Degree Of Fractional Integration Research Articles

Do global CO2 emissions from fossil-fuel consumption exhibit long memory? a fractional-integration analysis

ABSTRACTIn this article we use an autoregressive fractionally integrated moving average approach to measure the degree of fractional integration of aggregate world CO2 emissions and its five components – coal, oil, gas, cement, and gas flaring. We find that all variables are stationary and mean reverting, but exhibit long-term memory. Our results suggest that both coal and oil combustion emissions have the weakest degree of long-range dependence, while emissions from gas and gas flaring have the strongest. With evidence of long memory, we conclude that transitory policy shocks are likely to have long-lasting effects, but not permanent effects. Accordingly, permanent effects on CO2 emissions require a more permanent policy stance. In this context, if one were to rely only on testing for stationarity and non-stationarity, one would likely conclude in favour of non-stationarity, and therefore that even transitory policy shocks have permanent effects. Our fractional-integration analysis highlights that this is not the case.

COMBINING LONG MEMORY AND NONLINEAR MODEL OUTPUTS FOR INFLATION FORECAST

Long memory and nonlinearity have been proven as two models that are easily to be mistaken. In other words, nonlinearity is a strong candidate of spurious long memory by introducing a certain degree of fractional integration that lies in the region of long memory. Indeed, nonlinear process belongs to short memory with zero integration order. The idea of the forecast is to obtain the future condition with minimum error. Some researches argued that no matter what the model is, the important thing is we can generate a reliable forecast. Several tests have been proposed to solve the problem of distinguishing long memory and nonlinearity appears in a series. The power of the tests is somehow questionable in the sense that there is still a probability to obtain spurious result. To overcome this, model combination will be one of the solutions dealing with uncertainty in the model selection. In this case, it is assumed that both processes are candidates of best models with certain power to generate a good forecast. This research investigates the performance three model combination approaches to forecast the Indonesia inflation i.e., simple combination using balance weight as well as inverse Mean Prediction Error (MSPE) weight and Bayesian Model Averaging (BMA). These methods are capable to generate a reliable forecast in very short lead time. Combination using BMA outperforms the simple averaging for 1 ahead forecast, while MSPE performs best for long lead forecasts.

Steel consumption and economic activity in the UK: The integration and cointegration debate

This research examines whether a long-run stationary equilibrium relationship holds between economic activity and the consumption of crude steel within the UK. Using the theory of fractionally integrated and cointegrated processes, and allowing for the possibility that the equilibrium path changes abruptly at occasional points in time, it is possible to determine if steel consumption and economic activity follow a common stochastic trend or whether the two series randomly drift apart over time. Evidence is found to support such a long term relationship. This result is at odds with the conclusions drawn by previous researchers in the area. The reason for this difference may be due to these researchers concentrating only on I(0) and I(1) specifications, without consideration of fractional possibilities and also to a failure to account for structural breaks in the equilibrium relationship. Such conclusions are made within the framework of the ARFIMA methodology that yields reliable inferences on the degree of fractional integration and cointegration. Critical values for fractional contegration with an ARFIMA model in the presence of structural breaks are also derived in this paper.

Testing persistence in the context of conditional heteroscedasticity errors

This article examines the power of two well-known procedures of fractional integration in the context of conditional heteroskedasticity in the variance. One of the methods is parametric while the other is semiparametric. Several Monte Carlo experiments conducted in this article show that both methods perform well to detect the order of integration of the series under the assumption that the underlying disturbances follow Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-type errors. The methods are applied to 10 European stock market indices. The results indicate that the orders of integration of the series are close to 1 in all cases, being strictly higher than 1 in four countries. Moreover, taking the d-differenced processes, and estimating Fractionally Integrated GARCH (FI-GARCH) models on the squared residuals, fractional degrees of integration are obtained in the majority of the series.

