crises in developed countries over a period of more than 100 years. Our in-sample results indicate that income inequality has predictive power beyond loan growth and several other financial variables. Out-of-sample forecasts for individual predictors show that their predictive power tends to vary considerably over time, but income inequality has predictive power in each forecasting period. Could macroeconomic factors such as income inequality be the real root cause of financial crises? We explore a broad variety of financial and macroeconomic variables and employ a general-to-specific model selection process to find the most reliable predictors of financial crises in developed countries over a period of more than 100 years. Our in-sample results indicate that income inequality has predictive power beyond loan growth and several other financial variables. Out-of-sample forecasts for individual predictors show that their predictive power tends to vary considerably over time, but income inequality has predictive power in each forecasting period.

We study the directional predictability of monthly excess stock market returns in the U.S. and ten other markets using univariate and bivariate binary response models. We introduce a new bivariate (two-equation) probit model that allows us to examine the benefits of predicting the signs of returns jointly, focusing on the predictive power originating from the U.S. to foreign markets. Our in-sample and out-of-sample forecasting results indicate superior predictive performance of the new model over competing univariate binary response models, and conventional predictive regressions, by statistical measures and market timing performance. This highlights the importance of predictive information from the U.S. to the other markets providing also practical improvement in investors' market timing decisions.

This paper estimates the effects of fiscal policy shocks on GDP in the United States with a vector error correction (VEC) model in which shocks are identified by exploiting the non-normal distribution of the model residuals. Unlike previous research, the model used here takes into account cointegation between the variables, and applies a data driven method to identify fiscal policy shocks. The approach also allows statistical testing of previous identification strategies, which may help discriminate between them and hence also explain differences between various fiscal multiplier estimates. Our results show that a deficit financed government spending shock has a weak negative effect on output, whereas a tax increase to finance government spending has a positive impact on GDP.

We study the role of real oil prices on the directional predictability of excess stock market returns in the U.S. and 10 other countries using probit models. Previous studies have shown that oil price shocks have adverse effects on stock returns. We extend this literature by focusing on the sign component of excess returns. Our findings indicate that real oil prices are useful predictors of the direction of stock returns in a number of markets over and above commonly used predictors, but results vary substantially between countries. Interestingly, we find only limited evidence of asymmetric effects of oil price shocks.

Franses (Empir Econ, 2018. https://doi.org/10.1007/s00181-018-1417-8 ) criticised the practice in the empirical literature of replacing expected inflation by the sum of realised future inflation and an error in estimating the parameters of the new Keynesian Phillips curve (NKPC). In particular, he argued that this assumption goes against the Wold decomposition theorem and makes the error term in the hybrid NKPC equation correlated with future inflation, invalidating the maximum likelihood (ML) estimator of Lanne and Luoto (J Econ Dyn Control 37:561–570, 2013). We argue that despite the correlation, the Wold theorem is not violated, and the ML estimator is consistent.

The aim of this study was to investigate the clinical usefulness of MK-467 (vatinoxan; L-659'066) in dogs sedated for diagnostic imaging with medetomidine-butorphanol. It was hypothesised that MK-467 would alleviate bradycardia, hasten drug absorption and thus intensify the early-stage sedation. In a prospective, randomised, blinded clinical trial, 56 client-owned dogs received one of two IM treatments: (1) 0.5mg/m2 medetomidine+0.1mg/kg butorphanol (MB, n=29); or (2) 0.5mg/m2 medetomidine+0.1mg/kg butorphanol+10mg/m2 MK-467 (MB-MK, n=27). Heart rates and visual sedation scores were recorded at intervals. Plasma drug concentrations were determined in venous samples obtained approximately 14min after injection. Additional sedation (50% of original dose of medetomidine IM) and/or IM atipamezole for reversal were given when needed. The area under the sedation score-time curve for visual analogue scale (AUCVAS30) was calculated for the first 30min after treatment using the trapezoidal method. Repeated ANOVA, Mann-Whitney U test and Fisher's exact test were used for parametric, non-parametric and dichotomous data. Heart rate was significantly higher from 10 to 40min with MB-MK than with MB. AUCVAS30 was significantly higher after MB-MK. More dogs treated with MB-MK required additional sedation after 30min, but fewer needed atipamezole for reversal compared with MB. Plasma concentrations of both medetomidine and butorphanol were higher after MB-MK. All procedures were successfully completed. MK-467 alleviated the bradycardia, intensified the early stage sedation and shortened its duration in healthy dogs that received IM medetomidine-butorphanol.

