Fractional integration and cointegration in US financial time series data

This paper examines several US monthly financial time series using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with \(d < 1\) , which implies mean reversion. The multivariate framework exploiting recent developments in fractional cointegration allows to investigate in greater depth the relationships between financial series. We show that there might exist many (fractionally) cointegrated bivariate relationships among the variables examined, for some of which only standard cointegration tests had previously been carried out.     

Nominal and real convergence between the CEE countries and the EU: a fractional cointegration analysis

This paper examines the real and nominal convergence between the Central and Eastern European countries and the EU, using fractional cointegration analysis for the period 1980–2003. Fractional cointegration analysis is a flexible methodology, which allows for more subtle forms of mean reversion. The tests performed are those of Geweke and Porter-Hudak. The convergence processes are valid when macroeconomic time series used in the study are fractionally cointegrated. The results indicate that inflation and interest rates series of six sample countries are fractionally cointegrated with those of the EU. Therefore, nominal convergence has been achieved by some of the transition countries, but the equilibrium errors display long memory. Results also indicate that industrial outputs of most countries in the sample are not fractionally cointegrated with that of the EU. The results further indicate that both nominal and real convergence have been achieved only for Hungary.     

Bootstrap testing for cointegration of international commodity prices

This paper investigates cointegration with respect to nine commodity groups traded on international markets. Nonparametric bootstrapping is utilized in the testing procedure. Of the 21 pairs of price series, investigated here, for 13 the no-cointegration null hypothesis is rejected in favour for the cointegration of the series. In addition to five out of the remaining eight cases that were not cointegrated, a plausible explanation is the prevailing trade policy. Thus a great majority of the institutionally nonregulated cases turn out to get empirical support for being cointegrated. An important statistical finding is that the augmented Dickey-Fuller test for cointegration (CRADF) generally yields p-values that are close to the p-values obtained by the bootstrap testing. But once they differ substantially, it is usually an indication of irregular periods (e.g. structural changes) in the series. The paper conducts also a Monte Carlo simulation experiment to investigate the power and size properties of the tests. Generally the results indicate that the test procedures have pretty low power in small samples. Bootstrapping improves the testing somewhat by leading consistently to a bit more powerful inference.     

Fractional cointegration,long memory,and exchange rate dynamics

In this article, we examine empirically whether fractional cointegration exists in the system of seven exchange rates and this form of cointegration is associated with long memory. The results indicate that fractional cointegration in exchange rates is a feature for only the 1980–1984 sample, not for the entire post-1973 float, the subperiod before 1980, and the sample after 1984. The results show a significant long memory, mean-reverting behavior in equilibrium errors for the subperiod 1980–1984. The results also suggest that the exchange rates are cointegrated in the usual way for the 1985–1992 sample data. The current findings suggest a conjecture that the fractional cointegration feature of exchange rates, if exists, could be changing across varying time spans.     

The Feldstein–Horioka model re-visited for African countries

We study the relationship between the saving and investment rates for 20 African countries using a long period of data. A high correlation between saving and investment is often taken as evidence of capital immobility. We use the new Ng–Perron unit root tests to examine the stationarity of saving and investment rates. Both Johansen cointegration tests and fractional cointegration tests are used. The results are mixed. The Johansen cointegration tests show that the saving and investment rates are cointegrated only for Rwanda and South Africa. This implies that for the other 18 countries, there is evidence of capital mobility. The fractional cointegration test results are different. The two rates are found to be fractionally cointegrated for the following 12 countries: Algeria, Burundi, Egypt, Morocco, Niger, Rwanda, Senegal, South Africa, Swaziland, Tunisia, Tanzania and Zimbabwe. For Cote d’Ivoire, Kenya, Lesotho and Sierra Leone there is some evidence of capital mobility while the results for Ethiopia, Malawi, Mauritius and Nigeria are mixed.     

How did the Sovereign debt crisis affect the Euro financial integration? A fractional cointegration approach

This paper examines financial integration among stock markets in the Eurozone using the prices from each stock index. Monthly time series are constructed for four major stock indices for the period between 1998 and 2016. A fractional cointegrated vector autoregressive model is estimated at an international level. Our results show that there is a perfect and complete Euro financial integration. Considering the possible existence of structural breaks, this paper also examines the fractional cointegration within each regime, showing that Euro financial integration is very robust. However, in the financial and sovereign debt crisis regime, IBEX 35 appears to be the weak link in Euro financial integration, unless Euro financial integration recovers when this period ends.     

