Evidence on purchasing power parity from univariate models: the case of smooth transition trend‐stationarity

Recent research has found that trend‐break unit root tests derived from univariate linear models do not support the hypothesis of long‐run purchasing power parity (PPP) for US dollar real exchange rates. In this paper univariate smooth transition models are utilized to develop unit root tests that allow under the alternative hypothesis for stationarity around a gradually changing deterministic trend function. These tests reveal statistically significant evidence against the null hypothesis of a unit root for the real exchange rates of a number of countries against the US dollar. However, restrictions consistent with long‐run PPP are rejected for some of the countries for which a rejection of the unit root hypothesis is obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

Multivariate Small Area Estimation of Multidimensional Latent Economic Well-being Indicators

Factor analysis models are used in data dimensionality reduction problems where the variability among observed variables can be described through a smaller number of unobserved latent variables. This approach is often used to estimate the multidimensionality of well-being. We employ factor analysis models and use multivariate empirical best linear unbiased predictor (EBLUP) under a unit-level small area estimation approach to predict a vector of means of factor scores representing well-being for small areas. We compare this approach with the standard approach whereby we use small area estimation (univariate and multivariate) to estimate a dashboard of EBLUPs of the means of the original variables and then averaged. Our simulation study shows that the use of factor scores provides estimates with lower variability than weighted and simple averages of standardised multivariate EBLUPs and univariate EBLUPs. Moreover, we find that when the correlation in the observed data is taken into account before small area estimates are computed, multivariate modelling does not provide large improvements in the precision of the estimates over the univariate modelling. We close with an application using the European Union Statistics on Income and Living Conditions data.     

Canonical forms and tests of hypotheses: Part I: The general univariate mixed model

Abstract  A class of linear models is defined which contains many of the usual mixed and random models and allows the construction of tests for a wide class of hypotheses in a general manner. Characterizations are given for this class of models denoted as "regular linear models". Problems of estimation are briefly touched and some aids to practical applications are given, followed by two examples.     

Time series estimation of the bond default risk premium

The bond default risk premium, measured by the spread between higher and lower grade bond returns, is often estimated with univariate time series procedures and used as an input in financial models. In this paper, time series properties of the historical default risk premium are analyzed and forecasting results from univariate time series models are compared. An autoregressive model with an overreaction component provides the best statistical fit for the bond default risk premium series. A random walk model exhibits the worst fit. The findings are robust over a variety of model specifications and measurement choices. For all forms of the time series process the univariate time series models explain a small percentage of the variation in the default risk premium, raising questions about traditional approaches to estimating the expected default risk premium.     

Forecasting cryptocurrencies under model and parameter instability

This paper studies the predictability of cryptocurrency time series. We compare several alternative univariate and multivariate models for point and density forecasting of four of the most capitalized series: Bitcoin, Litecoin, Ripple and Ethereum. We apply a set of crypto-predictors and rely on dynamic model averaging to combine a large set of univariate dynamic linear models and several multivariate vector autoregressive models with different forms of time variation. We find statistically significant improvements in point forecasting when using combinations of univariate models, and in density forecasting when relying on the selection of multivariate models. Both schemes deliver sizable directional predictability.     

Applications of subsampling,hybrid, and size-correction methods

This paper analyzes the properties of subsampling, hybrid subsampling, and size-correction methods in two non-regular models. The latter two procedures are introduced in Andrews and Guggenberger (2009a). The models are non-regular in the sense that the test statistics of interest exhibit a discontinuity in their limit distribution as a function of a parameter in the model. The first model is a linear instrumental variables (IV) model with possibly weak IVs estimated using two-stage least squares (2SLS). In this case, the discontinuity occurs when the concentration parameter is zero. The second model is a linear regression model in which the parameter of interest may be near a boundary. In this case, the discontinuity occurs when the parameter is on the boundary.     

Moment-based estimation of smooth transition regression models with endogenous variables

Nonlinear regression models have been widely used in practice for a variety of time series and cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular, smooth transition regression (STR) models have been shown to be very useful for representing and capturing asymmetric behavior. Most STR models have been applied to univariate processes, and have made a variety of assumptions, including stationary or cointegrated processes, uncorrelated, homoskedastic or conditionally heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss moment-based methods for estimating STR models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity, developing an estimation procedure and a misspecification test for the STR model, presenting the results of Monte Carlo simulations to show the usefulness of the model and estimation method, and providing an empirical application for inflation rate targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated by a straightforward application of existing results in the literature.     