We propose imposing data-driven identification constraints to alleviate the multimodality problem arising in the estimation of poorly identified dynamic stochastic general equilibrium models under non-informative prior distributions. We also devise an iterative procedure based on the posterior density of the parameters for finding these constraints. An empirical application to the Smets and Wouters () model demonstrates the properties of the estimation method, and shows how the problem of multimodal posterior distributions caused by parameter redundancy is eliminated by identification constraints. Out-of-sample forecast comparisons as well as Bayes factors lend support to the constrained model.

A new mixture autoregressive model based on Student’s t–distribution is proposed. A key feature of our model is that the conditional t–distributions of the component models are based on autoregressions that have multivariate t–distributions as their (low-dimensional) stationary distributions. That autoregressions with such stationary distributions exist is not immediate. Our formulation implies that the conditional mean of each component model is a linear function of past observations and the conditional variance is also time-varying. Compared to previous mixture autoregressive models our model may therefore be useful in applications where the data exhibits rather strong conditional heteroskedasticity. Our formulation also has the theoretical advantage that conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear autoregressive models. An empirical example employing a realized kernel series constructed from S&P 500 high-frequency intraday data shows that the proposed model performs well in volatility forecasting. Our methodology is implemented in the freely available StMAR Toolbox for MATLAB.

Smooth transition autoregressive models are widely used to capture nonlinearities in univariate and multivariate time series. Existence of stationary solution is typically assumed, implicitly or explicitly. In this paper we describe conditions for stationarity and ergodicity of vector STAR models. The key condition is that the joint spectral radius of certain matrices is below 1, which is not guaranteed if only separate spectral radii are below 1. Our result allows to use recently introduced toolboxes from computational mathematics to verify the stationarity and ergodicity of vector STAR models., Comment: Accepted to Econometric Reviews

This paper provides new evidence on the role of exchange rates in forecasting commodity prices. Consistent with previous studies, we find that commodity currencies hold out-of-sample predictive power for commodity prices when using standard linear predictive regressions. After we reconsider the evidence using noncausal autoregressions, which provide a better fit to the data and are able to accommodate the effects of nonlinearities and omitted variables, the predictive power of exchange rates disappears. (C) 2017 Elsevier B.V. All rights reserved.

We apply a novel Bayesian structural vector autoregressive method to analyze the macroeconomic effects of unconventional monetary policy in Japan, the US and the euro area. The method exploits statistical properties of the data to uniquely identify the model without restrictions, and thus enables formal assessment of the plausibility of given sign restrictions. Unlike previous research, the data-based analysis reveals differences in the output and price effects of the Bank of Japan's, Federal Reserve's and European Central Bank's balance sheet operations.

This article is also available at onlinelibrary.wiley.com Understanding how a monophyletic lineage of a species diverges into several adaptive forms has received increased attention in recent years, but the underly- ing mechanisms in this process are still under debate. Postglacial fishes are excellent model organisms for exploring this process, especially the initial stages of ecological speciation, as postglacial lakes represent replicated discrete envi- ronments with variation in available niches. Here, we combine data of niche utilization, trophic morphology, and 17 microsatellite loci to investigate the diversification process of three sympatric European whitefish morphs from three northern Fennoscandian lakes. The morphological divergence in the gill raker number among the whitefish morphs was related to the utilization of dif- ferent trophic niches and was associated with reproductive isolation within and across lakes. The intralacustrine comparison of whitefish morphs showed that these systems represent two levels of adaptive divergence: (1) a consistent littoral – pelagic resource axis; and (2) a more variable littoral – profundal resource axis. The results also indicate that the profundal whitefish morph has diverged repeatedly from the ancestral littoral whitefish morph in sympatry in two different watercourses. In contrast, all the analyses performed revealed clus- tering of the pelagic whitefish morphs across lakes suggesting parallel postglacial immigration with the littoral whitefish morph into each lake. Finally, the analy- ses strongly suggested that the trophic adaptive trait, number of gill rakers, was under diversifying selection in the different whitefish morphs. Together, the results support a complex evolutionary scenario where ecological speciation acts, but where both allopatric (colonization history) and sympatric (within watercourse divergence) processes are involved.

We propose a new generalized forecast error variance decomposition with the attractive property that the proportions of the impact accounted for by innovations in each variable sum to unity. Our decomposition is based on the generalized impulse response function, and it can easily be obtained by simulation. The new decomposition is illustrated in an empirical application to US output growth and interest rate spread data.

