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.

Non-Linearities And Fractional Integration In The Us Unemployment Rate

This paper proposes a model of the US unemployment rate which accounts for both its asymmetry and its long memory. Our approach introduces fractional integration and nonlinearities simultaneously into the same framework, using a Lagrange Multiplier procedure with a standard null limit distribution. The empirical results suggest that the US unemployment rate can be specified in terms of a fractionally integrated process, which interacts with some non-linear functions of labour demand variables such as real oil prices and real interest rates. We also find evidence of a long-memory component. Our results are consistent with a hysteresis model with path dependency rather than a NAIRU model with an underlying unemployment equilibrium rate, thereby giving support to more activist stabilisation policies. However, any suitable model should also include business cycle asymmetries, with implications for both forecasting and policy-making

Mean Reversion in the Nikkei, Standard & Poor and Dow Jones indices

Three stock market indices (the Nikkei 225, the Standard and Poor’s 500 and the Dow Jones EURO STOXX 50) are analysed in this paper using a parametric procedure for fractional integration. We find that the orders of integration of these three series range between 0.75 and 1.25. A model selection criterion suggests that they can be specified as fractional processes of order 0.75, with AR(1) disturbances. This indicates that the three series exhibit mean reversion

Long memory and fractional integration in high frequency data on the US Dollar / British Pound spot exchange rate

This paper analyses the long-memory properties of a high-frequency financial time series dataset. It focuses on temporal aggregation and other features of the data, and how they might affect the degree of dependence of the series. Fractional integration or I(d) models are estimated with a variety of specifications for the error term. In brief, we find evidence that a lower degree of integration is associated with lower data frequencies. In particular, when the data are collected every 10 minutes there are several cases with values of d strictly smaller than 1, implying mean-reverting behaviour; however, for higher data frequencies the unit root null cannot be rejected. This holds for all four series examined, namely Open, High, Low and Last observations for the US dollar / British pound spot exchange rate and for different sample periods.This study is financially supported from the Ministry of Education of Spain (ECO2011-2014 – 28196 - ECON Y FINANZAS, Spain) and from a Jeronimo de Ayanz project of the Government of Navarra

Testing the PPP hypothesis in the sub-Saharan countries

This paper examines the PPP hypothesis in a number of Sub-Saharan countries by testing the order of integration in the log of their real exchange rate vis-à-vis the US dollar. I(d) techniques based on both asymptotic and finite sample results are used. The test results lead to the rejection of PPP in all cases: although orders of integration below 1 are found in fourteen countries, the unit root null cannot be rejected.This study is partly funded by the Ministerio de Ciencia y TecnologíaECO2011-2014 ECON Y FINANZAS, Spain) and from a Jeronimo de Ayanz project of the Government of Navarra

Modelling Stochastic Volatility In Asset Returns Using Fractionally Integrated Semiparametric Techniques

In this article we estimate the order of integration of the volatility process of several exchange rates and stock returns using fractionally integrated semiparametric techniques, namely a local Whittle semiparametric estimator. The results suggest that all series can be well described in terms of I(d) statistical models, with values of d higher than 0, indicating long-memory behaviour

Fractional Cointegration And Aggregate Money Demand Functions

This paper examines aggregate money demand relationships in five industrial countries by employing a two-step strategy for testing the null hypothesis of no cointegration against alternatives which are fractionally cointegrated. Fractional cointegration would imply that, although there exists a long-run relationship, the equilibrium errors exhibit slow reversion to zero, i.e. that the error correction term possesses long memory, and hence deviations from equilibrium are highly persistent. It is found that the null hypothesis of no cointegration cannot be rejected for Japan. By contrast, there is some evidence of fractional cointegration for the remaining countries, i.e., Germany, Canada, the US, and the UK (where, however, the negative income elasticity which is found is not theory-consistent). Consequently, it appears that money targeting might be the appropriate policy framework for monetary authorities in the first three countries, but not in Japan or in the UK

A Multivariate Long-Memory Model with Structural Breaks

This paper introduces a multivariate long-memory model with structural breaks. In the proposed framework, time series exhibit possibly fractional orders of integration which are allowed to be different in each subsample. The break date is endogenously determined using a procedure which minimises the residual sum of squares (RSS). Monte Carlo experiments show that this method for detecting breaks performs well in large samples. As an illustration, we estimate a trivariate VAR including prices, employment and GDP in both the US and Mexico. For the subsample preceding the break our findings are similar to those of earlier studies based on a standard VAR approach in both countries, in the sense that the variables exhibit integer degrees of integration. On the contrary, the series are found to be fractionally integrated after the break, with the fractional differencing parameters being higher than 1 in the case of Mexico

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.

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