London calling: Nonlinear mean reversion across national stock markets

This paper revisits empirical evidence of mean reversion of relative stock prices in international stock markets. We implement a strand of univariate and panel unit root tests for linear and nonlinear models of 18 national stock indices from 1969 to 2016. Our major findings are as follows. First, we find strong evidence of nonlinear mean reversion of the relative stock price with the UK index as the reference, calling attention to the stock index in the UK, but not with the US index. Our results imply an important role of the local common factor in the European stock markets. Second, panel tests yield no evidence of linear and nonlinear stationarity when the cross-section dependence is considered, which provides conflicting results from those of the univariate tests. Last, we show how to understand these results via dynamic factor analysis. When the stationary common factor dominates nonstationary idiosyncratic components in small samples, panel tests that filter out the stationary common factor may yield evidence against the stationarity null hypothesis in finite samples. We corroborate this conjecture via extensive Monte Carlo simulations.     

A unified approach to validating univariate and multivariate conditional distribution models in time series

Modeling conditional distributions in time series has attracted increasing attention in economics and finance. We develop a new class of generalized Cramer–von Mises (GCM) specification tests for time series conditional distribution models using a novel approach, which embeds the empirical distribution function in a spectral framework. Our tests check a large number of lags and are therefore expected to be powerful against neglected dynamics at higher order lags, which is particularly useful for non-Markovian processes. Despite using a large number of lags, our tests do not suffer much from loss of a large number of degrees of freedom, because our approach naturally downweights higher order lags, which is consistent with the stylized fact that economic or financial markets are more affected by recent past events than by remote past events. Unlike the existing methods in the literature, the proposed GCM tests cover both univariate and multivariate conditional distribution models in a unified framework. They exploit the information in the joint conditional distribution of underlying economic processes. Moreover, a class of easy-to-interpret diagnostic procedures are supplemented to gauge possible sources of model misspecifications. Distinct from conventional CM and Kolmogorov–Smirnov (KS) tests, which are also based on the empirical distribution function, our GCM test statistics follow a convenient asymptotic $N(0,1)$ distribution and enjoy the appealing “nuisance parameter free” property that parameter estimation uncertainty has no impact on the asymptotic distribution of the test statistics. Simulation studies show that the tests provide reliable inference for sample sizes often encountered in economics and finance.     

Identification in statistical inference

The paper deals with the concept of identification in inferential statistics. At first a general concept of identification is defined and developed. Thereafter, the general theory is applied to univariate linear regression and simultaneous equation systems. Finally, attention is paid to models with lagged variables and some new related problems are suggested.     

The impact of purchasing power parity on auto foreign trade

In this study, the validity of the assumption saying that the import and export are a function of prices as in the classical, neo-classical approaches is studied within the framework of the import and export of automobile vehicles between 1997 and 2003 in Turkey and the EU countries which are automobile manufacturers. The price here is considered as the purchasing power parity. The effect of the purchasing power parity on the automobile import and export is determined by using classical models with constant coefficients, and fixed and random effects models with constant slope coefficients and a constant term differing according to units and/or time. The models comprise balanced linear panel data models. The likelihood ratio test and F-test are used in the selection of fixed effects and classical models; and the Lagrange multiplier test is used in the selection of random effects and classical models. As for the selection of fixed and random effects models, the Hausman test is used. As a result of these tests, the fixed effects models covering both individual and time effects are selected as the most appropriate import and export models.     

On variable ordination of modified Cholesky decomposition for estimating time-varying covariance matrices

Estimating time-varying covariance matrices of the vector of interest is challenging both computationally and statistically due to a large number of constrained parameters. In this work, we consider an order-averaged Cholesky-log-GARCH (OA-CLGARCH) model for estimating time-varying covariance matrices through the orthogonal transformations of the vector based on the modified Cholesky decomposition. The proposed method is to transform the vector at each time as a linear transformation of uncorrelated latent variables and then to use simple univariate GARCH models to model them separately. But the modified Cholesky decomposition relies on a given order of variables, which is often not available, to sequentially orthogonalize the variables. The proposed method develops an order-averaged strategy for the Cholesky-GARCH method to alleviate the effect of order of variables. The merits of the proposed method are illustrated through simulations and real-data studies.     