This work develops likelihood-based unit root tests in the noncausal autoregressive (NCAR) model formulated by Lanne and Saikkonen (2011, Journal of Time Series Econometrics 3, Iss. 3, Article 2). The possible unit root is assumed to appear in the causal autoregressive polynomial and for reasons of identification the error term of the model is supposed to be non-Gaussian. In order to derive the tests, asymptotic properties of the maximum likelihood estimators are established under the unit root hypothesis. The limiting distributions of the proposed tests depend on a nuisance parameter determined by the distribution of the error term of the model. A simple procedure to handle this nuisance parameter dependence in applications is proposed. Finite sample properties of the tests are examined by means of Monte Carlo simulations. The results show that the size properties of the tests are satisfactory and the power against stationary NCAR alternatives is significantly higher than the power of conventional Dickey-Fuller tests and the M-tests of Lucas (1995, Econometric Theory 11, 331-346). In an empirical application to a Finnish interest rate series evidence in favour of a stationary NCAR model with leptokurtic errors is found.

In this paper, we propose a Bayesian estimation and prediction procedure for noncausal autoregressive (AR) models. Specifically, we derive the joint posterior density of the past and future errors and the parameters, which gives posterior predictive densities as a byproduct. We show that the posterior model probability provides a convenient model selection criterion and yields information on the probabilities of the alternative causal and noncausal specifications. This is particularly useful in assessing economic theories that imply either causal or purely noncausal dynamics. As an empirical application, we consider U.S. inflation dynamics. A purely noncausal AR model gets the strongest support, but there is also substantial evidence in favor of other noncausal AR models allowing for dependence on past inflation. Thus, although U.S. inflation dynamics seem to be dominated by expectations, the backward-looking component is not completely missing. Finally, the noncausal specifications seem to yield inflation forecasts which are superior to those from alternative models especially at longer forecast horizons.

In this paper, we examine the directional predictability of US excess stock market returns by lagged excess returns from industry portfolios and a number of other commonly used variables by means of dynamic probit models. We focus on the directional component of the market returns because, for investment purposes, forecasting the direction of return correctly is presumably more relevant than the accuracy of point forecasts. Our findings suggest that only a small number of industries have predictive power for market returns, meaning that we find little evidence of stock markets reacting with a delay to information contained in industry returns. We also find that the binary response models outperform conventional predictive regressions in forecasting the direction of the market return. Finally, we test trading strategies and find that some of the industry portfolios do contain information that can be used to improve investment returns. In this paper, we examine the directional predictability of US excess stock market returns by lagged excess returns from industry portfolios and a number of other commonly used variables by means of dynamic probit models. We focus on the directional component of the market returns because, for investment purposes, forecasting the direction of return correctly is presumably more relevant than the accuracy of point forecasts. Our findings suggest that only a small number of industries have predictive power for market returns, meaning that we find little evidence of stock markets reacting with a delay to information contained in industry returns. We also find that the binary response models outperform conventional predictive regressions in forecasting the direction of the market return. Finally, we test trading strategies and find that some of the industry portfolios do contain information that can be used to improve investment returns. In this paper, we examine the directional predictability of US excess stock market returns by lagged excess returns from industry portfolios and a number of other commonly used variables by means of dynamic probit models. We focus on the directional component of the market returns because, for investment purposes, forecasting the direction of return correctly is presumably more relevant than the accuracy of point forecasts. Our findings suggest that only a small number of industries have predictive power for market returns, meaning that we find little evidence of stock markets reacting with a delay to information contained in industry returns. We also find that the binary response models outperform conventional predictive regressions in forecasting the direction of the market return. Finally, we test trading strategies and find that some of the industry portfolios do contain information that can be used to improve investment returns.

In this paper, we propose a new noncausal vector autoregressive (VAR) model for non-Gaussian time series. The assumption of non-Gaussianity is needed for reasons of identifiability. Assuming that the error distribution belongs to a fairly general class of elliptical distributions, we develop an asymptotic theory of maximum likelihood estimation and statistical inference. We argue that allowing for noncausality is of importance in empirical economic research, which currently uses only conventional causal VAR models. Indeed, if noncausality is incorrectly ignored, the use of a causal VAR model may yield suboptimal forecasts and misleading economic interpretations. This is emphasized in the paper by noting that noncausality is closely related to the notion of nonfundamentalness, under which structural economic shocks cannot be recovered from an estimated causal VAR model. As detecting nonfundamentalness is therefore of great importance, we propose a procedure for discriminating between causality and noncausality that can be seen as a test of nonfundamentalness. The methods are illustrated with applications to fiscal foresight and the term structure of interest rates.

We propose an estimation method of the new Keynesian Phillips curve (NKPC) based on a univariate noncausal autoregressive model for the inflation rate. By construction, our approach avoids a number of problems related to the GMM estimation of the NKPC. We estimate the hybrid NKPC with quarterly U.S. data (1955:1–2010:3), and both expected future inflation and lagged inflation are found important in determining the inflation rate, with the former clearly dominating. Moreover, inflation persistence turns out to be intrinsic rather than inherited from a persistent driving process.