A bivariate fractionally cointegrated relationship in the context of cyclical structures

This paper deals with the analysis of cointegration in a bivariate system. However, we depart from the classic concept of cointegration in two aspects. First, we permit fractional degrees of integration in both the parent series and in their linear combination. Second, instead of assuming that the pole or singularity in the spectrum takes places at the zero frequency, we consider the case where the singularity occurs at a frequency λ in the interval (0, π]. We use a procedure that follows the same lines as the two-step testing strategy of R.F. Engle, and C.W.J. Granger, [Cointegration and error correction model. Representation, estimation and testing, Econometrica 55 (1987), pp. 251–276]. Thus, we test first the order of integration in the individual series, which are specified in terms of the Gegenbauer polynomials. Then, if the two series share the same degree of integration at a given frequency, we test the null hypothesis of no cointegration against the alternative of fractional cyclical cointegration, by testing the order of integration on the estimated residuals from the cointegrating regression. Finite sample critical values are obtained, and the power properties of the test are examined. An empirical application is also carried out at the end of the article.

Exchange rates and fractional integration revisited

Jin, et al. (2006) relied on a semi-parametric wavelet estimator of the degree of fractional integration and its associated t-statistic to conclude that many exchange rates appear to be fractionally integrated. This note demonstrates that several recent tests for fractional integration provide a much different view of the temporal properties of many exchange rates.

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 (Nelson CR, Plosser CI (1982) J Monetary Econ 10:139–162) 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 non-stationary, while the cyclical component is stationary.

Empirical evidence against the exchange rate anomaly: the Australian case

Though there is widespread agreement that the logarithmic spot and forward rates are both integrated of order one (I(1)) variables, so that their corresponding returns are I(0) stationary, it has been recently claimed that they may be long memory. In this article, we examine this hypothesis by means of fractional integration techniques. The results based on parametric and semiparametric tests show that though fractional degrees of integration are plausible alternatives, the confidence intervals include the unit root case in both series. In addition, the hypothesis of unbiasedness of the forward rate as a forecaster for the future spot rate cannot be rejected for the Australian daily exchange rate market.

Statistical Modeling of the Temperatures in the Northern Hemisphere Using Fractional Integration Techniques

AbstractThe temperatures in the Northern Hemisphere from 1854 to 1999 have been analyzed in this article by means of a testing procedure that permits one to consider fractional degrees of integration. The tests are valid under general forms of serial correlation and deterministic trends and do not require estimation of the fractional differencing parameter. The results show that the series follows a fractionally integrated process with the order of integration higher than zero and thus implying long memory behavior. The series was decomposed into four different subsamples, and it was observed that the degree of dependence between the observations substantially increased during the twentieth century.

Nonstationary, long memory and anti-persistence in several climatological time series data

In this article we examine the stochastic behaviour of several daily datasets describing sun (total irradiance at the top of the atmosphere and sunspot numbers) and various climatological anomaly series by looking at their orders of integration. We use a testing procedure that permits us to consider fractional degrees of integration. The tests are valid under general forms of serial correlation and deterministic trends and do not require estimation of the fractional differencing parameter. Results show that the series are all nonstationary, with increments that might be stationary for those variables affecting sun, and anti-persistent for those affecting air temperatures.

Fractional integration in total factor productivity: evidence from US data

This study examines the stochastic properties of different measures of Total Factor Productivity (TFP) in the USA and their components using fractional integration. The results show that its structure is more complicated than expected, formed by the interaction of various seasonal and non-seasonal unit (or fractional) processes. Thus, output (measured in terms of the GDP or the business sector value added) may be modelled as a unit root; the order of integration of capital is much higher than 1 and it may be specified even as an I(2) process, while labour contains a seasonal unit root. However, in all these cases, fractional degrees of integration may be even better characterizations for these series. As a result, the TFP series appear to be seasonally fractionally integrated, with d constrained between 0.5 and 1. A deeper investigation of the orders of integration at each of the frequencies shows that the order of integration at zero plays a much more important role that the seasonal frequencies, a result that is explained by the different stochastic nature of the components underlying the TFP.