The power of tests for equivalent ARMA models: The implications for practitioners

Analysts frequently find it convenient to use the same ARMA model to make forecasts for multiple time series. The trick is to know when it is safe to assume that multiple series are generated by the same underlying process. Although several authors have developed statistical procedures for testing whether two models are equivalent, no one has shown how to determine the power of these tests. This paper shows how to determine the power of the most general test for equivalent ARMA models. It also shows how to quantify the effect of model misspecification errors on the accuracy of the forecast. An illustrative example and flowchart are then used to show how calculating the power of the test can enable the practitioner to safeguard against a serious degradation in the accuracy of the forecast.Jel classification: C12, C22, C53First version received: March 2002/Final version received: December 2002     

An international study of persistence in output: Parametric estimates using the data dependent systems approach

This paper parametrically obtains estimates of persistence in output using Pandit's (1977, 1982) Data Dependent Systems approach for modelling autoregressive and moving average processes. The estimates are based on over a century of annual data for the rate of change of output in nine industrialized countries. The sensitivity of estimates to various model selection criteria is examined. While persistence in output is found to be sensitive to model selection criteria, the output of all countries including the United States is found to have a substantial degree of persistence if the ARMA models are chosen according to the Schwarz Bayesian Criterion, but excluding the ARMA models whose moving average roots are near the unit root (which involves pile-up phenomenon). Moreover, the parametric estimates of persistence are shown not to have the known upward bias problem commonly associated with parametric estimates of persistence relative to nonparametric estimates.     

The persistence of unemployment in the USA and Europe in terms of fractionally ARIMA models

This article examines the persistence of unemployment in the USA and four European countries by means of fractionally integrated ARMA (ARFIMA) models. In doing so, a type of flexibility in modelling low-frequency dynamics not achieved by non-fractionally ARIMA models can be provided. The results indicate that the unemployment series are much more persistent in some countries such as the UK and France, than in others including Germany or the USA.     

Estimating a mixture of stochastic frontier regression models via the em algorithm: A multiproduct cost function application

Researchers have become increasingly interested in estimating mixtures of stochastic frontiers. Mester (1993), Caudill (1993), and Polachek and Yoon (1987), for example, estimate stochastic frontier models for different regimes, assuming sample separation information is given. Building on earlier work by Lee and Porter (1984), Douglas, Conway, and Ferrier (1995) estimate a stochastic frontier switching regression model in the presence of noisy sample separation information. The purpose of this paper is to extend earlier work by estimating a mixture of stochastic frontiers assuming no sample separation information. This case is more likely to occur in practice than even noisy sample separation information. In order to estimate a mixture of stochastic frontiers with no sample separation information, an EM algorithm to obtain maximum likelihood estimates is developed. The algorithm is used to estimate a mixture of stochastic (cost) frontiers using data on U.S. savings and loans for the years 1986, 1987, and 1988. Statistical evidence is found supporting the existence of a mixture of stochastic frontiers. First version received: 3/13/01/Final version received: 6/17/02 RID="*" ID="*"  I am grateful to Ram Acharya, Janice Caudill, and especially James R. Barth for several helpful comments on an earlier version of the paper. During the revision process I benefitted greatly from the suggestions of the Associate Editor and three anonymous referees.     

The spectral representation of Markov switching ARMA models

In this paper we propose a method to derive the spectral density function of Markov switching ARMA models. We apply the Riesz-Fischer theorem which defines the spectral representation as the Fourier transform of the autocovariance functions.     

The dynamics of inflation: a study of a large number of countries

Over the last twenty years the statistical properties of inflation persistence has been the subject of intense investigation and debate without reaching a unanimous conclusion yet. In this article we attempt to shed further light to this debate using a battery of econometric techniques in order to provide robust evidence on the degree of inflation persistence and whether this has changed during the period in which several countries have followed inflation-targeting regimes or new monetary regimes. We consider the inflation rates of thirty developed and emerging economies using quarterly data for the period 1958 to 2007 which include alternative monetary policy regimes. The coefficient of the inflation parameter is estimated by Ordinary Least Squares (OLS), Autoregressive Moving Average (ARMA) and Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. Furthermore, the grid-bootstrap Median Unbiased (MUB) estimator approach developed by Hansen (1999) is used to estimate the finite sample OLS estimates coupled with the 95% symmetric confidence interval. We also examine parameter stability of persistence coefficients by estimating a model with time-varying parameters.     

