Fractional Cointegration Research Articles

The Effect of Economic Policy Uncertainty Under Fractional Integration

One of the most popular measures of economic policy uncertainty (EPU) is an index based on newspapers coverage of particular keywords. The constructed index is often then included in VAR models to examine the extent to which EPU affects economic activity. Researchers, however, have not investigated how the possibility of fractional integration in this index may affect the results. Under fractional integration, the effects of EPU on output in a standard VAR setting may be biased. In this paper, I first show that all EPU series posted in policyuncertainty.com are indeed fractionally integrated processes. In addition, I show that the residuals from Baker, Bloom, and Davis (2016)’s VAR model that includes output, EPU, and other covariates are also fractionally integrated. Next, I estimate a fractionally cointegrated VAR (FCVAR) model to evaluate the dynamic effects of EPU. Likelihood ratio tests indicate that fractional cointegration cannot be rejected at low lag orders. Lastly, I investigate the effect of EPU on ouput after applying various filters to remove the long-memory component. While I still find that EPU imparts a negative effect on output, relative to Baker et al. (2016)’s results, the effects are 50 to 90% smaller in magnitude and take place several months sooner. Long memory, therefore, appears to explain the bulk of the dynamic effect.

Modeling the volatility of gross domestic product based on the volatility of money supply, inflation, interest rate, and exchange rate using the fractional cointegration model

Economic growth is a quantitative index to determine the level of economic progress that can be measured by gross domestic product (GDP). Various literatures aim to solve problems regarding patterns of economic growth as well as about the determinants wherein the analysis volatility models are used. Some indicators of economic growth are money supply, inflation, interest rates, and exchange rates. Economic variables are recorded as time series data with different periods, and hence temporal aggregation is required to analyze. Economic time series data showing the existence of long memory and structural breaks, which leads to the difficulty on explaining the data only with a general model. Therefore, both long memory models and structural break are proposed to be taken into account in the model. In this analysis, the residual from a linear combination of economic variables follows a long memory process indicating a cointegration relationship between these variables. This paper models GDP volatility based on money supply, inflation, interest rate and exchange rate volatility in Indonesia, Philippines, Malaysia, and Singapore using the Fractional Cointegration model with long memory and structural break. The analysis shows that structural break is only found in the volatility of GDP of Indonesia, Malaysia, and Singapore while the nature of long memory is found in almost all economic variables’ volatility. Furthermore, we found the cointegration model, stationary and persistent noise in all countries.

Prospects for a Monetary Union in the East Africa Community: Some Empirical Evidence

AbstractThis paper examines generalised purchasing power parity (G‐PPP) and business cycle synchronisation in the East Africa Community with the aim of assessing the prospects for a monetary union. The univariate fractional integration analysis shows that the individual series exhibit unit roots and are highly persistent. The fractional bivariate cointegration tests suggest that there exist bivariate fractional cointegrating relationships between the exchange rate of the Tanzanian shilling and those of the other EAC countries, and also between the exchange rates of the Rwandan franc, the Burundian franc and the Ugandan shilling. The Fractionally Cointegrated Vector AutoRegressive (FCVAR) results imply the existence of a single cointegrating relationship between the exchange rates of the EAC countries. On the whole, there is evidence in favour of G‐PPP. In addition, there appears to be a high degree of business cycle synchronisation between these economies. On both grounds, one can argue that a monetary union should be feasible.

The EHTS and the persistence in the spread reconsidered. A fractional cointegration approach

In this paper, we consider the possibility that a fractionally cointegrated vector autoregressive (FCVAR) model could serve as a novel empirical tool for examining the US term structure of interest rates. This econometric approach allows one to test the existence of a long-run relationship between short- and long-term interest rates and spread persistence together. As one of the main contributions of this paper, we elaborate on new scenarios of the degree of noncontemplative EHTS fulfillment. Monthly time series are constructed with nine different maturities of interest rates for the period of 1993–2018. The results obtained contribute new scenarios not previously presented in the literature. We also find that the persistence of spread is the stronger the larger the difference in maturity is between considered interest rates, revealing a long memory process. Importantly, as the main implication of our study, we find that this persistence implies a gradual loss of controlling power over interest rates by FED.

