Deterministic versus stochastic seasonal fractional integration and?structural breaks

This paper considers a general model which allows for both deterministic and stochastic forms of seasonality, including fractional (stationary and nonstationary) seasonal orders of integration, and also incorporating endogenously determined structural breaks. Monte Carlo analysis shows that, in the case of a single break, the suggested procedure performs well even in small samples, accurately capturing the seasonal properties of the series, and correctly detecting the break date. As an illustration, the model is estimated using four US series (output, consumption, imports and exports). The results suggest that the seasonal patterns of these variables have changed over time: specifically, in the second subsample the systematic component of seasonality becomes insignificant, whilst the degree of persistence increases.     

Fractional integration and impulse responses: a bivariate application to real output in the USA and four Scandinavian countries

This article analyzes impulse response functions in the context of vector fractionally integrated time series. We derive analytically the restrictions required to identify the structural-form system. As an illustration of the recommended procedure, we carry out an empirical application based on a bivariate system including real output in the USA and, in turn, in one of the four Scandinavian countries (Denmark, Finland, Norway, and Sweden). The empirical results appear to be sensitive, to some extent, to the specification of the stochastic process driving the disturbances, but generally a positive shock to US output has a positive effect on the Scandinavian countries, which tend to disappear in the long run.     

Linear and segmented trends in sea surface temperature data

This paper deals with the analysis of the MET Office Hadley Centre's sea surface temperature data set (HadSST3) by using long-range dependence techniques. We incorporate linear and segmented trends using fractional integration, and thus permitting long memory behavior in the detrended series. The results indicate the existence of warming trends in the three series examined (Northern and Southern Hemispheres along with global temperatures), with orders of integration which are in the range (0.5, 1) and thus implying nonstationary long memory and mean reverting behavior. This is innovative compared with other works that assume short memory behavior in the detrended series. Allowing for segmented trends two features are observed: increasing values in the degree of dependence of the series across time and significant warming trends from 1940 onwards.     

Infant mortality rates: time trends and fractional integration

This paper examines the existence of time trends in the infant mortality rates in a number of countries in the twentieth century. We test for the presence of deterministic trends by adopting a linear model for the log-transformed data. Instead of assuming that the error term is a stationary I(0), or alternatively, a non-stationary I(1) 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 0<d<1, implying long-range dependence. As expected, the time trend coefficients are significantly negative, although of a different magnitude from those obtained assuming integer orders of differentiation.     

Long memory and data frequency in financial markets

This paper investigates persistence in financial time series at three different frequencies (daily, weekly and monthly). The analysis is carried out for various financial markets (stock markets, FOREX, commodity markets) over the period from 2000 to 2016 using two different long memory approaches (R/S analysis and fractional integration) for robustness purposes. The results indicate that persistence is higher at lower frequencies, for both returns and their volatility. This is true of the stock markets (both developed and emerging) and partially of the FOREX and commodity markets examined. Such evidence against the random walk behaviour implies predictability and is inconsistent with the Efficient Market Hypothesis (EMH), since abnormal profits can be made using trading strategies based on trend analysis.     

Persistence of the Misery Index in African Countries

This paper deals with the analysis of the misery index in a group of 55 African countries by using fractional integration or I(d) techniques. In doing so, we can measure the degree of persistence of the index in a more flexible way than with other methods that simply use integer degrees of differentiation (zero or one). Our results indicate a large degree of heterogeneity across the countries, with some showing short memory behaviour (d?=?0); others long memory mean reverting behaviour (0?<?d?<?1) and others indicating the presence of unit roots (d?=?1). Thus, shocks will have different effects depending on the country examined. Generally, we also find a positive relationship between the levels of persistence and income.

     

Estimation of the degree of dependence in the temperatures in the northern hemisphere using semi-parametric techniques

We are concerned in this article with the estimation of the degree of dependence between the observations of the monthly temperatures in the northern hemisphere from 1854 to 1989 by means of using fractionally integrated semi-parametric techniques. We use several estimation procedures proposed by P. M. Robinson in a number of papers, and the results indicate that the order of integration of the series is around 0.37, implying that the time series is stationary but with long memory behaviour. Separating the data in two subsamples (1854-1921 and 1922-89), the results show that there has been an increase in the degree of dependence across time by about 0.05-0.10, the order of integration oscillating around 0.3 (0.35) for the time period 1854-1921, and around 0.35 (0.40) for the period 1922-89.     

A fractional integration analysis of the population in some OECD countries

In this article we examine the degree of persistence of the population series in 19 OECD countries during the period 1948-2000 by means of using fractionally integrated techniques. We use a parametric procedure due to Robinson (1994) that permits us to test I(d) statistical models. The results show that the order of integration of the series substantially varies across countries and also depending on how we specify the I(0) disturbances. Overall, Germany and Portugal present the smallest degrees of integration while population in Japan appears as the most non-stationary series.     

Persistence,Mean-Reversion and Non-linearities in Infant Mortality Rates

This study examines the time series behavior of infant mortality rates within a long memory approach with non-linear trends using data for 37 countries. The main results show significant differences both in the degree of integration and non-linearities among the analyzed series. Furthermore, non-linearities in the time trends are found in most of the cases, in contrast with the main assumption of linearity used in the literature. Finally, the results on the integration order of the series have important policy implications in many areas, such as on international convergence in mortality rates, on the income and infant mortality relationship, and, on whether health policy interventions will have transitory or permanent effects on infant mortality rates.