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In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions. (C) 2019 Elsevier B.V. All rights reserved.

This paper considers estimation of factor-augmented panel data regression models. One of the most popular approaches towards this end is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 2006, 74, 967–1012, 2006). For the pooled version of this estimator to be consistent, either the number of observables must be larger than the number of unobserved common factors, or the factor loadings must be distributed independently of each other. This is a problem in the typical application involving only a small number of regressors and/or correlated loadings. The current paper proposes a simple extension to the CCE procedure by which both requirements can be relaxed. The CCE approach is based on taking the cross-section average of the observables as an estimator of the common factors. The idea put forth in the current paper is to consider not only the average but also other cross-section combinations. Asymptotic properties of the resulting combination-augmented CCE (C 3 E) estimator are provided and tested in small samples using both simulated and real data.

The predominant way of modelling mortality rates is the lee–carter model and its many extensions. The lee–carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in lee–carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models.

We extend the repeated observations forecasting analysis of Stark and Croushore (2002) to allow for regressors that may be of higher sampling frequencies than the regressand. For the U.S. GNP quarterly growth rate, we compare the forecasting performances of an autoregressive model with those of several mixed-frequency models, including the MIDAS approach. Using the additional dimension provided by different vintages, we compute several forecasts for a given calendar date with each model, then approximate the corresponding distribution of forecasts by a continuous density. Next, we combine these model-specific densities using scoring rules and analyze both the composition and the evolution of the implied weights over time. In so doing, not only do we investigate the sensitivity of model selection to the choice of which data release to consider, we also illustrate how revision process information can be incorporated into real time studies. As a consequence of these analyses, we introduce a new weighting scheme that summarizes the information contained in the revision process of the variables under consideration.

The bulk of existing work on the statistical forecasting of air quality is based on either neural networks or linear regressions, which are both subject to important drawbacks. In particular, while neural networks are complicated and prone to in-sample overfitting, linear regressions are highly dependent on the specification of the regression function. The present paper shows how combining linear regression forecasts can be used to circumvent all of these problems. The usefulness of the proposed combination approach is verified using both Monte Carlo simulation and an extensive application to air quality in Bogota, one of the largest and most polluted cities in Latin America.

In an influential paper, Pesaran [Pesaran, M.H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74, 967-1012] proposes a very simple estimator of factor-augmented regressions that has since then become very popular. In this note we demonstrate how the presence of correlated factor loadings can render this estimator inconsistent. (C) 2013 Elsevier B.V. All rights reserved.

In this paper, we consider a cointegrated panel data model with non-stationary common factors, which, because of its appeal in many economic applications, has received much attention in the recent literature. By deriving a Granger-type representation theorem, we obtain several equivalent model formulations, which have differing merits for empirical work. (C) 2013 Elsevier B.V. All rights reserved.

In this article, we investigate the validity of the univariate autoregressive sieve bootstrap applied to time series panels characterized by general forms of cross-sectional dependence, including but not restricted to cointegration. Using the final equations approach we show that while it is possible to write such a panel as a collection of infinite order autoregressive equations, the innovations of these equations are not vector white noise. This causes the univariate autoregressive sieve bootstrap to be invalid in such panels. We illustrate this result with a small numerical example using a simple DGP for which the sieve bootstrap is invalid, and show that the extent of the invalidity depends on the value of specific parameters. We also show that Monte Carlo simulations in small samples can be misleading about the validity of the univariate autoregressive sieve bootstrap. The results in this article serve as a warning about the practical use of the autoregressive sieve bootstrap in panels where cross-sectional dependence of general form may be present.

Practitioners are generally well aware of the fact that most standard approaches for estimation and inference in panel data regressions are based on assuming that the cross-sectional units are independent of each other, an assumption that is surely mistaken in applications, especially in macroeconomics and finance. Yet, applications involving anything but these standard approaches are very rare. The current paper can be seen as a reaction to this. The purpose is to point to some of the recent advances in the area of factor-augmented panel regressions, and to also provide some guidance regarding their implementation.

This article makes an analytical study of the effects of the presence of both common and idiosyncratic stochastic trends on the pooled least squares estimator. The results suggest that the usual result of asymptotic normality depends critically on the absence of the common stochastic trend.

Several panel unit root tests that account for cross section dependence using a common factor structure have been proposed in the literature recently, notably Pesaran (2003), Moon and Perron (2004) and Bai and Ng (2004). This paper is aimed at comparing these three proposed unit root tests for panels with dynamic factors. It makes fourcontributions: (1) it compares the three testing procedures in terms of similarities and difference in the data generation process, tests, null and alternative hypotheses considered,(2) it compares the small sample properties of the tests usingMonte Carlo results in models with up to two common factors, (3) it provides an application which illustrates the use of the tests, and (4) finally it discusses the use of the tests in modelling in general. The main conclusions are: Pesaran’s (2003) cross-sectionally augmented (CA)DF tests are designed for cases where cross-sectional dependence is due to a single factor. The Moon and Perron (2004) tests which use defactored data is similar in spirit but can account for mutiple common factors. The Bai and Ng (2004) tests allow to tests for unit roots in the common factors and/or the idiosyncratic factors. It would therefore be natural to use the Pesaran (2003) or Moon and Perron tests in a first step to find out whether there are unit roots in the data. Then in a second step of modelling, the Bai and Ng (2004) tests could be used to determine whether the unit roots arise in the common factors or in the idiosyncratic components. It is also found that the latter behave well when the observed nonstationarity in the data series comes exclusively from nonstationary common factors, e.g. when the series cointegrate along the cross sectional dimension of the panel.