Return predictability of variance differences: A fractionally cointegrated approach

AbstractThis paper examines the fractional cointegration between downside (upside) components of realized and implied variances. A positive association is found between the strength of their cofractional relation and the return predictability of their differences. That association is established via the common long‐memory component of the variances that are fractionally cointegrated, which represents the volatility‐of‐volatility factor that determines the variance premium. Our results indicate that market fears play a critical role not only in driving the long‐run equilibrium relationship between implied‐realized variances but also in understanding the return predictability. A simulation study further verifies these claims.

A comparison of semiparametric tests for fractional cointegration

There are various competing procedures to determine whether fractional cointegration is present in a multivariate time series, but no standard approach has emerged. We provide a synthesis of this literature and conduct a detailed comparative Monte Carlo study to guide empirical researchers in their choice of appropriate methodologies. Special attention is paid on empirically relevant issues such as assumptions about the form of the underlying process and the ability of the procedures to distinguish between short-run correlation and long-run equilibria. It is found that several approaches are severely oversized in presence of correlated short-run components and that the methods show different performance in terms of power when applied to common-component models instead of triangular systems.

Testing the validity of the tourism-led growth hypothesis under long-range dependence

ABSTRACT Traditionally, the relationship between tourism and economic growth has been studied using methods based on stationary or nonstationary models. In this paper, we explore the validity of the tourism-led growth hypothesis, applying fractional cointegration techniques and comparing the results with those obtained in previous studies. To do this, we study the long-run relationship between GDP and tourism series, using a two-step strategy. First, we apply fractional cointegration methods and then we test the null hypothesis of no cointegration against alternatives which are fractionally cointegrated. For the empirical analysis, we use seasonally adjusted quarterly data for GDP and tourist arrivals for seven European countries from 1990 to 2018. In the empirical exercise, evidence of cointegration is found only in very restricted cases. Therefore, the validity of the TLGH is less clear-cut when this methodology is applied.

Risk dependence and cointegration between pharmaceutical stock markets: The case of China and the USA

This paper analyses risk-integration and the degree of dependence between the Values-at-Risk (VaRs) estimates for the two major pharmaceutical stock markets in the world: USA and China. To do this, we study the dependence and fractional cointegration properties among risks. Using daily returns for an eleven-year period, we estimated the VaRs obtained for pharmaceutical market portfolios in China (Shanghai) and the USA (NYSE) using the market model and considering both long and short trading positions. We conclude that the Shanghai pharmaceutical market is riskier than NYSE, although is predictable and losses in both markets exhibit tail dependence between VaR estimates. Particularly, there is lower tail VaR dependence for long position and upper tail dependence for short positions, both being small and fairly constant. On the other hand, we have not found fractional cointegration between risks, suggesting that China’s pharmaceutical sector is not integrated into the global pharmaceutical market.

A real time leading economic indicator based on text mining for the Spanish economy. Fractional cointegration VAR and Continuous Wavelet Transform analysis

The main aim of this paper is to build a Real Time Leading Economic Indicator (RT-LEI) that improves Composite Leading Indicators (CLI)’s performance to anticipate GDP trends and turning points for the Spanish economy. The indicator has been constructed using a Factor Analysis and is composed of 21 variables concerning motor vehicle activity, financial activity, real estate activity, economic sentiment, and industrial sector. The data sources used are Google Trends and Thomson Reuters Eikon-Datastream. This work contributes to the literature, studying the dynamics of GDP, CLI and RT-LEI using Fractional Cointegration VAR (FCVAR model) and Continuous Wavelet Transform (CWT) for its resolution. The results show that the model does not present mean reversion and it is expected the RT-LEI reveals a bear trend in the next two years, alike IMF and Consensus FUNCAS′ forecasts. The reasons are mostly associated with escalating global protectionism, uncertainty related to Catalonia and faster monetary policy normalization.

