Unit and Fractional Roots in the Presence of Abrupt Changes with an Application to the Brazilian Inf

In this article we analyse the monthly structure of the Brazilian inflation rate by means of using fractionally integrated techniques. This series is characterized by strong government interventions to bring inflation to a low level. We use a testing procedure due to Robinson (1994) which permits us to model the underlying dynamics of the series in terms of an I(d) statistical model, with the government interventions being specified in terms of dummy variables. The results show that the series can be well described in terms of an I(0.75) process with some of the interventions having little impact on the series.

A fractionally integrated model for the Spanish real GDP

The annual structure of the Spanish real GDP is investigated in this article by means of fractional integration techniques. The results show that the series can be specified in terms of an I(d) process with d smaller than one and thus showing long memory and mean-reverting behaviour.fractional integration

Structural Change and the Order of Integration in Univariate Time Series

In this article I investigate whether the presence of structural breaks affects inference on the order of integration in univariate time series. For this purpose, we make use of a version of the tests of Robinson (1994) which allows us to test unit and fractional roots in the presence of deterministic changes. Several Monte Carlo experiments conducted across the paper show that the tests perform relatively well in the presence of both mean and slope breaks. The tests are applied to annual data on German real GDP, the results showing that the series may be well described in terms of a fractional model with a structural slope break due to World War II.

The Nature of the Relationship between International Tourism and International Trade: The Case of Ge

This paper deals with the relationship between international trade and tourism. In particular, we focus on the effect that German tourism to Spain has on German imports of Spanish wine. Due to the different stochastic properties of the series under analysis, which display different orders of integration, we use a methodology based on long memory regression models, where tourism is supposed to be exogenous. The results show that at the aggregate level, tourism has an effect on wine imports that lasts between two and nine months. Disaggregating the imports across the different types of wine it is observed that only for red wines from Navarra, Penedús and Valdepeñas, and to a certain extent for sparkling wine, tourism produces an effect on its future demand. From a policy-making perspective our results imply that the impact of tourism on the host economy is not only direct and short-term but also oblique and delayed, thus reinforcing the case for tourism as a means for economic development.

Long Memory at the Long Run and at the Cyclical Frequencies:Modelling Real Wages in England: 1260-1994

This paper examines historical data on daily real wages in England for the time period 1260-1994 by means of new statistical techniques suitable for modelling long memory both at the long run and the cyclical frequencies. Specifically, it uses a procedure due to Robinson (1994) which is based, for the cyclical component, on Gegenbauer processes. We test for the presence of unit (and fractional) roots at both the zero and the cyclical frequencies, and find that the root at the zero frequency plays a much more important role than the cyclical one, though the latter frequency also has a component of long memory behaviour. It also appears that the trending (zero frequency) component is nonstationary while the cyclical one is stationary, with shocks having permanent effects on the former, but transitory effects on the latter. Similar conclusions are reached when allowing for a break in 1875 (the beginning of the Second Industrial Revolution).

Technology Shocks and Hours Worked: A Fractional Integration Perspective

Previous research has found that the response of hours worked to a technology shock crucially depends on whether the variable hours is assumed to be an I(0) or an I(1) variable ex-ante. In this paper we employ a multivariate fractionally integrated model which allows us to determine simultaneously the order of integration of hours worked and the response of hours to a technology shock. We find that hours fall on impact in response to a positive technology shock.

Testing fractional integration in macroeconomic time series.

This thesis concentrates on testing fractional (and seasonally fractional) integration and cointegration in macroeconomic time series. Fractional integration has recently emerged in the literature as an alternative plausible way of modelling economic series, and here we focus mainly on some empirical applications of a testing procedure suggested by Robinson (1994c) for testing unit roots and other nonstationary hypotheses in raw time series. These tests, described in Chapter 2, are asymptotically most powerful against fractional alternatives, have asymptotic critical values given by a chi-squared distribution, and allow great flexibility in the choice of null and alternative hypotheses, which can entail one or more integer or fractional roots of arbitrary order anywhere on the unit circle in the complex plane. In Chapter 2 we also make some simulations, comparing the size-corrected versions of the tests with those based on asymptotic critical values, and other existing unit root tests. The tests of Robinson (1994c) are applied in Chapter 3 to an extended version of the data set used by Nelson and Plosser (1982). These are fourteen U.S. macroeconomic variables in annual data, and we focus here on cases where the root is located at zero frequency. In Chapter 4 we concentrate on seasonality. Robinson's (1994c) tests are now applied to quarterly U.K. and Japanese consumption and income series, using the same data as in Hylleberg, Engle, Granger and Yoo (HEGY, 1990) and Hylleberg, Engle, Granger and Lee (HEGY, 1993). We test for the presence of unit or fractional roots, not only at zero but also at seasonal frequencies. A multivariate version of the tests, based on the score, likelihood-ratio and Wald principles is obtained in Chapter 5 and some simulations, based on Monte Carlo experiments, are carried out at the end of the chapter. The multivariate tests of Chapter 5 are applied in Chapter 6 to some pairs of macroeconomic variables claimed to be cointegrated by many authors. Using the same data as in Engle and Granger (1987) and Campbell and Shiller (1987), we analyze the relationship between U.S. consumption and income, prices and wages, GNP and money and stock prices and dividends. A testing procedure to investigate if these pairs of variables are fractionally cointegrated is also described and applied in Chapter 6

The Nature of the Relationship Between International Tourism and International Trade: the Case of German Imports of Spanish Wine

This article deals with the relationship between international trade and tourism. We focus on the effect that German tourism to Spain has on German imports of Spanish wine. Due to the different stochastic properties of the series under analysis, which display different orders of integration, a methodology is used based on long memory regression models, where tourism is supposed to be exogenous. The period covered is January 1998 to November 2004. The results show that tourism has an effect on wine imports that lasts between two and nine months. Disaggregating the imports across the different types of wine it is observed that only for red wines from Navarra, Penedús and Valdepeñas, and to a certain extent for sparkling wine, tourism produces an effect on future import demand. From a policy-making perspective our results imply that the impact of tourism on the host economy is not only direct and short-term but also oblique and delayed, thus reinforcing the case for tourism as a means for economic development

Time Trends and Persistence in the Snowpack Percentages by Watershed in Colorado

In this paper we investigate the time trend coefficients in snowpack percentages by watershed in Colorado, US, allowing for the possibility of long range dependence or long memory processes. Nine series corresponding to the following watersheds are examined: Arkansas, Colorado, Gunnison, North Platte, Rio Grande, South Platte, San Juan-Animas-Dolores-San Miguel, Yampa & White and Colorado Statewide, based on annual data over the last eighty years. The longest series start in 1937 and all end in 2019. The results indicate that most of the series display a significant decline over time, showing negative time trend coefficients, and thus supporting the hypothesis of climate change and global warming. Nevertheless, there is no evidence of a long memory pattern in the data

New Revelations about Unemployment Persistence in Spain

This paper aims to re-examine the persistence of unemployment in Spain. For this purpose, we use time series and cross-section analysis. From a time series viewpoint we disaggregate unemployment by regions, and use unit root tests, AR coefficients and fractional differencing parameters as indicators of persistence. For the cross-section approach, we first estimate mean regressions of regional unemployment rates. Then, using a panel of 114 periods and 50 provinces, we estimate pooled, fixed and random effects models. Finally, following some recent developments, we implement several panel data unit root tests. Previous studies had already shown the strong persistence of Spanish unemployment. Our disaggregated analysis extends that finding to reveal that the persistence is greater in the most industrialised regions. The results also suggest that a structural break took place in 1994, implying a decline in the unemployment persistence since then.