Testing spatial regression models under nonregular conditions

In time series context, estimation and testing issues with autoregressive and moving average (ARMA) models are well understood. Similar issues in the context of spatial ARMA models for the disturbance of the regression, however, remain largely unexplored. In this paper, we discuss the problems of testing no spatial dependence in the disturbances against the alternative of spatial ARMA process incorporating the possible presence of spatial dependence in the dependent variable. The problems of conducting such a test are twofold. First, under the null hypothesis, the nuisance parameter is not identified, resulting in a singular information matrix (IM), which is a nonregular case in statistical inference. To take account of singular IM, we follow Davies (Biometrika 64(2):247–254, 1977; Biometrika 74(1):33–43, 1987) and propose a test procedure based on the supremum of the Rao score test statistic. Second, the possible presence of spatial lag dependence will have adverse effect on the performance of the test. Using the general test procedure of Bera and Yoon (Econom Theory 9:649–658, 1993) under local misspecification, we avoid the explicit estimation of the spatial autoregressive parameter. Thus our suggested tests are entirely based on ordinary least squares estimation. Tests suggested here can be viewed as a generalization of Anselin et al. (Reg Sci Urban Econ 26:77–104, 1996). We conduct Monte Carlo simulations to investigate the finite sample properties of the proposed tests. Simulation results show that our tests have good finite sample properties both in terms of size and power, compared to other tests in the literature. We also illustrate the applications of our tests through several data sets.     

Testing for changing shapes of income distribution: Italian evidence in the 1990s from kernel density estimates

By using nonparametric methods, this paper estimates the distribution of both household and size-adjusted real income in Italy between 1987–1998. Because of data sparseness in the distribution, an adaptive bandwidth is used, while to account for sample design a weighting variable is incorporated in the estimation procedure. The time invariance and the presence of modes in the distributions are tested by means of a nonparametric test and a bootstrap test, respectively. The empirical results suggest that the Italian income distribution significantly changed over time. During the eighties the density shifted rightwards, positively affecting the well being of a large fraction of Italian households. The 1993 recession altered the shape of income distribution increasing inequality and polarisation, and the following period of slow recovery did not show significant changes in the shape of distribution in terms of relative income with a consequent permanence of inequality. The polarisation of the distribution is more noticeable for size-adjusted income rather than whole household income, reflecting the influence of family size on income shape.Jel classification: C14, D31, I30The authors gratefully acknowledge financial support from the Italian Ministry of the Universities and Scientific Research (MIUR). We would like to thank two anonymous referees, Nicholas Longford, Aman Ullah and participants of the International workshop on Income Distribution and Welfare, Milan, May 2002 for their useful comments and suggestions. Obviously we are the solely responsible of any further error and omission.First version received: January 2002/Final version received: January 2003     

Modelling the Persistence of Unemployment in Canada

The persistence of unemployment in Canada is examined in this article by means of fractionally integrated techniques. Using Sowell's (1992) procedure of estimating ARFIMA models by maximum likelihood along with other techniques, we show that the order of integration of the series is higher than one, implying that unemployment is a highly persistent variable.     

