Compute PAR autocovariance matrix

Usage

pc.acf.parModel(parmodel, maxlag = NULL)

pcacfMat(parmodel)

Arguments

parmodel: PAR model, an object of class parModel.
maxlag: maximum lag

Details

pc.acf.parModel returns the autocovariances of a PAR model in season-lag form with maximum lag equal to maxlag. If maxlag is larger than the available precomputed autocovariances, they missing ones are computed using the Yule-Walker relations. Note that pc.acf.parModel assumes that there are enough precomputed autocovariances to use the Yule-Walker recursions directly.

TODO: pc.acf.parModel is tied to the old classes since it accesses their slots. Could be used as a template to streamline the method for autocovariances for class "PeriodicAutocovariance".

The season-lag form can be easily converted to other forms with the powerful indexing operator, see the examples and slMatrix-class.

pcacfMat is a convenience function for statistical inference. It creates a covariance matrix with dimension chosen automatically. This covariance matrix is such that the asymptotic covariance matrix of the estimated parameters can be obtained by dividing sub-blocks by innovation variances and inverting them. See, eq. (3.3) in the reference.

Value

for pcacfMat, a matrix for pc.acf.parModel, an slMatrix

References

McLeod AI (1994). “Diagnostic checking of periodic autoregression models with application.” Journal of Time Series Analysis, 15(2), 221--233.

Author

Georgi N. Boshnakov

Examples

x <- arima.sim(list(ar = 0.9), n = 1000)
proba1 <- fitPM(c(3,2,2,2), x)

acfb <- pc.acf.parModel(proba1, maxlag = 8)
acfb[4:(-2), 4:(-2), type = "tt"]
#>          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
#> [1,] 4.354767 4.076277 3.437176 3.145738 2.762350 2.631064 2.220523
#> [2,] 4.076277 4.690931 3.960936 3.625010 3.183214 3.031926 2.558836
#> [3,] 3.437176 3.960936 4.203584 3.834758 3.367974 3.207862 2.707318
#> [4,] 3.145738 3.625010 3.834758 4.462997 3.874579 3.693773 3.117554
#> [5,] 2.762350 3.183214 3.367974 3.874579 4.354767 4.076277 3.437176
#> [6,] 2.631064 3.031926 3.207862 3.693773 4.076277 4.690931 3.960936
#> [7,] 2.220523 2.558836 2.707318 3.117554 3.437176 3.960936 4.203584

pcacfMat(proba1)
#>          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
#> [1,] 4.354767 4.076277 3.437176 3.145738 2.762350 2.631064 2.220523
#> [2,] 4.076277 4.690931 3.960936 3.625010 3.183214 3.031926 2.558836
#> [3,] 3.437176 3.960936 4.203584 3.834758 3.367974 3.207862 2.707318
#> [4,] 3.145738 3.625010 3.834758 4.462997 3.874579 3.693773 3.117554
#> [5,] 2.762350 3.183214 3.367974 3.874579 4.354767 4.076277 3.437176
#> [6,] 2.631064 3.031926 3.207862 3.693773 4.076277 4.690931 3.960936
#> [7,] 2.220523 2.558836 2.707318 3.117554 3.437176 3.960936 4.203584