In this paper, the author discusses the appropriateness of treating explanatory variables of a single-equation error correction model as being weakly exogenous. He restates the derivation of the error correction model, and particularly the single-equation conditional error correction model, both in reduced and structural form. These allow the author to point out that the condition of weak endogeneity implicitly tested by usual orthogonality tests is generally not sufficient for single-equation conditional error correction models. The potential pitfalls of working within incomplete simultaneous dynamic equation models for exogeneity tests are also pointed out. The author illustrates this on some empirical studies. Copyright 1992 by Blackwell Publishing Ltd

Panel data framework has often been used to build Early Warning Systems for financial crises. This paper questions the implicit assumption that crises are homogenously caused by identical factors. It suggests a preliminary step aiming at forming optimal country clusters.

Panel unit‐root and no‐cointegration tests that rely on cross‐sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, Marcellino and Osbat [Econometrics Journal (2004), Vol. 7, pp. 322–340; Empirical Economics (2005), Vol. 30, pp. 77–91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit‐root tests using a common factor structure to model the cross‐sectional dependence, but not much work has been done yet for panel no‐cointegration tests. This paper proposes a model for panel no‐cointegration using an unobserved common factor structure, following the study by Bai and Ng [Econometrica (2004), Vol. 72, pp. 1127–1177] for panel unit roots. We distinguish two important cases: (i) the case when the non‐stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing residual‐based panel no‐cointegration tests, as suggested by Kao [Journal of Econometrics (1999), Vol. 90, pp. 1–44] and Pedroni [Econometric Theory (2004a), Vol. 20, pp. 597–625]. Under the data‐generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than inline image as for independent panels. We then examine the possibilities of testing for various forms of no‐cointegration by extracting the common factors and individual components from the observed data directly and then testing for no‐cointegration using residual‐based panel tests applied to the defactored data.

In this paper we derive permanent‐transitory decompositions of non‐stationary multiple times series generated by (r)nite order Gaussian VAR(p) models with both cointegration and serial correlation common features. We extend existing analyses to the two classes of reduced rank structures discussed in Hecq, Palm and Urbain (1998). Using the corresponding state space representation of cointegrated VAR models in vector error correction form we show how decomposition can be obtained even in the case where the number of common feature and cointegration vectors are not equal to the number of variables. As empirical analysis of US business fluctuations shows the practical relevance of the approach we propose.

The effect which the oil price time series has on the long run properties of Vector AutoRegressive (VAR) models for price levels and import demand is investigated. As the oil price variable is assumed to be weakly exogenous for the long run parameters, a cointegration testing procedure allowing for weakly exogenous variables is developed using a LU decomposition of the long run multiplier matrix. The likelihood based cointegration test statistics, Wald, Likelihood Ratio and Lagrange Multiplier, are constructed and their limiting distributions derived. Using these tests, we find that incorporating the oil price in a model for the domestic or import price level of seven industrialized countries decreases the long run memory of the inflation rate. Second, we find that the results for import demand can be classified with respect to the oil importing or exporting status of the specific country. The result for Japan is typical as its import price is not influenced by GNP in the long run, which is the case for all other countries.

To study non-durable import demand, we extend previous work done by Clarida (1994) and Ceglowski (1991) by considering a two-good version of the lifecycle model in which we introduce time-non-separability in the households' preferences. The model is estimated using quarterly data for the USA and France. Using the information contained in the observed stochastic and deterministic trends, we derive a cointegration restriction used to estimate curvature parameters of the instantaneous utility function. The remaining parameters are estimated in a second step by GMM. The constancy of the different parameters is investigated, in both the long and the short run. Habit formation turns out to be an important factor of import demand. (C) 1998 John Wiley & Sons, Ltd.

SUMMARY This paper reports results of an extensive analysis of statistical demand functions for food using household survey data and aggregate time-series data on food consumption in the USA and The Netherlands. Using the model put forward by Tobin (1950) for survey data, we find that socio-economic information on the composition, education, and status of households adds little to the explanation of food consumption. The income elasticity of food consumption decreases over time in the USA but increases in The Netherlands. Applying multivariate cointegration analysis to the time-series data, we find that strict price homogeneity, structural stability, and weak exogeneity of prices have to be rejected statistically at conventional significance levels, whereas weak exogeneity of food consumption cannot be rejected. The long-run income elasticity tends to decrease over time for US data and is roughly constant for Dutch data. The findings corroborate earlier findings for the survey data. The rejection of price exogeneity is consistent with Tobin’s model which treats prices as endogenous. #1997 John Wiley & Sons, Ltd.

We use recently developed time series techniques to analyse long historical data on the budget of the Court of Nivelles (Belgium) in the late Middle Ages. The unidirectional causality from receipts to expenditures supports the idea that the medieval system under consideration is a fine-focused (tax-oriented) control system. However, empirical evidence on the presensce of changes in receipt collection around 1520 favours the hypothesis of the decline of the medieval, urban based, tax oriented system and its transformation into a punishment-focused system.

In this paper we discuss and illustrate the relative merits and pitfalls of modelling cointegrated systems in partial or in complete system set-up. We follow both the complete VAR based approach advocated by Hendry and Mizon (1993) and the partial system approach based on so-called structural error correction models proposed by Boswijk (1991,1992). The issue of exogeneity is discussed and illustrated using quarterly data for Belgian aggregate imports. Several economically interesting questions related to price effects in international trade are raised in the empirical analysis.

In this paper, we investigate the long run relationship among five major Pacific-Basin stock markets. We focus on the common long run behaviour of their stock price indices over a sample period of 20 years. Using cointegration theory, we find that while there exists a rather integrated Pacific Basin financial area, the regional aspects (Asian versus Pacific) play important roles.