Linear Cointegration Research Articles

Linear and Nonlinear Cointegration of Purchasing Power Parity: Further Evidence from Developing Countries

In this study, we search for evidence of empirical validity of long-run purchasing power parity (PPP) in case of eight developing countries. We consider both a linear and non-linear model of PPP based on cointegration analysis and apply firstly Johansen's linear approach and then conduct Breitung's rank and score tests to search for any non-linear cointegrating relationship. The results obtained from Breitung's rank test suggest that once the sources of non-linearities are taken into account, the results provide stronger evidence on the empirical fulfillment of PPP.

The Spanish term structure of interest rates revisited: Cointegration with multiple structural breaks, 1974–2010

In this paper we consider the possibility that a linear cointegrated regression model with multiple structural changes would provide a better empirical description of the Spanish term structure of interest rates. Our methodology is based on instability tests recently proposed in Kejriwal and Perron (2008, 2010) as well as the cointegration tests developed in Arai and Kurozumi (2007) and Kejriwal (2008). The results obtained are consistent with the existence of linear cointegration between the long and the short run Spanish interest rates. However, our empirical results also show that the cointegrating relationship has changed over time. In particular, the Kejriwal–Perron tests for testing multiple structural breaks in cointegrated regression models suggest a model of two regimes.

Dynamic misspecification in nonparametric cointegrating regression

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The limit properties of the Nadaraya–Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent, in general, with a “pseudo-true function” limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centred on the pseudo-true function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification (hn, h is a bandwidth term) but the variance of the limit distribution is larger. The practical import of the results for index models, functional regression models, temporal aggregation and specification testing are discussed. Two nonparametric linearity tests are considered. The proposed tests are robust to dynamic misspecification. Under the null hypothesis (linearity), the first test has a χ2 limit distribution while the second test has limit distribution determined by the maximum of independently distributed χ2 variates. Under the alternative hypothesis, the test statistics attain a hn divergence rate.

The Integration of Direct Real Estate and Stock Markets in Asia

Currently, there exists relatively little research investigating the long-term association between stock and direct real estate markets. Using appropriate transaction-based property indices, this study focuses on the relationship between stock and direct real estate markets in nine Asian countries from the period 1980 to 2012 through both linear and nonlinear cointegration techniques. We find empirical evidence of linear cointegration of stock and property markets in Taiwan, fractional cointegration in Singapore and Hong Kong and no evidence of cointegration in China, Japan, Thailand, Malaysia, Indonesia and South Korea. It is concluded that segmentation of property markets from stock markets does not appear to be linked to the differences in the maturity of national financial markets and that the differing degrees of integration across Asia may instead be reflective of a range of factors impacting upon the underlying economic structures in each country.

Testing for Nonlinear Spatial Integration in Roundwood Markets

Abstract Prior studies have frequently not supported spatial market integration and the law of one price in roundwood markets. However, these studies have relied on cointegration tests that have low power in the presence of nonlinearities. Roundwood markets may display these effects due to high transactions costs between regions. In this article, we revisited the question of spatial integration in roundwood markets by using tests that have no cointegration as a null hypothesis and threshold cointegration as an alternative. For testing, a dataset of monthly New Zealand roundwood prices from four regional markets over the period from January 1995 to April 2010 were used. Similar to standard linear cointegration tests, the null hypothesis of no cointegration could not be rejected for most of the regional price pairs. One interpretation is that regional markets are segregated. Another interpretation is that the power of these nonlinear tests, although an improvement over that of their linear counterparts, is still relatively low.

Threshold Cointegration in the Greek Milk Market

This article investigates the nonlinear adjustment between consumer and producer prices in the Greek milk sector using a threshold error correction autoregressive model. The results reject the null hypothesis of linear cointegration in favor of a 2-regime threshold cointegration model. A cointegrating relationship is expected only when equilibrium consumer price is decreased more than 24.12% or the equilibrium relative markup is squeezed more than 62.74%. In this case consumer prices have to increase faster than producer prices to restore the long-run equilibrium between consumer-producer milk prices.

Price Transmission and Volatility in the Greek Broiler Sector: A Threshold Cointegration Analysis

This article investigates the non-linear adjustment and price volatility between consumer and producer prices in the Greek broiler sector, using a threshold error correction autoregressive model and two multivariate GARCH models, i.e. DVEC(1,1) and BEKK(1,1). The results reject the null hypothesis of linear cointegration in favor of a three-regime threshold cointegration model. A cointegrating relationship is expected either when the relative markup is squeezed more than 30.89%, i.e. the price system is found in the lower regime, or if it increases more than 39.10%, i.e. the system is found in the upper regime. In the first case, the consumer price has to increase, while in the latter case, the producer price has to increase. Both price changes tend to bring the price system into the middle regime where the average relative markup is about 35.90%. The volatility results obtained from the estimation of the two multivariate GARCH models indicate that producer and consumer broiler prices present a significant level of persistence and that producer price volatility shows higher persistence than consumer price volatility. The results also indicate that consumer price volatility is higher in the first regime than in the middle regime, while producer price volatility is higher in the third regime than in the middle regime. Finally, the results suggest that the broiler price system is moving from the first to the middle regime via an increase in both the consumer price level and the consumer price volatility, while the price system is moving from the third to the middle regime via an increase in both the producer price level and the producer price volatility.