Subjective evaluation of composite econometric policy inputs

Studies have suggested that a composite forecast may be preferred to a single forecast. In addition, forecasting objectives are often conflicting. For example, one forecast may have the smallest sum of absolute forecast errors, while another has the smallest maximum absolute error. This paper examines the appropriateness of using multiple objective linear programming to determine weighted linear combinations of forecasts to be used as inputs for policy analysis. An example is presented where the methodology is used to combine the forecasts for several policy variables. The forecasts are selected from large econometric, consensus, and univariate time series models.     

Forecasting with nonstationary dynamic factor models

In this paper we analyze the structure and the forecasting performance of the dynamic factor model. It is shown that the forecasts obtained by the factor model imply shrinkage pooling terms, similar to the ones obtained from hierarchical Bayesian models that have been applied successfully in the econometric literature. Thus, the results obtained in this paper provide an additional justification for these and other types of pooling procedures. The expected decrease in MSE for using a factor model versus univariate ARIMA and shrinkage models are studied for the one factor model. Monte Carlo simulations are presented to illustrate this result. A factor model is also built to forecast GNP of European countries and it is shown that the factor model can provide a substantial improvement in forecasts with respect to both univariate and shrinkage univariate forecasts.     

On tests concerning coefficient matrices of linear restriction with normal regression models

Summary As an application of tests of general linear hypotheses methods are presented for testing the equality of coefficient matrices of linear restrictions with normal univariate and multivariate regression models. Geometrical interpretations of the results are given. The present paper generalizes some of the earlier results obtained byTocher, andBennett.     

Modeling and forecasting U.S. sex differentials in mortality

"This paper examines differentials in observed and forecasted sex-specific life expectancies and longevity in the United States from 1900 to 2065. Mortality models are developed and used to generate long-run forecasts, with confidence intervals that extend recent work by Lee and Carter (1992). These results are compared for forecast accuracy with univariate naive forecasts of life expectancies and those prepared by the Actuary of the Social Security Administration."     

Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data

Recent literature on panel data emphasizes the importance of accounting for time-varying unobservable individual effects, which may stem from either omitted individual characteristics or macro-level shocks that affect each individual unit differently. In this paper, we propose a simple specification test of the null hypothesis that the individual effects are time-invariant against the alternative that they are time-varying. Our test is an application of Hausman (1978) testing procedure and can be used for any generalized linear model for panel data that admits a sufficient statistic for the individual effect. This is a wide class of models which includes the Gaussian linear model and a variety of nonlinear models typically employed for discrete or categorical outcomes. The basic idea of the test is to compare two alternative estimators of the model parameters based on two different formulations of the conditional maximum likelihood method. Our approach does not require assumptions on the distribution of unobserved heterogeneity, nor it requires the latter to be independent of the regressors in the model. We investigate the finite sample properties of the test through a set of Monte Carlo experiments. Our results show that the test performs well, with small size distortions and good power properties. We use a health economics example based on data from the Health and Retirement Study to illustrate the proposed test.     

Selecting the best linear regression model: A classical approach

In this paper, we apply the model selection approach based on likelihood ratio (LR) tests developed in Vuong (1986) to the problem of choosing between two normal linear regression models which are non-nested. We explicitly derive the procedure when the competing linear models are both misspecified. Some simplifications arise when the models are contained in a larger correctly specified linear regression model, or when one computing linear model is correctly specified.     

Three Corrected Score Tests for Generalized Linear Models with Dispersion Covariates

We develop three corrected score tests for generalized linear models with dispersion covariates, thus generalizing the results of Cordeiro , Ferrari and Paula (1993) and Cribari-Neto and Ferrari (1995) . We present, in matrix notation, general formulae for the coefficients which define the corrected statistics. The formulae only require simple operations on matrices and can be used to obtain analytically closed-form corrections for score test statistics in a variety of special generalized linear models with dispersion covariates. They also have advantages for numerical purposes since our formulae are readily computable using a language supporting numerical linear algebra. Two examples, namely, iid sampling without covariates on the mean or dispersion parameter oand one-way classification models, are given. We also present some simulations where the three corrected tests perform better than the usual score test, the likelihood ratio test and its Bartlett corrected version. Finally, we present a numerical example for a data set discussed by Simonoff and Tsai (1994) .