Fractional Cointegration Analysis Research Articles

Long-Run Linkages Between us Stock Prices and Cryptocurrencies: A Fractional Cointegration Analysis

AbstractThis paper applies fractional integration and cointegration methods to examine respectively the univariate properties of the four main cryptocurrencies in terms of market capitalization (BTC, ETH, USDT, BNB) and of four US stock market indices (S&P500, NASDAQ, Dow Jones and MSCI for emerging markets) as well as the possible existence of long-run linkages between them. Daily data from 9 November 2017 to 28 June 2022 are used for the analysis. The results provide evidence of market efficiency in the case of the cryptocurrencies but not of the stock market indices considered. The results also indicate that in most cases there are no long-run equilibrium relationships linking the assets in question, which implies that cryptocurrencies can be a useful tool for investors to diversify and hedge when required in the case of the US markets.

Stock market indices and interest rates in the US and Europe: persistence and long-run linkages

Purpose This paper aims to analyse the persistence of the S&P500 and DAX 30 stock indices as well as of the Fed’s Effective Federal Funds rate and of the European Central Bank’s Marginal Lending Facility rate, and the long-run linkages between stock prices and interest rates in the USA and Europe, respectively. Design/methodology/approach The methodology is based on the concepts of fractional integration and cointegration. Findings Using monthly data from January 1999 to December 2022, the results can be summarised as follows. All series examined are non-stationary: stock prices are found to be I(1) while interest rates display orders of integration substantially above 1, which implies a rejection of the hypothesis of mean reversion in all cases examined. Originality/value This paper uses an appropriate econometric framework to obtain new, reliable empirical evidence. All four series are highly persistent, and mean reversion does not occur in any single case. Moreover, the fractional cointegration analysis suggests that stock prices and interest rates are not linked in the long run.

Coronavirus, Vaccination and the Reaction of Consumer Sentiment in The United States: Time Trends and Persistence Analysis

At the beginning of the COVID-19 pandemic, the entire world was waiting for a medical solution (for example, vaccines) in order to return to normality. Sanitary restrictions changed our consumption behaviors and feelings. Therefore, this paper analyzes the stochastic properties of consumer sentiment during the COVID-19 episode and the appearance of vaccines against the virus in December 2020 in the United States of America. This study adds a new dimension to the literature because it is the first research paper that uses advanced methodologies based on fractional integration and fractional cointegration analysis to understand the statistical properties of these time series and their behavior in the long term. The results using fractional integration methodologies exhibit a high degree of persistence, finding behavior of mean reversion during the pandemic episode. Therefore, the shock duration in consumer sentiment will be transitory, recovering to its previous trend in the short run. Focusing on the cointegrating part, we arrive at two main conclusions. First, an increase in total vaccination produces a positive reaction or impact on the behavior of consumers. On the other hand, an increase in new COVID-19 cases negatively affects the behavior of the consumer.

On the relationship between Bitcoin and other assets during the outbreak of coronavirus: Evidence from fractional cointegration analysis

This article tries to investigate the connectedness between Bitcoin and Crude Oil, S&P500 and Natural Gas with the health crisis. That is why one might apply fractional cointegration analysis on daily data over the period 01/09/2019–30/04/2020. Our results indicate the presence of fractional integration in residual series, implying the existence of a fractional cointegration relationship. A short-run joint dynamics between Bitcoin and some other assets (Crude Oil, S&P500 and Natural Gas) is nevertheless well-pronounced. Such analysis of the long and short-term dependencies between different assets could be interesting from a portfolio perspective.

Presidential approval in Peru: an empirical analysis using a fractionally cointegrated VAR

Presidential approval in Peru depends on economic outcomes. However, voters are unable to distinguish between outcomes resulting from economic policies and those caused by exogenous external factors. Estimation results from seven Fractional Cointegrated VAR (FCVAR) models suggest that presidential approval increases with the monetary policy interest rate, the terms of trade, and manufacturing employment; and decreases with the nominal PEN/USD exchange rate and inflation volatility. Additionally, a Principal Components Analysis (PCA) conducted over a large set of macroeconomic indicators points to a greater influence of external over domestic factors in explaining presidential approval; i.e., economic outcomes that determine the dynamics of presidential approval are not under presidential control in Peru. It can be argued that these findings identify a significant source of political instability and a considerable challenge to democratic governance. To the authors’ best knowledge, this is the first application of fractional cointegration analysis to political economy in Latin America.

Long-Run Linkages between US Stock Prices and Cryptocurrencies: A Fractional Cointegration Analysis

Long-Run Linkages between US Stock Prices and Cryptocurrencies: A Fractional Cointegration Analysis

Testing for no cointegration in vector autoregressions with estimated degree of fractional integration

Confirming the existence of long-run relations between persistent variables is an important empirical goal. Fractional (co)integration allows for flexible modelling of such variables. The persistence of many fractional VAR processes is characterized by the integration parameter d and, under cointegration, by the persistence of the equilibrium deviations, where both are typically unknown in practice. To deal with unknown persistence of equilibrium deviations, we linearize here the involved fractional difference filter. When d is known, this results in test statistics possessing standard (normal or χ2) asymptotic distributions. For unknown d, conditions are provided, under which plugging in consistent estimators of d does not affect the standard asymptotics; the key insight is that letting the number of lags increase as the sample size goes to infinity accounts for the estimation error of d. The proposed approach is illustrated in Monte Carlo experiments and a fractional cointegration analysis of short-term U.S. T-bills.