Goodness-of-fit techniques for count data models: an application to the demand for dental care in Spain

This paper compares the practical performance of alternative goodness-of-fit techniques for count data models in the context of a study of the determinants of demand for dental care in Spain. We apply alternative goodness-of-fit techniques to different specifications. In particular, we implement recently proposed specification tests which are consistent in the direction of general nonparametric alternatives. The analysis suggests that a negative binomial model is an appropriate specification for dental care demand. Dental health and income are identified as important predictors of individuals' behavior. First version received: April 2000/Final version received: March 2001     

Quantile estimation of frontier production function

The purpose of the paper is to provide new information on the performance of frontier estimation methods, using data from Italian hotel industry. Quantile regression is also suggested as solution to frontier production function estimation. It is shown that, while the choice of estimation methods among conventional techniques significantly affects the economic analysis, quantile regression provides valuable new information by estimating the whole spectrum of production functions corresponding to different efficiency levels. In addition, the method makes available a coherent framework to analyze the performance of the conventional techiniques. Jel classification: C14, C16, D24We would like to thank the Co-Editor, the Associate Editor and an anonymous referee for comments and suggestions. The research was supported by the University Research Council and the National Research Council. The usual disclaimer applies.The estimates were computed using the Roger Koenker and StatLibS-Plus routine of quantile regression and the Tim Coelli and CEPA Web site FRONTIER 4.1 Program. The data set is provided by the Ho.Re.Ca. survey conducted by ISTAT in 1992.First version received: June 2001/Final version received: December 2002     

On estimating long-run effects in models with lagged dependent variables

A common procedure in economics is to estimate long-run effects from models with lagged dependent variables. For example, macro panel studies frequently are concerned with estimating the long-run impacts of fiscal policy, international aid, or foreign investment.Our analysis points out the hazards of this practice. We use Monte Carlo experiments to demonstrate that estimating long-run impacts from dynamic models produces unreliable results.Biases can be substantial, sample ranges very wide, and hypothesis tests can be rendered useless in realistic data environments. There are three reasons for this poor performance. First, OLS estimates of the coefficient of a lagged dependent variable are downwardly biased in finite samples. Second, small biases in the estimate of the lagged, dependent variable coefficient are magnified in the calculation of long-run effects. And third, and perhaps most importantly, the statistical distribution associated with estimates of the LRP is complicated, heavy-tailed, and difficult to use for hypothesis testing. While many of the underlying problems have been long-known in the literature, the continued widespread use of the associated empirical procedures suggests that researchers are unaware of the extent and severity of the estimation problems. This study aims to illustrate their practical importance for applied research.     

Cointegration,common features,and persistence in U.S. farm output

This paper determines the persistence of shocks to U.S. farm output at the sectoral and sub-sectoral level using a disaggregated vector autoregression framework. The persistence is measured under models that impose short-run common feature and long-run cointegration restrictions. The sub-sectoral outputs are found to have a relatively high degree of comovement in the short-run and a relatively low degree of comovement in the long-run. The common feature and cointegration restrictions are found to improve the precision of persistence and cross-persistence estimates. Subsectoral persistence shows considerable variation; persistence in Poultry & Eggs sub-sector is nearly three times the persistence in the Fruits & Nuts sub-sector. Two sub-sectors that share long-run common trends, Food Grains and Feed, Hay & Forage, also have significant cross-persistence, implying technological spillovers.     

Early warning signals using AVaRs of infinitely divisible GARCH models — evidence from stock index markets

Classical time series models have failed to properly assess the risks that are associated with large adverse stock price behaviour. This article contributes to autoregressive moving average model–GARCH (ARMA–GARCH) models with standard infinitely divisible innovations and assesses the performance of these models by comparing them with other time series models that have normal innovation. We discuss the limitations of value at risk (VaR) and aim to develop early warning signal models using average value at risk (AVaRs) based on the ARMA–GARCH model with standard infinitely divisible innovations. Empirical results for the daily Dow Jones Industrial Average Index, the England Financial Times Stock Exchange 100 Index and the Japan Nikkei 225 Index reveal that estimating AVaRs for the ARMA–GARCH model with standard infinitely divisible innovations offers an improvement over prevailing models for evaluating stock market risk exposure during periods of distress in financial markets and provides a suitable early warning signal in both extreme events and highly volatile markets.     