Fiscal dependence on trade taxes and the level of economic development:: a comment

We test for fractional dynamics in US monetary series, their various formulations and components, and velocity series. Using the spectral regression method, we find evidence of a fractional exponent in the differencing process of the monetary series (both simple-sum and Divisia indices), in their components (with the exception of demand deposits, savings deposits, overnight repurchase agreements, and term repurchase agreements), and the monetary base and money multipliers. No evidence of fractional behaviour is found in the velocity series. Granger's (Journal of Econometrics, 25, 1980) aggregation hypothesis is evaluated and implications of the presence of fractional monetary dynamics are drawn.     

New panel results on cointegration of international health expenditure and GDP

This article tests for existence of cointegration between health expenditure and GDP using data from 25 OECD countries for the period 19607ndash;1997. The empirical modelling is based on a heterogeneous bivariate vector error correction panel model that allows for trending data as well as intercepts and trends in the cointegrating relations. Univariate country-by-country and panel unit root tests generally fail to reject the null of a unit root in the health expenditure and GDP variables. Country-by-country results based on the Johansen multivariate likelihood-based inference indicate somewhat mixed results on country-specific cointegration with a rank of one found for 12 countries and a rank of zero for the remaining 13 countries. Application of a new panel test for cointegration rank with higher power than the individual tests indicates that health expenditure and GDP are cointegrated around linear trends.     

Blaming suicide on NASA and divorce on margarine: the hazard of using cointegration to derive inference on spurious correlation

Contrary to common belief, cointegration testing may not distinguish between spurious relations and genuine ones. It is demonstrated that highly correlated series appear as cointegrated, even though common sense tells us that the underlying relation does not make sense. Empirical testing using simulated data, data from daily life and historical data on interest rates shows that cointegration may fail not only to detect spurious correlation but also to capture cointegration in a genuine relation. Cointegration testing to reveal spurious correlation can only be used in conjunction with theory, common sense and intuition.     

Empirical proxies for the consumption–wealth ratio

Using a log-linearized approximation to an aggregate budget constraint, it is possible to show that the ratio of consumption to total (human and non-human) wealth summarizes agents' expectations concerning both future labor income and future asset returns. In a series of recent papers, Lettau and Ludvigson construct an empirical analogue to the consumption–wealth ratio by approximating total wealth with a linear combination of labor income and observable non-human wealth. If valid, this framework suggests that consumption, assets, and labor income will be cointegrated. We demonstrate, however, that standard tests fail to reject the hypothesis of no cointegration once one employs measures of consumption, assets, and labor income that are jointly consistent with an underlying budget constraint. We also show that deviations of consumption, assets, and income from an estimated common trend are unable to predict future excess returns on stocks out of sample once theoretically consistent measures are used.     

Seasonal Cointegration and Long‐Run Neutrality of Money in the USA

Using the notion of seasonal cointegration and a monetarist model, this paper re‐examines the long‐run monetary neutrality hypothesis, based on the seasonally unadjusted quarterly data of the US over the period 1959Q1–2004Q4. The results indicate that money is cointegrated with price at all possible frequencies while real output is cointegrated with price only at an annual frequency. The cointegration between money and price at the zero frequency, and non‐cointegration between real output and money at all possible frequencies, suggests that money affects nominal but not real variables in the long run.     

The intertemporal relation between government revenue and expenditure in the United Kingdom, 1750 to 2004

We examine the intertemporal relation between government revenue and expenditure in the UK during 1750 to 2004. We pay particular attention to long run trends by applying a battery of unit root and cointegration techniques to the data, and we use a modified Granger causality test on data spans organized around structural breaks in the series. The results suggest that, allowing for structural breaks, UK real revenue and spending are I(1) series and cointegrated and that Granger causality runs from government spending to revenue. As such, the ‘spend-tax’ hypothesis appears to best characterize the long run intertemporal relation between government revenue and spending in the UK.     

国内、国际期货市场期货价格之间的关联研究

该文利用协整检验和Granger因果检验等技术,首次对国内和国际期货市场的铜、铝、大豆和小麦的期货价格之间的动态关系进行了实证研究.结果显示:上海期货交易所与伦敦金属交易所铜、铝的期货价格之间存在长期均衡关系,大连商品交易所与芝加哥期货交易所大豆的期货价格之间存在协整关系;相对而言,国外市场的影响力较大;郑州商品交易所与芝加哥期货交易所小麦期货价格之间不存在协整关系.     