Structural Breaks and the Fisher Effect

There is scant empirical support in the literature for the Fisher effect in the long run, though it is often assumed in theoretical models. We argue that a break in the cointegrating relation introduces a spurious unit root that leads to a rejection of cointegration. We applied new break tests and tested for nonlinearity in the cointegrating relation with post World War II data for 15 countries. Our empirical results support cointegration, after accounting for breaks, and a linear Fisher relation in the long run. This is in contrast to several recent studies that found no support for linear cointegration.

Testing for Cointegration between House Prices and Economic Fundamentals

Economic theory predicts three possibilities for the cointegration relationship between house prices and economic fundamentals: linear cointegration, nonlinear cointegration and no cointegration. In contrast, the empirical literature has only examined linear cointegration. This article argues that ignoring nonlinear cointegration may lead to misleading conclusions that no cointegration exists between house prices and the fundamentals. To illustrate this point, I test for cointegration for ten U.S. cities and find that only one city shows evidence of linear cointegration. Further analysis using the two‐step testing procedure yields evidence of nonlinear cointegration for six other cities. Still, there are three cities left out without evidence of nonlinear cointegration. Further studies are needed to test for other forms of nonlinear cointegration before a conclusion of no cointegration can be reached for the remaining three cities.

Does nonlinearity help resolve the Fisher effect puzzle?

Even though there is little evidence for linear cointegration, Christopoulos and Léon-Ledesma (2007) recently have found nonlinear cointegrating relations between the US quarterly nominal interest rate and CPI inflation rate. Through Monte Carlo simulations, they also show that the nonlinear relations are responsible for the ‘Fisher effect puzzle’ of less than a proportional coefficient of inflation in the linear Fisher relation. We provide, in this study, an explanation of their simulation results on the Fisher effect puzzle and further examine if nonlinear relations really help resolving the puzzle.

Assessing fiscal sustainability subject to policy changes: a Markov switching cointegration approach

We propose a Markov switching cointegration approach to assess long run fiscal sustainability. This method allows us to simultaneously: (1) test for cointegration in the presence of significant fiscal policy changes; (2) assess the type of fiscal regime that a country experienced at a given period and (3) analyse the timing of the transition between the estimated regime types. Given its flexibility, our approach enable us to uncover a richer and more complex dynamics in the analysis of fiscal sustainability, which standard linear cointegration methods fail to capture.

Testing for Nonlinear Threshold Cointegration in the Monetary Model of Exchange Rates with a Century of Data

The monetary model suggests that nominal exchange rates between two countries will be determined by important macroeconomic variables. The existence of a cointegrating relationship among these fundamental variables is the backbone of the monetary model. In a recent paper, Rapach and Wohar (2002, Journal of International Economics) advance the literature by testing for linear cointegration in the monetary model using a century of data to increase power. They find evidence of cointegration in five or six of ten countries. We extend their work to the nonlinear framework by performing threshold cointegration tests that allow for asymmetric adjustments in two regimes. Asymmetric adjustments in exchange rates can occur, for example, if transactions costs are present or if policy makers react asymmetrically to changing fundamentals. Moreover, whereas Rapach and Wohar (2002) found it necessary to exclude the relative output variable in some cases to maintain the validity of their cointegration tests, we can include this variable as a stationary covariate to increase power. Overall, using their same long-span data, we find more support for cointegration in a nonlinear framework.

ARMS RACE BETWEEN TURKEY AND GREECE: A THRESHOLD COINTEGRATION ANALYSIS

The ongoing Turkish–Greek antagonism has triggered the interest of defense economists to investigate the various aspects of the arms race between Turkey and Greece. However, empirical studies examining the long‐run relationship between the military expenditures of the two countries offer little evidence in favor of such an interaction. This paper attributes the poor results of the previous literature to the adherence to linear cointegration techniques and argues that if the adjustment towards long‐run equilibrium is asymmetric, nonlinear co‐integration models should be employed. Accordingly, this paper considers threshold autoregressive (TAR) and momentum threshold autoregressive (M‐TAR) models as alternative adjustment processes for the cointegration relationship, following Enders and Siklos (2001). The results indicate that the relationship between the variables can be characterized by a threshold cointegration specification following an M‐TAR type adjustment process.

