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.

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

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

Infant mortality rates: Time trends and fractional integration

This paper examines the time trends in infant mortality rates in a number of countries in the 20th century. Rather than imposing that the error term is a stationary I(0) process, we allow for the possibility of fractional integration and hence for a much greater degree of flexibility in the dynamic specification of the series. Indeed, once the linear trend is removed, all series appear to be I(d) with d > 0 rather than I(0), implying longrange dependence. As expected, the time trend coefficients are significantly negative, although of a different magnitude from to those obtained assuming I(0) disturbances

Persistence in youth unemployment

This paper examines the degree of persistence of youth unemployment (total, male and female) in twenty-four countries by using two alternative measures: the AR coefficient and the fractional differencing parameter, based on short- and long-memory processes respectively. The evidence suggests that persistence is particularly high in Japan and some EU countries such as Spain, Portugal, Ireland and Finland, where appropriate policy actions are of the essence. Specifically, active labour market policies are necessary to prevent short-term unemployment from becoming structural (long-term).The first-named author gratefully acknowledges financial support from a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under the project IRSES GA-2010-269134, and the second-named author from the Ministerio de Ciencia y Tecnologia (ECO2012-2014, n.28196 ECON Y FINANZAS, Spain) and from a Jeronimo de Ayanz project of the Government of Navarra

Long Run And Cyclical Dynamics In The Us Stock Market

This paper examines the long-run dynamics and the cyclical structure of the US stock market using fractional integration techniques. We implement a version of the tests of Robinson (1994a), which enables one to consider unit roots with possibly fractional orders of integration both at the zero (long-run) and the cyclical frequencies. We examine the following series: inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run or zero frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long-run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, we use six different criteria to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results show that the former outperform the others in a number of cases

Persistence and cycles in the US Federal Funds rate

This paper uses long-range dependence techniques to analyse two important features of the US Federal Funds effective rate, namely its persistence and cyclical behaviour. It examines annual, monthly, bi-weekly and weekly data, from 1954 until 2010. Two models are considered. One is based on an I(d) specification with AR(2) disturbances and the other on two fractional differencing structures, one at the zero and the other at a cyclical frequency. Thus, the two approaches differ in the way the cyclical component of the process is modelled. In both cases we obtain evidence of long memory and fractional integration. The in-sample goodness-of-fit analysis supports the second specification in the majority of cases. An out-of-sample forecasting experiment also suggests that the long-memory model with two fractional differencing parameters is the most adequate one, especially over long horizons.This study is partly funded by the Ministerio de Ciencia y Tecnología ECO2011-2014 ECON Y FINANZAS, Spain) and from a Jeronimo de Ayanz project of the Government of Navarra

US disposable personal income and housing price index: A fractional integration analysis

This paper examines the relationship between US disposable personal income (DPI) and house price index (HPI) during the last twenty years applying fractional integration and long-range dependence techniques to monthly data from January 1991 to July 2010. The empirical findings indicate that the stochastic properties of the two series are uch that cointegration cannot hold between them, as mean reversion occurs in the case of DPI but not of HPI. Also, recursive analysis shows that the estimated fractional parameter is relatively stable over time for DPI whilst it increases throughout the sample for HPI. Interestingly, the estimates tend to converge toward the unit root case fter 2008 once the bubble had burst. The implications for explaining the recent financial crisis and choosing appropriate policy actions are discussed.The second named-author gratefully acknowledges financial support from the Ministerio de Ciencia y Tecnología (ECO2008-03035 ECON Y FINANZAS, Spain) and from a PIUNA Project from the University of Navarra

Testing For Deterministic And Stochastic Cycles In Macroeconomic Time Series

In this paper we use a statistical procedure which is appropriate to test for deterministic and stochastic (stationary and nonstationary) cycles in macroeconomic time series. These tests have standard null and local limit distributions and are easy to apply to raw time series. Monte Carlo evidence shows that they perform relatively well in the case of functional misspecification in the cyclical structure of the series. As an example, we use this approach to test for the presence of cycles in US real GDP

The weekly structure of US stock prices

In this paper we use fractional integration techniques to examine the degree of integration of four US stock market indices, namely the Standard and Poor, Dow Jones, Nasdaq and NYSE, at a daily frequency from January 2005 till December 2009. We analyse the weekly structure of the series and investigate their characteristics depending on the specific day of the week. The results indicate that the four series are highly persistent; a small degree of mean reversion (i.e., orders of integration strictly smaller than 1) is found in some cases for S&P and the Dow Jones indices. The most interesting findings are the differences in the degree of dependence for different days of the week. Specifically, lower orders of integration are systematically observed for Mondays and Fridays, consistently with the “day of the week” effect frequently found in financial data.The second-named author gratefully acknowledges financial support from the the Ministerio de Ciencia y Tecnología (ECO2008-03035 ECON Y FINANZAS, Spain) and from a PIUNA Project from the University of Navarra