Economic Policy Uncertainty: Persistence and Cross-Country Linkages

This paper provides new evidence on the stochastic behaviour of the EPU (Economic Policy Uncertainty (EPU) index constructed by Baker et al. (2016) in six of the biggest economies (Canada, France, Japan, US, Ireland, and Sweden) over the period from January 1985 to October 2019. In particular, it uses fractional integration methods to shed light on its degree of persistence, and also carries out appropriate break tests. Further, the possible co-movement of this index between countries is examined applying a fractional cointegration method which tests for the possible existence of a long-run equilibrium relationship linking the individual indices. EPU is found to be in most cases a non-stationary, mean-reverting series which is characterised by long memory. Several breaks are also detected in each country. Finally, there is very little evidence of cross-country linkages.

Modeling bivariate long‐range dependence with general phase

Bivariate time series models are considered that are suitable for estimation, that have interpretable parameters and that can capture the general semi‐parametric formulation of bivariate long‐range dependence, including a general phase. The models also allow for short‐range dependence and fractional cointegration. A simulation study to test the performance of a conditional maximum likelihood estimation method is carried out, under the proposed models. Finally, an application is presented to the U.S. inflation rates in goods and services where models not allowing for general phase suffer from misspecification.

Modeling fractional cointegration between high and low stock prices in Asian countries

The present study analyzes the interrelationship among daily high and low stock market indices in some developing stock markets with the perspective of fractional integration and cointegration. The analysis is performed by applying fractionally cointegrated vector error correction models (FVECM) as they can explain the short-run and long-run dynamics of high and low stock prices simultaneously. This study employs daily stock market index data from six major Asian countries and finds that daily (log) highs and lows do follow a long-run relationship. We find very slow hyperbolic decay of autocorrelations in the range series for all observed stock prices, and this dependence supports the hypothesis of nonstationary volatility in some cases. Forecasted highs and lows based on the FVECM provide better forecasts than traditional models based on the MSE and MAE. The FVECM range forecasts also show better out of sample performance over the HAR and ARFIMA models fitted to the range series.

A fractional cointegration VAR analysis of Islamic stocks: A global perspective

In this study, we analyse the behaviour of Islamic stocks from a global perspective covering an array of regional Islamic stock markets. Both the fractional integration and fractional cointegration techniques are employed. Thus, we are able to establish whether Islamic stocks are individually integrated with a fractional order on the one hand and whether they are fractionally cointegrated on the other hand. We find that all the regional Islamic stock markets exhibit long memory but are mean reverting regardless of the choice of fractional integration technique and data sample. Second, using the fractional cointegration VAR (FCVAR) approach of Johansen and Nielsen (2012), we find that all the regional stock markets are cointegrated with a fractional order and this behaviour may be influenced by global economic conditions. Further analyses suggest that ignoring the fractional integration property of Islamic stocks when modelling their long run behaviour may lead to wrong conclusions. Also, the economic significance test conducted indicates that Islamic financial markets offer risk hedging characteristics and the results are robust to alternative data frequencies.

Asymptotics of bivariate local Whittle estimators with applications to fractal connectivity

Several methodological and numerical issues behind the local Whittle estimation of long and short memory in bivariate stationary time series with possible fractional cointegration are reexamined. These issues include the asymptotic normality for all model parameters, local Whittle plots for phase parameter and fractal connectivity, and others. For fractal connectivity, in particular, it is advocated to work with a model parametrization for which the model parameters associated with this phenomenon are identifiable and could be tested naturally within the local Whittle estimation framework. A simulation study and data applications are also considered.

A test for inflation persistence in Nigeria using fractional integration & fractional cointegration techniques

This study seeks to test for inflation persistence in Nigeria using the recently developed fractional cointegration VAR model by Johansen and Nielsen (2012) and complemented with univariate fractional integration techniques. The empirical results suggest evidence of high inflation persistence in Nigeria albeit with a lower trend after the global financial crisis. Also, the major classes of inflation – headline, core and food inflation rates, share long run properties regardless of the sample used. This suggests that any policy action directed at a particular class of inflation will have a spill-over effect on the other classes given the strong association among them. The ability to also exploit the fractional cointegration in a multivariate set-up when modeling inflation is a major contribution of this study and ignoring same may lead to wrong conclusions. However, the results are sensitive to the choice of data frequency.