We use noncausal autoregressions to examine the persistence properties of quarterly US consumer price inflation from 1970:1 to 2012:2. These nonlinear models capture the autocorrelation structure of the inflation series as accurately as their conventional causal counterparts, but they allow for persistence to depend on the size and sign of shocks to inflation as well as the inflation rate. Inflation persistence has decreased since the early 1980s, after which persistence is also greater following small and negative shocks than large and positive ones. At high levels of inflation, shocks are absorbed more slowly before the early 1980s and faster thereafter compared to low levels of inflation.

Simulation-based forecasting methods for a non-Gaussian noncausal vector autoregressive (VAR) model are proposed. In noncausal autoregressions the assumption of non-Gaussianity is needed for reasons of identifiability. Unlike in conventional causal autoregressions the prediction problem in noncausal autoregressions is generally nonlinear, implying that its analytical solution is unfeasible and, therefore, simulation or numerical methods are required in computing forecasts. It turns out that different special cases of the model call for different simulation procedures. Monte Carlo simulations demonstrate that gains in forecasting accuracy are achieved by using the correct noncausal VAR model instead of its conventional causal counterpart. In an empirical application, a noncausal VAR model comprised of U.S. inflation and marginal cost turns out superior to the best-fitting conventional causal VAR model in forecasting inflation.

In this paper, we compare the forecasting performance of univariate noncausal and conventional causal autoregressive models for a comprehensive data set consisting of 170 monthly U.S. macroeconomic and financial time series. The noncausal models consistently outperform the causal models. For a collection of quarterly time series, the improvement in forecast accuracy due to allowing for noncausality is found even greater.

Recently Stock and Watson (2007) showed that since the mid-1980s it has been hard for backward-looking Phillips curve models to improve on simple univariate models in forecasting U.S. inflation. While this indeed is the case when the benchmark is a causal autoregression, little change in forecast accuracy is detected when a noncausal autoregression is taken as the benchmark. In this note, we argue that a noncausal autoregression indeed provides a better characterization of U.S. inflation dynamics than the conventional causal autoregression and it is, therefore, the appropriate univariate benchmark model.

The heterogametic sex chromosomes (i.e. mammalian Y and avian W) do not usually recombine with the homogametic sex chromosomes which is known to lead into rapid degeneration of Y and W due to accumulation of deleterious mutations. On the other hand, some 96% of amphibian species have homomorphic, i.e. non-degenerate Y chromosomes. Nicolas Perrin's fountain-of-youth hypothesis states that this is a result of recombination between X and Y chromosomes in sex-reversed individuals. In this study, I model the consequences of such recombination for the dynamics of a deleterious mutation occurring in Y chromosomes. As expected, even relatively low levels of sex reversal help to purge deleterious mutations. However, the population-dynamic consequences of this depend on the type of selection that operates on the population undergoing sex reversal. Under fecundity selection, sex reversal can be beneficial for some parameter values, whereas under survival selection, it seems to be always harmful.

In this paper, we propose a simulation-based method for computing point and density forecasts for univariate noncausal and non-Gaussian autoregressive processes. Numerical methods are needed for forecasting such time series because the prediction problem is generally nonlinear and therefore no analytic solution is available. According to a limited simulation experiment, the use of a correct noncausal model can lead to substantial gains in forecast accuracy over the corresponding causal model. An empirical application to US inflation demonstrates the importance of allowing for noncausality in improving point and density forecasts.

This paper proposes a new nonlinear vector autoregressive (VAR) model referred to as the Gaussian mixture vector autoregressive (GMVAR) model. The GMVAR model belongs to the family of mixture vector autoregressive models and is designed for analyzing time series that exhibit regime-switching behavior. The main difference between the GMVAR model and previous mixture VAR models lies in the definition of the mixing weights that govern the regime probabilities. In the GMVAR model the mixing weights depend on past values of the series in a specific way that has very advantageous properties from both theoretical and practical point of view. A practical advantage is that there is a wide diversity of ways in which a researcher can associate different regimes with specific economically meaningful characteristics of the phenomenon modeled. A theoretical advantage is that stationarity and ergodicity of the underlying stochastic process are straightforward to establish and, contrary to most other nonlinear autoregressive models, explicit expressions of low order stationary marginal distributions are known. These theoretical properties are used to develop an asymptotic theory of maximum likelihood estimation for the GMVAR model whose practical usefulness is illustrated in a bivariate setting by examining the relationship between the EUR–USD exchange rate and a related interest rate data.