Testing Cointegrating Rank with Level Shift at Unknown time

The function cajolst implements the procedure by Luetkepohl et al. to test for the cointegration rank of a VAR process with a level shift at an unknown time.

Usage

cajolst(x, trend = TRUE, K = 2, season = NULL)

Arguments

x: Data matrix to be investigated for cointegration.
trend: A linear trend is included in the auxiliary regressions for data adjustment (default is TRUE).
K: The lag order of the series (levels) in the VAR, must be at least equal to \(K = 2\).
season: If seasonal dummies should be included, the data frequency must be set accordingly, i.e ‘4’ for quarterly data.

Details

Note, that the slot "x" of the returned object contains the adjusted data series, that is, a matrix adjusted for the temptative break point, and if applicable, a linear trend and/or seasonal effects. The VECM is then estimated and tested for cointegration rank subject to the adjusted matrix. The break point is contained in the slot "bp". Please note, that the transitory VECM specification is estimated and that only the trace test is available. The critical values are taken from Trenkler, Carsten (2003).

Value

Returns an object of class ca.jo.

References

L\"utkepohl, H., Saikkonen, P. and Trenkler, C. (2004), Testing for the Cointegrating Rank of a VAR Process with Level Shift at Unknown Time, Econometrica, Vol. 72, No. 2, 647–662.

Trenkler, Carsten (2003), A new set of critical values for systems cointegration tests with a prior adjustment for deterministic terms, Economics Bulletin, Vol. 3, No. 11, 1–9.

Author

Bernhard Pfaff

Examples

data(denmark)
sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
sjd.lst <- cajolst(sjd, trend=TRUE, K=2, season=4)
summary(sjd.lst)
#> 
#> ###################### 
#> # Johansen-Procedure # 
#> ###################### 
#> 
#> Test type: trace statistic , with linear trend in shift correction 
#> 
#> Eigenvalues (lambda):
#> [1] 0.42098147 0.27098513 0.17330604 0.06127991
#> 
#> Values of teststatistic and critical values of test:
#> 
#>           test 10pct  5pct  1pct
#> r <= 3 |  3.15  5.42  6.78 10.04
#> r <= 2 | 11.62 13.78 15.83 19.85
#> r <= 1 | 24.33 25.93 28.45 33.76
#> r = 0  | 42.95 42.08 45.20 51.60
#> 
#> Eigenvectors, normalised to first column:
#> (These are the cointegration relations)
#> 
#>           LRM.l1     LRY.l1     IBO.l1     IDE.l1
#> LRM.l1 1.0000000   1.000000  1.0000000  1.0000000
#> LRY.l1 0.8490645  -2.319498 -1.8603632 -0.2148260
#> IBO.l1 6.0747337   6.824430  0.8571653  0.4685797
#> IDE.l1 1.0858006 -11.662840  2.7346259 -0.5253649
#> 
#> Weights W:
#> (This is the loading matrix)
#> 
#>           LRM.l1       LRY.l1      IBO.l1       IDE.l1
#> LRM -0.146180842 -0.034940907  0.04306167 -0.066397980
#> LRY -0.081222325  0.090040394  0.10130486 -0.011416802
#> IBO -0.021090906  0.002883555 -0.01985965  0.030806000
#> IDE  0.004947721  0.022143257 -0.03940262  0.008027878
#>