How persistent and dynamic inter-dependent are pricing of Bitcoin to other cryptocurrencies before and after 2017/18 crash?

The present paper investigates persistence and inter-dependence of bitcoin on other popular alternative coins. We employ fractional integration approach in our analysis of persistence, while a more recent fractional cointegration technique in VAR set-up, proposed by Johansen (2008), is used to investigate inter-dependence in pricing of the paired cryptocurrencies. Having partitioned the series into periods before and after the 2017/2018 cryptocurrency price crash, as determined by Bitcoin pricing, we obtain some interesting results. Higher persistence of price shocks is observed after the crash, which is probably due to speculative transactions among cryptocurrency traders, and more evidences of non-mean reversions are revealed, implying chances of further price fall in cryptocurrencies. Cointegration relationships between bitcoin and alternative coins exist in both periods, with weak correlations observed mostly in the post-crash period. Our results further indicate the possibility of market efficiency between pair of cryptocurrency. Generally, we hope the findings will serve as guide to investors in cryptocurrency markets.

Fixed Bandwidth Inference for Fractional Cointegration

In a fractional cointegration setting we derive the fixed bandwidth limiting theory of a class of estimators of the cointegrating parameter which are constructed as ratios of weighted periodogram averages. These estimators offer improved limiting properties over those of more standard approaches like ordinary least squares or narrow band least squares estimation. These advantages have been justified by means of traditional asymptotic theory and here we explore whether these improvements still hold when considering the alternative fixed bandwidth theory and, more importantly, whether this latter approach provides a more accurate approximation to the sampling distribution of the corresponding test statistics. This appears to be relevant, especially in view of the typical oversizing displayed by Wald statistics when confronted to the standard limiting theory. A Monte Carlo study of finite‐sample behaviour is included.

Long-term interest rates in Europe: A fractional cointegration analysis

This paper uses fractional integration/cointegration techniques to examine the stochastic behaviour of long-term interest rates (on government securities with 10-year maturity) in 23 European countries as well as their long-run linkages on a pairwise basis over the period January 2001–February 2018. The results are mixed and sensitive to the (parametric and semi-parametric) estimation methods. Evidence is found for both unit roots and mean reversion in the series analysed. Various rates (especially in the case of smaller economies) appear to be fractionally cointegrated, but interestingly German, French and UK rates are not found to be linked to any other European rates.

Stock Market Linkages between the ASEAN Countries, China and the Us: A Fractional Cointegration Approach

This paper examines stock market integration between the ASEAN five and the US and China, respectively, over the period from November 2002 to March 2018. The linkages between both aggregate and financial sector stock indices (both weekly and monthly) are analysed using fractional integration and fractional cointegration methods. Further, recursive cointegration analysis is carried out for the weekly series to study the impact of the 2007-8 global financial crisis and the 2015 China stock market crash on the pattern of stock market co-movement. The main findings are the following. All stock indices exhibit long memory. There is cointegration between the ASEAN five and the US but almost none between the former and China, except between Indonesia and China in the case of the financial sector. The 2007-8 global financial crisis and the 2015 Chinese stock market plunge weakened the linkages between the ASEAN five and both China and the US. The implications of these results for market participants and policy makers are discussed.

A fractional cointegration var analysis of exchange rate dynamics

In their seminal work, Baillie and Bollerslev (1994) carried out an analysis of deviations from the cointegrating relationship of seven important exchange rates. They suggested that the exchange rate series possess long memory and therefore such processes could be well described as fractionally integrated processes. Hence, the influence of shocks to the equilibrium exchange rates may only vanish at very long horizons. In this work we analyze the cointegrating structure of five exchange rates to the US dollar, namely the British pound, the Euro, the Swedish Krona, the Canadian Dollar and the Swiss Franc. The series possess long memory and we show that they can be modeled through fractional integration. In fact, standard cointegration is rejected with the more traditional Johansen CVAR methodology. By using the recently introduced Fractionally Cointegrated VAR by Johansen and Nielsen (2012) we provide a cointegrating relationship taking into account fractional integration.