Testing unit root based on partially adaptive estimation

This paper proposes unit tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adptive estimation using nonparametric methods. The limiting distribution of the proposed test is a combination of standard normal and the traditional Dickey-Fuller (DF) distribution, including the traditional ADF test as a special case when using Gaussian density. Taking into a account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, wich includes te normal distribution as a limiting case. Monte Carlo Experiments indicate that, in the presence of heavy tail distributions or innovations that are contaminated by outliers, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit roots is not found in real exchange rate and nominal interest rate even haevy-tail is taken into a account.

Efficient Unit Root Tests of real Exchange Rates in the Post-Bretton Woods Era

We apply the efficient unit-roots tests of Elliott, Rothenberg, and Stock (1996), and Elliott (1998) to twenty-one real exchange rates using monthly data of the G-7 countries from the post-Bretton Woods floating exchange rate period. Our results indicate that, for eighteen out of the twenty-one real exchange rates, the null hypothesis of a unit root can be rejected at the 10% significance level or better using the Elliot et al (1996) DF-GLS test. The unit-root null hypothesis is also rejected for one additional real exchange rate when we allow for one endogenously determined break in the time series of the real exchange rate as in Perron (1997). In all, we find favorable evidence to support long-run purchasing power parity in nineteen out of twenty-one real exchange rates. Second, we find no strong evidence to suggest that the use of non-U.S. dollar-based real exchange rates tend to produce more favorable result for long-run PPP than the use of U.S. dollar-based real exchange rates as Lothian (1998) has concluded.

Unit Root Analysis of Traffic Time Series in Toll Highways

Concession contracts in highways often include some kind of clauses (for example, a minimum traffic guarantee) that allow for better management of the business risks. The value of these clauses may be important and should be added to the total value of the concession. However, in these cases, traditional valuation techniques, like the NPV (net present value) of the project, are insufficient. An alternative methodology for the valuation of highway concession is one based on the real options approach. This methodology is generally built on the assumption of the evolution of traffic volume as a GBM (geometric Brownian motion), which is the hypothesis analyzed in this paper. First, a description of the methodology used for the analysis of the existence of unit roots (i.e., the hypothesis of non-stationarity) is provided. The Dickey-Fuller approach has been used, which is the most common test for this kind of analysis. Then this methodology is applied to perform a statistical analysis of traffic series in Spanish toll highways. For this purpose, data on the AADT (annual average daily traffic) on a set of highways have been used. The period of analysis is around thirty years in most cases. The main outcome of the research is that the hypothesis that traffic volume follows a GBM process in Spanish toll highways cannot be rejected. This result is robust, and therefore it can be used as a starting point for the application of the real options theory to assess toll highway concessions.

Are state–local government expenditures converging? New evidence based on sequential unit root tests

Large and persistent gaps in subnational public expenditure have important implications regarding growth, equity, and migration. In this context, we revisit the question of expenditure convergence across the American states to provide more nuanced evidence than found by a small number of previous studies. We employ a methodology due to Smeekes (Bootstrap sequential tests to determine the stationary units in a panel, 2011) that sequentially tests for unit roots in pairwise (real per capita) expenditure gaps based on user specified fractions. In a panel of 48 combined state–local government units (1957–2008), we found that expenditures on highways, sanitation, utility, and education were far more convergent than expenditures on health and hospitals, police and fire protection, and public welfare. There was little evidence of “club convergence” based on the proportion of intraregional convergent pairs. Several historically high-grant receiving states showed relatively strong evidence of convergence. Our results bode well for future output convergence and opportunities for Tiebout-type migration across jurisdictions. They also imply a diminished role for public infrastructure and education spending in business location choices over time and a mixed role for federal grants in inducing convergence.

Seasonal Stability Tests in gretl. An Application to International Tourism Data

The seasonal stability tests of Canova & Hansen (1995) (CH) provide a method complementary to that of Hylleberg et al. (1990) for testing for seasonal unit roots. But the distribution of the CH tests are unknown in small samples. We present a method to numerically compute critical values and P-values for the CH tests for any sample size and any seasonal periodicity. In fact this method is applicable to the types of seasonality which are commonly in use, but also to any other.

A Note on Wavelet Correlation and Cointegration

In a recent paper Leong-Huang:2010 {Journal of Applied Statistics 37, 215–233} proposed a wavelet-correlation-based approach to test for cointegration between two time series. However, correlation and cointegration are two different concepts even when wavelet analysis is used. It is known that statistics based on nonstationary integrated variables have non-standard asymptotic distributions. However, wavelet analysis offsets the integrating order of nonstationary series so that traditional asymptotics on stationary variables suffices to ascertain the statistical properties of wavelet-based statistics. Based on this, this note shows that wavelet correlations cannot be used as a test of cointegration.

