Carry out IID tests using sample autocorrelations

Carry out tests for IID from sample autocorrelations.

Usage

acfIidTest(acf, n, npar = 0, nlags = npar + 1,
           method = c("LiMcLeod", "LjungBox", "BoxPierce"),
           interval = 0.95, expandCI = TRUE, ...)

Arguments

acf: autocorrelations.
n: length of the corresponding time series.
npar: number of df to subtract.
nlags: number of autocorrelations to use for the portmonteau statistic, can be a vector to request several such statistics.
method: a character string, one of "LiMcLeod", "LjungBox" or "BoxPierce".
interval: a number or NULL.
expandCI: logical flag, if TRUE return a CI for each lag up to max(nlags). Used only if CI's are requested.
...: additional arguments passed on to methods. In particular, some methods have argument x for the time series.

Details

Performs one of several tests for IID based on sample autocorrelations. A correction of the degrees of freedom for residuals from fitted models can be specified with argument npar. nlags specifies the number of autocorrelations to use in the test, it can be a vector to request several tests.

The results of the test are gathered in a matrix with one row for each element of nlags. The test statistic is in column "ChiSq", degrees of freedom in "DF" and the p-value in "pvalue". The method is in attribute "method".

If interval is not NULL confidence intervals for the autocorrelations are computed, under the null hypothesis of independence. The coverage probability (or probabilities) is speciified by interval.

If argument expandCI is TRUE, there is one row for each lag, up to max(nlags). It is best to use this feature with a single coverage probability.

If expandCI to FALSE the confidence intervals are put in a matrix with one row for each coverage probability.

Value

a list with components "test" and (if requested) "ci", as described in Details

Methods

signature(acf = "ANY"): In this method acf contains the autocorrelations.
signature(acf = "missing"): The autocorrelations are computed from argument x (the time series).
signature(acf = "SampleAutocorrelations"): This is a convenience method in which argument n is taken from acf and thus does not need to be specified by the user.

References

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

Author

Georgi N. Boshnakov

Examples

set.seed(1234)
ts1 <- rnorm(100)

a1 <- drop(acf(ts1)$acf)

