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) orders of integration, and also incorporating endogenously determined structural breaks. Monte Carlo analysis shows that 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 for four different 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

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) orders of integration, and also incorporating endogenously determined structural breaks. Monte Carlo analysis shows that 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 for four different 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.deterministic and stochastic seasonality, fractional integration, structural breaks

The Nature of Occupational Unemployment Rates in the United States: Hysteresis or Structural?

This paper provides new evidence on the nature of occupational differences in unemployment dynamics, which is relevant for the debate between the structural or hysteresis hypotheses. We develop a procedure that permits us to test for the presence of a structural break at unknown date. Our approach allows the investigation of a broader range of persistence than the 0/1 paradigm about the order of integration, usually implemented for testing the hypothesis of hysteresis in occupational unemployment. In almost all occupations, we find support for both the structuralist and the hysteresis hypotheses, but stress the importance of estimating the degree of persistence of seasonal shocks along with the degree of long-run persistence on raw data without applying seasonal filters. Indeed hysteresis appears to be underestimated when data are initially adjusted using traditional seasonal filters.fractional integration, structural break, occupational unemployment, structuralist, hysteresis

Distinguishing between long-range dependence and deterministic trends

We provide a method for distinguishing long-range dependence from deterministic trends such as structural breaks. The method is based on the comparison of standard log-periodogram regression estimation of the memory parameter with its tapered counterpart. The difference of these estimators provides the desired test. Its asymptotic distribution depends on the true memory parameter under the null, and is therefore estimated by bootstrapping. The test is applied to inflation rates of three industrialized countries. --Long memory,trends,log-periodogram regression,inflation rates

Fractional integration and cointegration in stock prices and exchange rates

This paper examines the relationships between the CAC40 index, the Dow Jones index and the Euro/USD exchange rate using daily data over the period 1999-2008. We find that these variables are I(1) nonstationary series, but they are fractionally cointegrated: equilibrium errors exhibit slow mean reversion, responding slowly to shocks. Therefore, with regard to the recent empirical cointegration literature, taking into account fractional cointegration techniques appears as a promising way to study the long-run relationships between stock prices and exchange rates.fractional cointegration, long memory, stock prices, exchange rates

Modelling Ireland’s exchange rates: from EMS to EMU

This paper attempts to model the nominal and real exchange rate for Ireland, relative to Germany and the UK from 1975 to 2003. It offers an overview of the theory of purchasing power parity (PPP), focusing particularly on likely sources of nonlinearity. Potential difficulties in placing the analysis in the standard I(1)/I(0) framework are highlighted and comparisons with previous Irish studies are made. Tests for fractional integration and nonlinearity, including random field regressions, are discussed and applied. The results obtained highlight the likely inadequacies of the standard cointegration and STAR approaches to modelling, and point instead to multiple structural changes models. Using this approach, both bilateral nominal exchange rates are effectively modelled, and in the case of Ireland and Germany, PPP is found to be valid not only in the long run, but also in the medium term. JEL Classification: C22, C51, F31, F41fractional Dickey-Fuller tests, multiple structural changes models, purchasing power parity, random field regression, smooth transition autoregression

Long Run and Cyclical Dynamics in the US Stock Market

This paper examines the long-run dynamics and the cyclical structure of various series related to the US stock market using fractional integration. We implement a procedure 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 outperforms the others in a number of cases.stock market, fractional cycles, long memory, Gegenbauer processes

An econometric approach to macroeconomic risk. A cross country study

A contribution to the study of volatility and country risk is made in order to achieve a successful crosscountry comparison. We present a methodology for the evaluation of country risk that include endogenous detection of multiple structural breaks (also identifying its different kinds), determination of persistence of shocks through their structural-break free fractional integration order and determination of the adjusted volatility which best characterizes the economy. This methodology is applied to developed and emerging countries' GDPs (taking 9 countries from each group). Although the former have fewer structural breaks than the latter, these breaks are extremely relevant in 14 of the 18 countries. This affects the calculation of the series persistence and volatility. Comparing a traditional risk indicator to our suggested one we find that the cluster of reference of 60% of the countries changes. Most countries present fractional integration (long memory) being the distribution between both groups heterogeneous. Country volatility varies strongly if we isolate structural breaks that present a probabilistic distribution different from intrinsic GDP volatility. Clusters arrangement is different with some risk country evaluation methodologies.Risk, Volatility, Persistence, Structural breaks, Forescastability, Macroeconomic variables, Cross country analysis

Fractional integration and cointegration in stock prices and exchange rates

This paper examines the relationships between the CAC40 index, the Dow Jones index and the Euro/USD exchange rate using daily data over the period 1999-2008. We find that these variables are I(1) nonstationary series, but they are fractionally cointegrated: equilibrium errors exhibit slow mean reversion, responding slowly to shocks. Therefore, with regard to the recent empirical cointegration literature, taking into account fractional cointegration techniques appears as a promising way to study the long-run relationships between stock prices and exchange rates.fractional cointegration; long memory; stock prices; exchange rates