White noise tests

White noise tests.

Usage

whiteNoiseTest(object, h0, ...)

Arguments

object

an object, such as sample autocorrelations or partial autocorrelations.

h0

the null hypothesis, currently "iid" or "garch".

...

additional arguments passed on to methods.

Details

whiteNoiseTest carries out tests for white noise. The null hypothesis is identified by argument h0, based on which whiteNoiseTest chooses a suitable function to call. The functions implementing the tests are also available to be called directly and their documentation should be consulted for further arguments that are available.

If h0 = "iid", the test statistics and rejection regions can be use to test if the underlying time series is iid. Argument method specifies the method for portmanteau tests: one of "LiMcLeod" (default), "LjungBox", "BoxPierce".

If h0 = "garch", the null hypothesis is that the time series is GARCH, see Francq & Zakoian (2010). The tests in this case are based on a non-parametric estimate of the asymptotic covariance matrix.

Portmonteau statistics and p-values are computed for the lags specified by argument nlags. If it is missing, suitable lags are chosen automatically.

If argument interval is TRUE, confidence intervals for the individual autocorrelations or partial autocorrelations are computed.

Value

a list with component test and, if ci=TRUE, component

ci.

References

Francq C, Zakoian J (2010). GARCH models: structure, statistical inference and financial applications. John Wiley & Sons. ISBN 978-0-470-68391-0.

Li WK (2004). Diagnostic checks in time series. Chapman & Hall/CRC Press.

Author

Georgi N. Boshnakov

Note

Further methods will be added in the future.

See also

acfGarchTest (h0 = "garch"), acfIidTest (h0 = "iid");

acfMaTest

Examples

n <- 5000
x <- sarima:::rgarch1p1(n, alpha = 0.3, beta = 0.55, omega = 1, n.skip = 100)
x.acf <- autocorrelations(x)
x.pacf <- partialAutocorrelations(x)

x.iid <- whiteNoiseTest(x.acf, h0 = "iid", nlags = c(5,10,20), x = x, method = "LiMcLeod")
x.iid
#> $test
#>          ChiSq DF    pvalue
#> [1,]  1.142892  5 0.9502373
#> [2,]  6.425240 10 0.7783615
#> [3,] 19.813720 20 0.4696354
#> attr(,"method")
#> [1] "LiMcLeod"
#> 
#> $ci
#>               int           
#>  [1,] -0.02771808 0.02771808
#>  [2,] -0.02771808 0.02771808
#>  [3,] -0.02771808 0.02771808
#>  [4,] -0.02771808 0.02771808
#>  [5,] -0.02771808 0.02771808
#>  [6,] -0.02771808 0.02771808
#>  [7,] -0.02771808 0.02771808
#>  [8,] -0.02771808 0.02771808
#>  [9,] -0.02771808 0.02771808
#> [10,] -0.02771808 0.02771808
#> [11,] -0.02771808 0.02771808
#> [12,] -0.02771808 0.02771808
#> [13,] -0.02771808 0.02771808
#> [14,] -0.02771808 0.02771808
#> [15,] -0.02771808 0.02771808
#> [16,] -0.02771808 0.02771808
#> [17,] -0.02771808 0.02771808
#> [18,] -0.02771808 0.02771808
#> [19,] -0.02771808 0.02771808
#> [20,] -0.02771808 0.02771808
#> attr(,"level")
#> [1] 0.95
#> 

x.iid2 <- whiteNoiseTest(x.acf, h0 = "iid", nlags = c(5,10,20), x = x, method = "LjungBox")
x.iid2
#> $test
#>          ChiSq DF    pvalue
#> [1,]  1.140803  5 0.9504289
#> [2,]  6.424512 10 0.7784265
#> [3,] 19.832409 20 0.4684563
#> attr(,"method")
#> [1] "LjungBox"
#> 
#> $ci
#>               int           
#>  [1,] -0.02771808 0.02771808
#>  [2,] -0.02771808 0.02771808
#>  [3,] -0.02771808 0.02771808
#>  [4,] -0.02771808 0.02771808
#>  [5,] -0.02771808 0.02771808
#>  [6,] -0.02771808 0.02771808
#>  [7,] -0.02771808 0.02771808
#>  [8,] -0.02771808 0.02771808
#>  [9,] -0.02771808 0.02771808
#> [10,] -0.02771808 0.02771808
#> [11,] -0.02771808 0.02771808
#> [12,] -0.02771808 0.02771808
#> [13,] -0.02771808 0.02771808
#> [14,] -0.02771808 0.02771808
#> [15,] -0.02771808 0.02771808
#> [16,] -0.02771808 0.02771808
#> [17,] -0.02771808 0.02771808
#> [18,] -0.02771808 0.02771808
#> [19,] -0.02771808 0.02771808
#> [20,] -0.02771808 0.02771808
#> attr(,"level")
#> [1] 0.95
#> 

x.garch <- whiteNoiseTest(x.acf, h0 = "garch", nlags = c(5,10,20), x = x)
x.garch
#> $test
#>       h          Q      pval
#> [1,]  5  0.5452572 0.9903723
#> [2,] 10  4.7304542 0.9084415
#> [3,] 20 17.2858687 0.6343406
#> 
#> $ci
#>               int           
#>  [1,] -0.04316442 0.04316442
#>  [2,] -0.04180554 0.04180554
#>  [3,] -0.03876060 0.03876060
#>  [4,] -0.03604820 0.03604820
#>  [5,] -0.03508113 0.03508113
#>  [6,] -0.03319458 0.03319458
#>  [7,] -0.03167507 0.03167507
#>  [8,] -0.03151315 0.03151315
#>  [9,] -0.03082342 0.03082342
#> [10,] -0.03031157 0.03031157
#> [11,] -0.03010730 0.03010730
#> [12,] -0.02881384 0.02881384
#> [13,] -0.02767999 0.02767999
#> [14,] -0.02809412 0.02809412
#> [15,] -0.02776439 0.02776439
#> [16,] -0.02827813 0.02827813
#> [17,] -0.02735102 0.02735102
#> [18,] -0.02801310 0.02801310
#> [19,] -0.02805033 0.02805033
#> [20,] -0.02855553 0.02855553
#>