acfIidTest(a1, n = 100, nlags = c(5, 10, 20))
#> $test
#>         ChiSq DF       pvalue
#> [1,] 102.7351  5 1.400761e-20
#> [2,] 115.6877 10 3.785190e-20
#> [3,] 123.1473 20 7.429551e-17
#> attr(,"method")
#> [1] "LiMcLeod"
#> 
#> $ci
#>              int          
#>  [1,] -0.1959964 0.1959964
#>  [2,] -0.1959964 0.1959964
#>  [3,] -0.1959964 0.1959964
#>  [4,] -0.1959964 0.1959964
#>  [5,] -0.1959964 0.1959964
#>  [6,] -0.1959964 0.1959964
#>  [7,] -0.1959964 0.1959964
#>  [8,] -0.1959964 0.1959964
#>  [9,] -0.1959964 0.1959964
#> [10,] -0.1959964 0.1959964
#> [11,] -0.1959964 0.1959964
#> [12,] -0.1959964 0.1959964
#> [13,] -0.1959964 0.1959964
#> [14,] -0.1959964 0.1959964
#> [15,] -0.1959964 0.1959964
#> [16,] -0.1959964 0.1959964
#> [17,] -0.1959964 0.1959964
#> [18,] -0.1959964 0.1959964
#> [19,] -0.1959964 0.1959964
#> [20,] -0.1959964 0.1959964
#> attr(,"level")
#> [1] 0.95
#> 
acfIidTest(a1, n = 100, nlags = c(5, 10, 20), method = "LjungBox")
#> $test
#>         ChiSq DF       pvalue
#> [1,] 105.7423  5 3.249445e-21
#> [2,] 119.6584 10 5.935593e-21
#> [3,] 126.8248 20 1.532370e-17
#> attr(,"method")
#> [1] "LjungBox"
#> 
#> $ci
#>              int          
#>  [1,] -0.1959964 0.1959964
#>  [2,] -0.1959964 0.1959964
#>  [3,] -0.1959964 0.1959964
#>  [4,] -0.1959964 0.1959964
#>  [5,] -0.1959964 0.1959964
#>  [6,] -0.1959964 0.1959964
#>  [7,] -0.1959964 0.1959964
#>  [8,] -0.1959964 0.1959964
#>  [9,] -0.1959964 0.1959964
#> [10,] -0.1959964 0.1959964
#> [11,] -0.1959964 0.1959964
#> [12,] -0.1959964 0.1959964
#> [13,] -0.1959964 0.1959964
#> [14,] -0.1959964 0.1959964
#> [15,] -0.1959964 0.1959964
#> [16,] -0.1959964 0.1959964
#> [17,] -0.1959964 0.1959964
#> [18,] -0.1959964 0.1959964
#> [19,] -0.1959964 0.1959964
#> [20,] -0.1959964 0.1959964
#> attr(,"level")
#> [1] 0.95
#> 
acfIidTest(a1, n = 100, nlags = c(5, 10, 20), interval = NULL)
#> $test
#>         ChiSq DF       pvalue
#> [1,] 102.7351  5 1.400761e-20
#> [2,] 115.6877 10 3.785190e-20
#> [3,] 123.1473 20 7.429551e-17
#> attr(,"method")
#> [1] "LiMcLeod"
#> 
acfIidTest(a1, n = 100, method = "LjungBox", interval = c(0.95, 0.90), expandCI = FALSE)
#> $test
#>         ChiSq DF       pvalue
#> [1,] 103.0303  1 3.300609e-24
#> attr(,"method")
#> [1] "LjungBox"
#> 
#> $ci
#>             int          
#> [1,] -0.1959964 0.1959964
#> [2,] -0.1644854 0.1644854
#> attr(,"level")
#> [1] 0.95 0.90
#> 


## acfIidTest() is called behind the scenes by methods for autocorrelation objects
ts1_acrf <- autocorrelations(ts1)
class(ts1_acrf)  # "SampleAutocorrelations"
#> [1] "SampleAutocorrelations"
#> attr(,"package")
#> [1] "sarima"
whiteNoiseTest(ts1_acrf, h0 = "iid", nlags = c(5,10,20), method = "LiMcLeod")
#> $test
#>          ChiSq DF    pvalue
#> [1,]  3.969382  5 0.5538326
#> [2,] 15.709796 10 0.1082467
#> [3,] 24.323983 20 0.2285263
#> attr(,"method")
#> [1] "LiMcLeod"
#> 
#> $ci
#>              int          
#>  [1,] -0.1959964 0.1959964
#>  [2,] -0.1959964 0.1959964
#>  [3,] -0.1959964 0.1959964
#>  [4,] -0.1959964 0.1959964
#>  [5,] -0.1959964 0.1959964
#>  [6,] -0.1959964 0.1959964
#>  [7,] -0.1959964 0.1959964
#>  [8,] -0.1959964 0.1959964
#>  [9,] -0.1959964 0.1959964
#> [10,] -0.1959964 0.1959964
#> [11,] -0.1959964 0.1959964
#> [12,] -0.1959964 0.1959964
#> [13,] -0.1959964 0.1959964
#> [14,] -0.1959964 0.1959964
#> [15,] -0.1959964 0.1959964
#> [16,] -0.1959964 0.1959964
#> [17,] -0.1959964 0.1959964
#> [18,] -0.1959964 0.1959964
#> [19,] -0.1959964 0.1959964
#> [20,] -0.1959964 0.1959964
#> attr(,"level")
#> [1] 0.95
#> 
plot(ts1_acrf)


## use 10% level of significance in the plot:
plot(ts1_acrf, interval = 0.9)