Real convergence in per capita output and growth in Eurozone: A time-series approach

The real convergence hypothesis has spurred a myriad of empirical tests and approaches in the economic literature. This Work Project intends to test for real output and growth convergence in all N(N-1)/2 possible pairs of output and output growth gaps of 14 Eurozone countries. This paper follows a time-series approach, as it tests for the presence of unit roots and persistence changes in the above mentioned pairs of output gaps, as well as for the existence of growth convergence with autoregressive models. Overall, significantly greater evidence has been found to support growth convergence rather than output convergence in our sample.

Sostenibilidad fiscal: una aproximación con datos panel para 8 países Latinoaméricanos

Este documento examina la hipótesis de sostenibilidad fiscal para 8 países de Latinoamérica. A partir de un modelo de datos panel, se determina si los ingresos y gasto primario de los Gobiernos entre 1960 - 2009 están cointegrados, es decir, si son sostenibles a largo plazo. Para esto, se utilizaron pruebas de raíz unitaria y cointegración de segunda generación con datos panel macroeconómicos, lo que permite tener en cuenta la dependencia cruzada entre los países, así como los posibles quiebres estructurales en la relación que estén determinados de manera endógena; en particular, se usan la prueba de estacionariedad de Hadri y Rao (2008) y la prueba de cointegración de Westerlund (2006). Como resultado del análisis se encontró evidencia empírica de que en el período bajo estudio el déficit primario en los 8 países latinoamericanos es sostenible pero en sentido débil.

Seasonal adjustment and cointegration

El documento examina el efecto de filtros de ajuste en el tamaño y poder de prueba de cointegración que usan los residuales como pruebas ADF y PP, mediante procedimientos MonteCarlo y una aplicación empírica. Nuestros resultados indican que el uso de filtros distorsiona el tamaño y reduce el poder de estas pruebas.

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Examining the behaviour of visitor arrivals to Australia from 28 different countries

Testing the integrational properties of visitor arrivals has important implications for policy, for if visitor arrivals are integrated of order one (nonstationary) then it implies that shocks to visitor arrivals are permanent. However, if visitor arrivals are found to be integrated or order zero (stationary) then this implies that shocks to visitor arrivals are temporary. In this paper we examine whether visitor arrivals to Australia are stationary or nonstationary, using the recently developed univariate and panel Lagrange multiplier tests, and the Im, Pesaran and Shin [Im, K.S., Pesaran, M.H., Shin, Y., 1997. Testing for Unit Roots in Heterogeneous Panels. Manuscript, Department of Applied Economics, University of Cambridge; Im, K.S., Pesaran, M.H., Shin, Y., 2003. Testing for Unit Roots in Heterogeneous Panels. Journal of Econometrics, 115, 53–74] panel t-test. Our exercise involves Australia’s 28 tourist source markets. Our main findings are: (1) that visitor arrivals to Australia from 28 tourist source markets are stationary, implying that any shock will have only a temporary effect and (2) the second structural break, which mainly coincides with the September 11 terrorist attacks and the Asian financial crisis, has slowed down the growth rate in visitor arrivals to Australia from 22 out of 28 (79%) of the tourism source markets.

Are shocks to energy consumption permanent or temporary? evidence from 182 countries

This article applies univariate and panel data unit root tests to annual panel data for 182 countries over the period 1979–2000 to examine the stationarity properties of per capita energy consumption. The univariate unit root test can only reject the unit root null for 56 countries or 31% of the sample at the 10% level or better. However, univariate unit root tests have low power with short spans of data and therefore failure to reject the unit root null should be treated with caution. When we apply the panel data unit root test we find overwhelming evidence that energy consumption is stationary. We discuss the policy implications of these findings and offer suggestions for future research.

Testing for a random walk in Italy's inflation in the post-war period, 1947-1996

This paper investigates the unit root properties of Italy’s inflation rate in the post-war period (1947-1996). To achieve the aim of this study, the Zivot and Andrews (1992) one break test and the Lumsdaine and Papell (1997) two breaks test for unit roots are applied. It is found that inflation for Italy was a non-stationary breakpoint for the period 1947-1996. This result has important implications for econometric modeling and in understanding the behavior of shocks to Italy’s inflation.