Fundamental Responsiveness in European Electricity Prices

We estimate fundamental pricing relationships in selected European day-ahead electricity markets. Using a fractionally integrated panel data model with unobserved common effects, we quantify the responsiveness of hourly electricity prices to two fundamental leading indicators of day-ahead markets: the predicted load and renewable generation. The application of fractional cointegration analysis techniques gives further insight into the pricing mechanism of power delivery contracts, enabling us to measure the persistence of fundamental shocks.

On the Relationship between Bitcoin and Other Assets During the Outbreak of Coronavirus: Evidence from Fractional Cointegration Analysis

This article tries to investigate the connectedness between Bitcoin and Crude Oil, S&P500 and Natural Gas with the health crisis. That is why one might apply fractional cointegration analysis on daily data over the period 01/09/2019-30/04/2020. Our results indicate the presence of fractional integration in residual series, implying the existence of a fractional cointegration relationship. A short-run joint dynamics between Bitcoin and some other assets (Crude Oil, S&P500 and Natural Gas) is nevertheless well-pronounced. Such analysis of the long and short-term dependencies between different assets could be interesting from a portfolio perspective.

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.

Government bond yields in Germany and Spain—empirical evidence from better days

This paper tries to link the uncovered interest rate parity condition to the discussion about interest rate convergence in currency unions. Techniques of fractional cointegration analysis are used to examine the relationship between German and Spanish government bond yields with maturities of two, five, seven and ten years in the period 05 January 2001 to 29 December 2006. Back then (in the good times of the currency union) financial markets did not have to fear exchange rate risk and sovereign credit risk. Thus, the risk premia to be observed were small and driven by liquidity risk. Economic theory suggests that a cointegration vector of between the interest rates can only exist when markets do not expect exchange rate movements and the risk premium is not interest rate sensitive (or practically speaking the sensitivity is low). Given the data set examined here, it is probably no surprise that the interest rates of the two countries are cointegrated and that the cointegration vector of German and Spanish government bond yields with maturities of two, five and seven years seems to be . We then have also examined the degree of interest rate sensitivity of the yield spread between Spain and Germany. The differential between the yields of the two countries in all maturity brackets do not react to the level of interest rates in the currency union. This fits perfectly to our results with regard to the cointegration vector.

The relationship between healthcare expenditure and disposable personal income in the US states: a fractional integration and cointegration analysis

Luis Gil-Alana gratefully acknowledges financial support from the Ministerio de Economia y Competitividad (ECO2014-55236). Juncal Cunado gratefully acknowledges financial support from the Ministerio de Economia y Competitividad (ECO2014-55496).

Testing for substitutability in the mackerel market: a new method using fractional cointegration

ABSTRACTThis article seeks to extend knowledge of the mackerel (Scomber scombrus) market in the Basque Country (a region in Spain) by analysing possible relationships between this and other species with similar characteristics such as the sardine (Sardina pilchardus), the horse mackerel (Trachurus trachurus) and the Atlantic chub mackerel (Scomber colias), all of them landed at the ports of the Basque Country. Specifically, the goal is to learn whether these other species can be considered as mackerel substitutes. To that end, a fractional cointegration analysis of different series of historical prices is performed using a novel method never before used in studies of this type. The results indicate that mackerel have no substitutes, and thus form a mono-species regional market. This implies, among other things, that their price is not influenced by the prices of other species, and this should be taken into account by managers when designing management measures and policies to improve the sustainability of the fishing of this species.

Germany's nuclear power plant closures and the integration of electricity markets in Europe

This paper examines the potential implications of national policies that lead to a sudden increase of wind power in the electricity mix for interconnected European electricity markets. More specifically, it examines market integration before and after the closures of eight nuclear power plants that occurred within a period of a few months in Germany during 2011. The short- and- long run interrelationships of daily electricity spot prices, from November 2009 to October 2012, in: APX-ENDEX, BELPEX, EPEX-DE, EPEX-FR, NORDPOOL, OMEL and SWISSIX; and wind power in the German system are analysed. Two MGARCH (Multivariate Generalized Autoregressive Conditional Heteroscedasticity) models with dynamic correlations are used to assess spot market behaviour in the short run, and a fractional cointegration analysis is conducted to investigate changes in the long-run behaviour of electricity spot prices. Results show: positive time-varying correlations between spot prices in markets with substantial shared interconnector capacity; a negative association between wind power penetration in Germany and electricity spot prices in the German and neighbouring markets; and, for most markets, a decreasing speed in mean reversion.