Dynamic Misspecification in Nonparametric Cointegrating Regression

Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspecified lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression under misspecified lag structure are derived, showing the NW estimator to be inconsistent with a 'pseudo-true function' limit that is a local average of the true regression function. In this respect nonlinear cointegrating regression differs importantly from conventional linear cointegration which is invariant to time translation. When centered on the pseudo-function and appropriately scaled, the NW estimator still has a mixed Gaussian limit distribution. The convergence rates are the same as those obtained under correct specification but the variance of the limit distribution is larger. Some applications of the limit theory to non-linear distributed lag cointegrating regression are given and the practical import of the results for index models, functional regression models, and temporal aggregation are discussed.

Structural Nonparametric Cointegrating Regression

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill-posed inverse problems. In functional cointegrating regressions where the regressor is an integrated or near-integrated time series, it is shown here that inverse and ill-posed inverse problems do not arise. Instead, simple nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving straightforward asymptotics that are useable in practical work. It is further shown that use of augmented regression, as is common in linear cointegration modeling to address endogeneity, does not lead to bias reduction in nonparametric regression, but there is an asymptotic gain in variance reduction. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series when there is a single integrated or near-integrated regressor. The methods may be applied to a range of empirical models where functional estimation of cointegrating relations is required.

Structural Breaks, Cointegration and the Fisher Effect

There is scant empirical support in the literature for the Fisher effect in the long run, though it is often assumed in theoretical models. We argue that a break in the cointegrating relation introduces a spurious unit root that leads to a rejection of cointegration. We applied new break tests and tested for nonlinearity in the cointegrating relation with post-war data for 15 countries. Our empirical results support cointegration, after accounting for breaks, and a linear Fisher relation in the long run. This is in contrast to several recent studies that found no support for linear cointegration.

Financial Crisis and Asian Real Estate Securities Market Interdependence: Some Additional Evidence

This paper investigates empirically the changes in long‐run relationship and short‐term linkage among the US, UK and eight Asian real estate securities markets before, during, and after the 1997–1998 Asian financial crisis as well as in the most recent period. Using a combination of Johansen linear cointegration, Bierens nonlinear cointegration, Granger causality tests, variance decomposition analysis and volatility spillover methodology, our results indicate that the degree of market interdependence in Asian real estate securities markets appears to have become stronger in the long run and short term since the Asian financial crisis. Further, this market interdependence seems to be on a rising trend ten years after the Asian financial crisis. This stronger market relationship between the Asian and US markets implies a portfolio combination of these markets is less likely to provide diversification benefit in the form of minimum risk. One important lesson to learn from our study is that portfolio managers should constantly review their international diversification models and strategies with respect to the constituent markets because of possible changes in market interdependence triggered by a major crisis.

Threshold cointegration and nonlinear adjustment between stock prices and dividends

According to several empirical studies, the linear present-value model fails to explain the behaviour of stock prices in the long run. We analyse the possible presence of threshold cointegration between real stock prices and dividends for the US market during the period from 1871:1 to 2004:6. According to our results, the null hypothesis of linear cointegration between stock prices and dividends is rejected in favour of a two-regime threshold cointegration model. We find also that stock prices do not respond to equilibrium error, and dividends respond to the past divergence only if the deviation from the equilibrium error does not exceed the estimated threshold parameter. This in turn would support theoretical models assuming that the stock price–dividend relation is nonlinear.

Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics

We develop a representation of nonlinear integrated vector processes based on the martingale representation theorem of Hall and Heyde (1980). In the representation, linear combinations of the components of the vector process may be stationary, so the system may be linearly cointegrated, yet exhibit nonlinear stationary, or short-run, dynamics. We test for linear cointegration relations with nonlinear dynamics in weekly U.S. interest rates. We find that the individual rates are I(1) and that the system is linearly cointegrated. Furthermore, both cointegration relations exhibit nonlinear dynamics so the the system's short-run dynamics are nonlinear.

Cointegration applied to purchasing‐power analysis of mean Ukrainian total wages

AbstractThe main purpose of this study is to propose Johansen's [6] methodology of linear cointegration analysis as a tool to measure the purchasing power of the Ukrainian mean total wages (MTW) within the period of November 1993 to December 2004 expressed in terms of prices of some basic food products or of the Consumer Price Index (CPI). Nineteen monthly price time series of basic food products, the CPI and MTW published by the State Committee of Statistics of Ukraine (Derzhkomstat) have been selected. Preliminary studies of stationarity are undertaken to establish their degree of integratedness with a battery of adequate unit root tests. A cointegration analysis of couples of one of these price time series of some basic food products, respectively the CPI and the MTW time series are realised, yielding linear functions between both selected series, establishing tentative long‐run equilibrium relations for subperiods shorter than the interval 1993 to 2004. The results show that the purchasing power of the MTW, expressed in terms of the prices of some basic food products, respectively the CPI, gradually increased from 1993 to 2004. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)