Some simulation studies of nonparametric estimators

This paper constructs a number of Monte Carlo studies to assess the quality of various nonparametric estimators that have been proposed recently for the estimation of nonlinear econometric models. We consider both kernel and Fourier series based methods of estimation, and also examine techniques that have been suggested to improve the bias properties of the kernel estimator. The two models examined are a production function and a model emphasising the effects of risk. The Fourier estimator does very well in estimating the first of these, but not the second, while the kernel estimator shows substantial bias for the first, which is only partially alleviated by the procedures advocated for bias correction, and good results for the second.     

Fractional integration and business cycle features

We show in this article that fractionally integrated univariate models for GDP lead to a better replication of the main business cycle characteristics. We firstly show that the business cycle features are clearly affected by the degree of integration as well as by the other short run (AR, MA, etc.) components of the series. Then, we model the real GDP in the UK and the US by means of fractionally ARIMA (ARFIMA) model, and show that the time series can be specified in terms of this type of model with orders of integration higher than one but smaller than two. Comparing the ARFIMA specifications with those based on ARIMA models, we show via simulations that the former better describe the business cycles features of the data.Jel classification: C12, C15, C22The authors want to thank two anonymous referees for wise remarks. We have also benefited from questions and comments of the attendances at the econometric seminar of the Humboldt Universität zu Berlin and the ESEM2001 congress in Lausanne. Remaining errors and omissions are ours. All correspondence to: Luis A. Gil-Alana.First version received: February 2002/Final version received: December 2002     

Semiparametric Estimation of Simultaneous-Equation Microeconometric Models with Index Restrictions

This article introduces semiparametric methods for the estimation of simultaneous-equation microeconometric models with index restrictions. The methods are motivated by a semiparametric minimum-distance procedure, which unifies the estimation of both regression-type and linear or nonlinear simultaneous-equation models without emphasis on the construction of instrumental variables. Single-equation and systematic estimation methods and optimal weighting procedures are considered. The estimators are √ n -consistent and asymptotically normal. For the estimation of nonparametric regression and some sample selection models where the variances of disturbances are functions of the same indices, the optimal weighted estimator attains Chamberlain's efficient bound for models with conditional moment restrictions. The weighted estimator is shown to be optimal within a class of semiparametric instrumental variables estimators.
JEL classification numbers: C14, C24, C34.     

Interval regression models with endogenous explanatory variables

We consider the estimation of linear models where the dependent variable is observed by intervals and some continuous regressors may be endogenous. Our approach, an IV version of the technique devised by Stewart (Rev Econ Stud 50(3):737?C753, 1983), is fully parametric and two estimators are proposed: a two-step estimator and a limited-information maximum-likelihood estimator. The results can be summarized as follows: the two-step estimator has an intuitive appeal, and a Monte Carlo experiment suggests that its relative efficiency is rather satisfactory. The limited-information maximum-likelihood estimator, however, is probably simpler to implement and has the advantage of providing a framework in which several testing procedures are more straightforward to perform. The application of two-stage least squares to a proxy of the dependent variable built by taking midpoints, on the other hand, leads to inconsistent estimates; Monte Carlo evidence suggests that the bias arising from the ??midpoint?? technique is much worse than the effect of distributional misspecification. An example application is also included, which uses Australian data on migrants?? remittances; endogeneity effects are substantial and using conventional estimation methods leads to substantially misleading inference.     

Nonparametric quantile regression analysis of R&D-sales relationship for Korean firms

This paper applies the nonparametric quantile regression estimation procedure to the analysis of the innovation-firm size relationship using Korean manufacturing firms data. Due to the high asymmetric distribution of R&D expenditure, the mean regression does not capture properly the stylized facts of R&D behavior; hence it underestimates the sales elasticity. Comparing the parametric estimates and nonparametric estimates allows us to see that there exists a nonlinear relationship in innovative activity and sales. Dividing the data into three groups according to the sales volume, the elasticity in the medium-sized firms is the biggest for scientific firms. This result conforms that the findings of Scherer (1965) coincide with findings from Korean manufacturing firms data in the sense that R&D expenditure tends to increase faster than firm size with size up to a point and then more slowly among larger firms. For the non-scientific firms, it steadily increases showing increasing returns to scale in innovative activity in large firms.