Seasonal fractional integration with structural break. An application to the German GNP data

This paper deals with the analysis of the German nominal GNP quarterly data (1973q1 – 1996q4) using a new approach based on seasonal fractional integration that allows us to incorporate a structural break that is endogenously determined by the model. The results show that the break occurs at 1990q2, the time of the German re-unification, and the order of integration is slightly above 1 before the break, and strictly smaller than 1 (though highly persistent) after the unification.

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

Fractional integration and structural breaks at unknown periods of time

This paper deals with the analysis of structural breaks in the context of fractionally integrated models. We assume that the break dates are unknown and that the different sub-samples possess different intercepts, slope coefficients and fractional orders of integration. The procedure is based on linear regression models using a grid of values for the fractional differencing parameters and least squares estimation. Several Monte Carlo experiments conducted across the paper show that the procedure performs well if the sample size is large enough. Two empirical applications are carried out at the end of the article.

Long run and cyclical strong dependence in macroeconomic time series. Nelson and Plosser revisited

This paper deals with the presence of long range dependence at the long run and the cyclical frequencies in macroeconomic time series. We use a procedure that allows us to test unit roots with fractional orders of integration in raw time series. The tests are applied to an extended version of Nelson and Plosser’s (1982) dataset, and the results show that, though the classic unit root hypothesis cannot be rejected in most of the series, fractional degrees of integration at both the zero and the cyclical frequencies are plausible alternatives in some cases. Additionally, the root at the zero frequency seems to be more important than the cyclical one for all series, implying that shocks affecting the long run are more persistent than those affecting the cyclical part. The results are consistent with the empirical fact observed in many macroeconomic series that the long-term evolution is nonstationary, while the cyclical component is stationary.

Testing of I(d) processes in the real output

The real GDP series of sixteen European countries along with Japan, Canada and the US are examined in this paper by means of fractional integration techniques. The results crucially depend on how we specify the I(0) disturbances, as white noise or autoregressions. Thus, in the former case the orders of integration are higher than 1 in all cases, while using autoregressions the values are all strictly smaller than 1 implying mean reverting behaviour.

Testing of Fractional Cointegration in Macroeconomic Time Series

We propose in this article a two-step testing procedure of fractional cointegration in macroeconomic time series. It is based on Robinson’s (1994) univariate tests and is similar in spirit to the one proposed by Engle and Granger (1987), testing initially the order of integration of the individual series and then, testing the degree of integration of the residuals from the cointegrating relationship. Finite-sample critical values of the new tests are computed and Monte Carlo experiments are conducted to examine the size and the power properties of the tests in finite samples. An empirical application, using the same datasets as in Engle and Granger (1987) is also carried out at the end of the article.

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.

Deterministic Seasonality versus Seasonal Fractional Integration

We propose in this article the use of a testing procedure due to Robinson (1994) for testing deterministic seasonality versus seasonal fractional integration. A new statistic, based on the score principle, is developed to simultaneously test both the order of integration of the seasonal component and the need of seasonal dummies. Both tests have standard null and local limit distributions. However, finite-sample critical values of the tests are computed, and experiments based on Monte Carlo show that the sizes of the asymptotic tests are too large, these larger sizes being also associated with some superior rejection frequencies compared with the finite-sample-based tests. Using quarterly data for real consumption and income in Canada, the UK and Japan, the results show that both variables are seasonally fractionally integrated for the three countries without need of deterministic seasonal dummies. We also find evidence that the series may be seasonally fractionally cointegrated.

Time series modelling of sunspot numbers using long range cyclical dependence

This paper deals with the analysis of the monthly structure of sunspot numbers using a new technique based on cyclical long range dependence. The results show that sunspot numbers have a periodicity of 130 months, but more importantly, that the series is highly persistent, with an order of cyclical fractional integration slightly above 0.30. That means that the series displays long memory, with a large degree of dependence between the observations that tends to disappear very slowly in time

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.