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.

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.

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.

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

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.

Fractional Integration and Business Cycles Features

We show in this article that fractionally integrated univariate models for GDP may lead to a better replication of business cycle characteristics. We firstly show that the business cycle features are clearly affected by the degree of integration as well as by the other short run components of the series. Then, we model the real GDP in France, the UK and the US by means of fractionally ARIMA (ARFIMA) models, and show that the three time series can be specified in terms of this type of models with orders of integration higher than one but smaller than two. Comparing the ARFIMA specifications with those based on ARIMA models, we show via simulations that the former better describes the business cycles features of the data at least for the cases of the UK and the US.

The explaining role of the Earning-Price Ratio in the Spanish Stock Market

In this paper we study the suitability of the CAPM to the Spanish Stock Market Interconnection System (SIBE) for the period 1988-2000, by means of time series and cross-section multivariate tests. Even though there is no enough empirical evidence to reject this model, it is shown that the relation between risk beta and stock returns is weak. Therefore, we look for several fundamental variables –using Fama and MacBeth OLS (Ordinary Least Squares) and LTS (Least Trimmed Squares) estimators– which could explain, with or without beta, the cross-section of stock returns. We conclude that there is a strong earning-price ratio effect in the Spanish Stock Market and that beta is able to explain the cross-section of expected returns, not solely, but jointly with earningprice ratio. On the other hand, there is neither size nor book-to-market ratio effects. However, there is evidence of turn-of-the year effect, which suggests tax-loss selling and window-dressing phenomena.CAPM; anomalies; tax-loss selling; window-dressing

Interest rate dynamics in Kenya : commercial banks' rates and the 91 day treasury bill rate

This paper analyses the implicit dynamics underlying the interest rate structure in Kenya. For this purpose we use data on four commercial banks’ interest rates (Deposits, Savings, Lending and Overdraft) together with the 91-Day Treasury Bill rate, for the time period July 1991 – August 2010, and apply various techniques based on long-range dependence and, in particular, on fractional integration. The results indicate that all series examined are nonstationary with orders of integration equal to or higher than 1. The analysis of various spreads suggests that they also are nonstationary I(1) variables, the only evidence of mean reversion being obtained in the case of the Deposits – Treasury Bill rate spread with autocorrelated errors

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

This paper 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 properties of the series under analysis, which display different orders of integration, a long memory regression model is used, 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, depending on the type of tourism series employed. Disaggregating the imports across the different types of wine it is observed that only for quality 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.international trade, tourism, long memory, Spanish wine, International Relations/Trade, F14, C22, Q13, L83,