Estimation of Common Long Memory Components in Cointegrated Systems

Gonzalo, Jesús; Granger, Clive W. J.

doi:10.1017/cbo9780511753978.013

Cited by 148 publications

(320 citation statements)

References 18 publications

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“…Finally, Π can be of reduced rank n − r > 1 or r < n , implying that there are r linear combinations of x t that are stationary or cointegrated and thus β′ x t σ I (0). In this situation the Π matrix can be decomposed into two n × r matrices such that Π=αβ′ where β is the matrix of CIVs, which implies n − r common (stochastic) trends (see, e.g ., Kasa 1992, Gonzalo and Granger 1995), while α is the matrix of error correction coefficients that measures the average speed of adjustment toward the cointegrating relationship. The significance of the β and α coefficients will further indicate which of the variables participate in the cointegrating space and which of the variables are weakly exogenous, respectively.…”

Section: Cointegration Testsmentioning

confidence: 99%

Increasing Convergence Between U.S. and International Securitized Property Markets: Evidence Based on Cointegration Tests

Yunus

2009

Real Estate Economics

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This article examines the degree of interdependence among the securitized property markets of six major countries and the United States. Long-run results indicate that, over a period beginning January 1990 and ending August 2007, the property markets of Australia, Hong Kong, Japan, the United Kingdom and the United States are tied together, implying that from the perspective of the U.S. investor the markets of the Netherlands and France provide the greater diversification benefits. Further, the United States and Japan are found to be the sources of the common trends, suggesting that the two larger property markets lead the five (cointegrated) markets toward the long-run equilibrium relationships. Copyright (c) 2009 American Real Estate and Urban Economics Association.

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Section: Cointegration Testsmentioning

confidence: 99%

Increasing Convergence Between U.S. and International Securitized Property Markets: Evidence Based on Cointegration Tests

Yunus

2009

Real Estate Economics

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“…In what follows, we employ the permanent‐transitory (PT) decomposition of Gonzalo and Granger (1995) to identify the common permanent component of each pair of variances. To facilitate the PT decomposition, we follow Dolatabadi, Narayan, Nielsen, and Xu (2018) by constructing a fully specified framework which accommodates long‐run and short‐run effects in a system containing fractionally cointegrated variables.…”

Section: Resultsmentioning

confidence: 99%

“…With the estimated parameters of the FCVAR, we then obtain the PT decomposition as follows

X_{t} = A_{1} L M_{t} + A_{2} S M_{t},

where the common long‐memory component of

X_{t}

is given by

L M_{t} = α_{⊥}' X_{t}

with

α_{⊥}' α = 0

and the transitory component is constituted by

S M_{t} = β' X_{t}

. Additional details relating to the construction of

A_{1}

and

A_{2}

may be found in Gonzalo and Granger (1995). For a given value of the transitory component, a high value of

L M_{t}

increases the magnitude of the forecast of the conditional variance, which renders the

L M_{t}

closely associated with the vol‐of‐vol discussed in Bollerslev et al (2009).…”

Section: Resultsmentioning

confidence: 99%

“…To explain the association between fractional cointegration detected in pairs of variances and the return predictability implicit in their differences, we extract the common long‐memory components in variances using the permanent‐transitory decomposition proposed by Gonzalo and Granger (1995). This procedure is implemented within a parametric fractionally cointegrated VAR framework.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Return predictability of variance differences: A fractionally cointegrated approach

Izzeldin

Yao

2020

Journal of Futures Markets

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This 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 longmemory 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. K E Y W O R D S fractional cointegration, return predictability, variance risk premium J E L C L A S S I F I C A T I O N C14; C32; C51 | INTRODUCTIONNumerous empirical studies suggest that, unlike the variance, the variance risk premium (VRP) carries nontrivial predictive power for aggregate stock market returns over quarterly to annual horizons, where the degree of return predictability is greater than that afforded by more conventional predictors, see, Bollerslev, Tauchen, and Zhou (2009), Drechsler and Yaron (2010), Bollerslev, Marrone, Xu, and Zhou (2014), and Bali and Zhou (2016), among others. Those studies also provide strong evidence that much of the predictability implicit in the VRP may be attributed to its close relation with macroeconomic uncertainty and aggregate risk aversion.The VRP is formally defined as the wedge between option-implied and realized variances. It is measured as the difference between (the square of) the CBOE VIX index and the statistical expectation of the future return variation. In Bollerslev et al. (2009), Drechsler andYaron (2010) and Bollerslev, Sizova, and Tauchen (2012), the return predictability of the VRP is investigated using a self-contained general equilibrium model. This is in the spirit of the long-run risks (LRR) model pioneered by Bansal and Yaron (2004). Specifically, Bollerslev et al. (2009) andBollerslev et al. (2012) extend the LRR model by allowing the time-varying volatility-of-volatility (vol-of-vol) within the economy to be generated by its own stochastic process. They further show that the difference between the risk-neutral and the objective expectations of return variation isolates the vol-of-vol factor, which then serves as the sole source of the true VRP. The VRP, therefore, displays good predictive power for future returns in cases where the vol-of-vol plays a more dominant role in determining variation in the equity premium. A direct link between the VRP and the vol-of-vol is also demonstrated in a purely probabilistic model introduced by Barndorff-Nielsen and Veraart (2013). U D . The SJ and IVA are, respectively, measured as the difference between RV U and RV D and the difference between IV U and IV D . Using a semiparametric approach, we demonstrate the existence of a fractionally cointegrating relation in each pair of the semivariances...

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“…Banerjee, Marcellino and Osbat (2004) uses Monte Carlo simulations to study this issue in small samples and found that the consequences of cross‐sectional cointegration on existing panel cointegration tests can be quite severe. The authors suggest testing for the presence of cross‐sectional cointegration by using the procedure developed by Gonzalo and Granger (1995), which involves first extracting the common trends from each cross‐section and then testing for cointegration among these trends. When we employ this approach to the saving and investment data, we end up marginally rejecting the null of no cointegration on the 1% level on one occasion.…”

Section: An Application To the Current Accountmentioning

confidence: 99%

Testing for Panel Cointegration with Multiple Structural Breaks*

Westerlund¹

2006

Oxf Bull Econ Stat

267

252

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This paper proposes a Lagrange multiplier (LM) test for the null hypothesis of cointegration that allows for the possibility of multiple structural breaks in both the level and trend of a cointegrated panel regression. The test is general enough to allow for endogenous regressors, serial correlation and an unknown number of breaks that may be located at different dates for different individuals. We derive the limiting distribution of the test and conduct a small Monte Carlo study to investigate its finite sample properties. In our empirical application to the solvency of the current account, we find evidence of cointegration between saving and investment once a level break is accommodated.

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Estimation of Common Long Memory Components in Cointegrated Systems

Cited by 148 publications

References 18 publications

Increasing Convergence Between U.S. and International Securitized Property Markets: Evidence Based on Cointegration Tests

Increasing Convergence Between U.S. and International Securitized Property Markets: Evidence Based on Cointegration Tests

Return predictability of variance differences: A fractionally cointegrated approach

Testing for Panel Cointegration with Multiple Structural Breaks*

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