An example PAR autocorrelation function

ex1 is the autocorrelation function used in the reference as an example when the solution of the periodic Yule-Walker system gives an invalid PAR model. This can happen only if Lambert-Lacroix's condition on the PAR order is not satisfied, see pdSafeParOrder.

Format

A function of two arguments

See also

pdSafeParOrder

Source

See pp. 429--430 of the reference.

References

Lambert-Lacroix S (2005). `` Extension of autocovariance coefficients sequence for periodically correlated processes.'' Journal of Time Series Analysis, 26(6), pp. 423-435.

Examples

data(ex1f)
## compute the first few autocorrelations
pc3 <- slMatrix(period = 2, maxlag = 5, f = ex1f, type = "tt")
## Fir a PAR(0,2) model
res0p2 <- alg1(pc3[],c(0,2))
## model is invalid since a partial autocorrelation is larger than one:
res0p2$be
#>      [,1] [,2]     [,3]
#> [1,]    1  0.0 0.000000
#> [2,]    1  0.9 2.064742
## Find a modified order:
pdSafeParOrder(c(0,2)) # PAR(1,2)
#> [1] 1 2
## now the parcor's are fine:
res1p2 <- alg1(pc3[],c(1,2))
res1p2$be
#>      [,1] [,2]      [,3]
#> [1,]    1 0.81 0.0000000
#> [2,]    1 0.90 0.6689647