A cointegration analysis of agricultural,energy and bio-fuel spot,and futures prices

This article features an analysis of the cointegration relationships among agricultural commodity, ethanol and Cushing crude oil spot, and future prices. The use of grains for the creation of bio-fuels has sparked fears that these demands are inflating food prices. We analyse approximately 10 years of daily spot and futures prices for corn, wheat, sugar ethanol, and oil prices from Datastream for the period 19 July 2006 to 2 July 2015. The analysis features Engle-Granger pairwise cointegration and partial cointegration. Pairs of series, that are cointegrated, are analysed using Markov-switching VECM and Impulse Response Analysis, which confirms that these markets have significant linkages that vary according to whether they are in low or high volatility regimes.     

Testing for Granger non-causality using the autoregressive metric

A new non-causality test based on the notion of distance between ARMA models is proposed in this paper. The advantage of this test is that it can be used in possible integrated and cointegrated systems, without pre-testing for unit roots and cointegration. The Monte Carlo experiments indicate that the proposed method performs reasonably well in finite samples. The empirical relevance of the test is illustrated via an application.     

Empirical evidence on the resource curse hypothesis in oil abundant economy

This present study investigates the relationship between natural resource abundance and economic growth for Venezuelan economy. We have applied the ARDL bounds testing approach to cointegration developed by Pesaran et al. (2001) to examine its long run relationship amid the variables. The VECM Granger causality is applied to test the direction of causality among the variables. This study covers the period of 1971–2011.Our empirical evidence indicated that variables are found to be cointegrated. The results confirm that natural resource abundance impedes economic growth. Financial development, capital stock and trade openness enhance economic growth. The feedback hypothesis is also found between natural resource abundance and economic growth.     

Export-led Growth and Import Compression: Further Time Series Evidence From LDCs

This paper conducts tests of the export-led growth and the import-compression hypotheses for four less developed countries (LDCs) – India, Nigeria, Fiji and Papua New Guinea (PNG). Based on Johansen's multiple cointegration test preceded by unit root tests, we test for cointegration between real output, exports and imports. Non-rejection of cointegration between the variables excludes the possibility of Granger non-causality and suggests at least one way Granger causality. Real output, exports and imports are found to be cointegrated in two of the countries and the resulting error-correction models suggest that Granger causality runs from exports and imports to real output in these cases. Exogeneity tests are conducted for exports with respect to real output. However, while the assumption of weak exogeneity is validated in two of the countries, the null hypothesis of super exogeneity is rejected. The test results therefore cast doubts on policy recommendations for the LDCs based on the export-led growth hypothesis.     

Spurious regressions between stationary generalized long memory processes

This paper shows that a spurious regression can occur between two stationary generalized fractional processes, as long as their generalized fractional differencing parameters sum up to a value greater than 0.5 and their spectral densities have poles at the same location. This theoretical finding is supported by simulations.     

Forecasting nonstationary time series—Some methodological aspects

The Box-Jenkins approach to time series analysis, which is an efficient way of analyzing stationary time series, recommends differencing as a general method for transforming a nonstationary time series into a stationary one. This paper gives a methodological discussion of some other ways of transforming a nonstationary series, in particular removing linear trends. It is argued that in many cases removing trends is superior to differencing in several respects. For example, when the process generating the time series is an ARMA(p,q) process added to a linear trend, differencing will produce an ARMA(p,q + 1) process that violates the invertibility conditions and is therefore difficult to estimate. The discussion is extended to time series with seasonal patterns.     

Implications of seeing economic variables through an aggregation window

A variety of cross-sectional and temporal aggregation cases are considered. It is shown that if cointegration is found at an aggregate level then, strictly, many surprising constraints are implied at the micro level. However, a suitable approximation is suggested using common factors. It is shown that series may not be cointegrated at the time period of generation, but that after temporal aggregation cointegration could occur. This possibility arises because temporal aggregation can move a nuit root at a seasonal frequency to the zero frequency. Finally, the possibility of aggregating income distributions is considered and it is shown that, strictly, the Pareto distribution does not have the required property.