The Relationship between Healthcare Expenditure and Disposable Personal Income in the US States: A Fractional Integration and Cointegration Analysis

This study examines the relationship between healthcare expenditure and disposable income in the 50 US states over the period 1966-2009 using fractional integration and cointegration techniques. The degree of integration and nonlinearity of both series are found to vary considerably across states, whilst the fractional cointegration analysis suggests that a long-run relationship exists between them in only 11 out of the 50 US states. The estimated long-run income elasticity of healthcare expenditure suggests that health care is a luxury good in these states. By contrast, the short-run elasticity obtained from the regressions in first differences is in the range (0,1) for most US states, which suggests that health care is a necessity good instead. The implications of these results for health policy are also discussed.

Reassessing the integration of European electricity markets: A fractional cointegration analysis

This study extends existing literature on the assessment of electricity market integration in Europe, by developing and testing hypotheses on the convergence of electricity wholesale prices, and adopting a time-varying fractional cointegration analysis. In addition, the potential impacts of some special events that may affect system capacity (new interconnection, market coupling, increase in share of intermittent generation) on spot and forward markets are considered and evaluated. Daily spot prices from February 2000 to March 2013 of nine European electricity spot markets (APX-UK, APX-NL, Belpex, EPEX-FR, EPEX-DE, IPEX, Nordpool, Omel and OTE) and month-ahead prices in four markets (French, British, German and Dutch) from November 2007 to December 2012 are investigated. Results show that unit root tests, which are generally used in the literature to test market integration, are inadequate for assessing electricity spot market convergence, because spot prices are found to be fractionally integrated and mean-reverting time series. Furthermore, spot price behaviour and their association with different markets change over time, reflecting changes in the EU electrical system. One-month-ahead prices, by contrast, were found to have become more resilient to shocks and to follow more stable trends.

Residual-based test for fractional cointegration

By allowing deviations from equilibrium to follow a fractionally integrated process, the notion of fractional cointegration analysis encompasses a wide range of mean-reverting behaviors. For fractional cointegrations, asymptotic theories have been extensively studied, and numerous empirical studies have been conducted in finance and economics. But as far as testing for fractional cointegration is concerned, most of the testing procedures have restrictions on the integration orders of observed time series or integrating error and some tests involve determination of bandwidth. In this paper, a general fractional cointegration model with the observed series and the cointegrating error being fractional processes is considered, and a residual-based testing procedure for fractional cointegration is proposed. Under some regularity conditions, the test statistic has an asymptotic standard normal distribution under the null hypothesis of no fractional cointegration and diverges under the alternatives. This test procedure is easy to implement and works well in finite samples, as reported in a Monte Carlo experiment.

A fractional cointegration analysis of Fisher hypothesis: evidence from Turkey

This paper examines the validity of Fisher hypothesis in Turkey over the period from 1990:01 through 2010:03 by using cointegration and fractional cointegration approaches. The findings from Engle and Granger cointegration test indicate that inflation and nominal interest rate series are cointegrated. Since the conventional cointegration tests do not provide strong evidence on the long run relationship, we also use fractional cointegration definition suggested by Cheung and Lai (J Bus Econ Stat 11:103–112, 1993) which requires only a mean reverting (d < 1) relationship between the series. The results from fractional cointegration tests based on GPH and Robinson methods show that inflation and nominal interest rate series are fractionally cointegrated. These findings support the validity of the Fisher hypothesis in Turkey.

Fractional Cointegration Analysis of Securitized Real Estate

This paper uses fractional cointegration analysis to examine whether long-run relations exist between securitized real estate returns and three sets of variables frequently used in the literature as the factors driving securitized real estate returns. That is, we examine whether such relationships are characterized by long memory (long-range dependence), short memory (short-range dependence), mean reversion (no long-run effects) or no mean reversion (no long-run equilibrium). The forecasting implications are also considered. Empirical analyses are conducted using data for the U.S., the U.K., and Australia. We find strong evidence of fractional cointegration between securitized real estate and the three sets of variables. Such relationships are mainly characterized by short memory although long memory is sometimes present. The use of fractional cointegration for forecasting purposes proves particularly useful since the start of the financial crisis.

Long Memory and Tail Dependence in Trading Volume and Volatility

In this paper we investigate the relationship between volatility, measured by realized volatility, and trading volume. We show that volume and volatility are long memory but they are not driven by the same latent factor as suggested by the fractional cointegration analysis. We analyze the degree of tail dependence of the two series finding that this is induced by the extreme dependence in the volatility and volume innovations. Tail dependence is particularly interesting, since, it is informative on the specific behavior of the volatility and volume when large surprising news impact the market. We use a fractionally integrated VAR with shock distributions modeled with a mixture of copulae functions to describe the joint dynamics. The model is able to capture the main characteristic of the series, say long memory, marginal non-normality and tail dependence. Once that long memory is removed, past volume are informative about the present volatility, and this result can be exploited for forecasting purposes. This evidence should be therefore taken into account when building a realistic model, linking volatility and volume.