coint: Test procedures for the cointegration rank

In pvars: VAR Modeling for Heterogeneous Panels

Test procedures for the cointegration rank

Description

Performs test procedures for the rank of cointegration in a single VAR model. The p-values are approximated by gamma distributions, whose moments are automatically adjusted to potential period-specific deterministic regressors and weakly exogenous regressors in the partial VECM.

Usage

coint.JO(
  y,
  dim_p,
  x = NULL,
  dim_q = dim_p,
  type = c("Case1", "Case2", "Case3", "Case4", "Case5"),
  t_D1 = NULL,
  t_D2 = NULL
)

coint.SL(y, dim_p, type_SL = c("SL_mean", "SL_trend"), t_D = NULL)

Arguments

y	Matrix. A (K \times (p+T)) data matrix of the K endogenous time series variables.
dim_p	Integer. Lag-order p for the endogenous variables y.
x	Matrix. A (L \times (q+T)) data matrix of the L weakly exogenous time series variables.
dim_q	Integer. Lag-order q for the weakly exogenous variables x. The literature uses dim_p (the default).
type	Character. The conventional case of the deterministic term in the Johansen procedure.
t_D1	List of vectors. The activating break periods \tau for the period-specific deterministic regressors in d_{1,t}, which are restricted to the cointegration relations. The accompanying lagged regressors are automatically included in d_{2,t}. The p-values are calculated for up to two breaks resp. three sub-samples.
t_D2	List of vectors. The activating break periods \tau for the period-specific deterministic regressors in d_{2,t}, which are unrestricted.
type_SL	Character. The conventional case of the deterministic term in the Saikkonen-Luetkepohl (SL) procedure.
t_D	List of vectors. The activation periods \tau for the period-specific deterministic regressors in d_{t} of the SL-procedure. The accompanying lagged regressors are automatically included in d_{t}. The p-values are calculated for up to two breaks resp. three sub-samples.

Value

A list of class 'coint', which contains elements of length K for each r_{H0}=0,\ldots,K-1:

r_H0	Rank under each null hypothesis.
stats_TR	Trace (TR) test statistics.
stats_ME	Maximum eigenvalue (ME) test statistics.
pvals_TR	p-values of the TR test.
pvals_ME	p-values of the ME test. NA if moments of the gamma distribution are not available for the chosen data generating process.
lambda	Eigenvalues, the squared canonical correlation coeffcients (saved only for the Johansen procedure).
args_coint	List of characters and integers indicating the cointegration test and specifications that have been used.

Functions

• coint.JO(): Johansen procedure.

• coint.SL(): (Trenkler)-Saikkonen-Luetkepohl procedure.

References

Johansen, S. (1988): "Statistical Analysis of Cointegration Vectors", Journal of Economic Dynamics and Control, 12, pp. 231-254.

Doornik, J. (1998): "Approximations to the Asymptotic Distributions of Cointegration Tests", Journal of Economic Surveys, 12, pp. 573-93.

Johansen, S., Mosconi, R., and Nielsen, B. (2000): "Cointegration Analysis in the Presence of Structural Breaks in the Deterministic Trend", Econometrics Journal, 3, pp. 216-249.

Kurita, T., Nielsen, B. (2019): "Partial Cointegrated Vector Autoregressive Models with Structural Breaks in Deterministic Terms", Econometrics, 7, pp. 1-35.

Saikkonen, P., and Luetkepohl, H. (2000): "Trend Adjustment Prior to Testing for the Cointegrating Rank of a Vector Autoregressive Process", Journal of Time Series Analysis, 21, pp. 435-456.

Trenkler, C. (2008): "Determining p-Values for Systems Cointegration Tests with a Prior Adjustment for Deterministic Terms", Computational Statistics, 23, pp. 19-39.

Trenkler, C., Saikkonen, P., and Luetkepohl, H. (2008): "Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break", Journal of Time Series Analysis, 29, pp. 331-358.

Examples

### reproduce basic example in "urca" ###
library("urca")
data(denmark)
sjd = denmark[ , c("LRM", "LRY", "IBO", "IDE")]

# rank test and estimation of the full VECM as in "urca" #
R.JOrank = coint.JO(y=sjd,      dim_p=2, type="Case2", t_D2=list(n.season=4))
R.JOvecm = VECM(y=sjd, dim_r=1, dim_p=2, type="Case2", t_D2=list(n.season=4))

# ... and of the partial VECM, i.e. after imposing weak exogeneity #
R.KNrank = coint.JO(y=sjd[ , c("LRM"), drop=FALSE],   dim_p=2,
                    x=sjd[ , c("LRY", "IBO", "IDE")], dim_q=2, 
                    type="Case2", t_D1=list(t_shift=36), t_D2=list(n.season=4))
R.KNvecm = VECM(y=sjd[ , c("LRM"), drop=FALSE],   dim_p=2,
                x=sjd[ , c("LRY", "IBO", "IDE")], dim_q=2, dim_r=1, 
                type="Case2", t_D1=list(t_shift=36), t_D2=list(n.season=4))

### reproduce Oersal,Arsova 2016:22, Tab.7.5 "France" ###
data("ERPT")
names_k = c("lpm5", "lfp5", "llcusd")  # variable names for "Chemicals and related products"
names_i = levels(ERPT$id_i)[c(1,6,2,5,4,3,7)]  # ordered country names
L.data  = sapply(names_i, FUN=function(i) 
   ts(ERPT[ERPT$id_i==i, names_k], start=c(1995, 1), frequency=12), 
   simplify=FALSE)
R.TSLrank = coint.SL(y=L.data$France, dim_p=3, type_SL="SL_trend", t_D=list(t_break=89))

pvars documentation built on Nov. 5, 2025, 6:57 p.m.