ind_test: Independence tests
In hotneim/lg: Locally Gaussian Distributions: Estimation and Methods

Description Usage Arguments Details Value References Examples

Independence tests based on the local Gaussian correlation

ind_test(
  lg_object,
  h = function(x) x^2,
  S = function(y) as.logical(rep(1, nrow(y))),
  bootstrap_type = "plain",
  block_length = NULL,
  n_rep = 1000
)

`lg_object`	An object of type `lg`, as produced by the `lg_main`-function. The data must be two dimensional.
`h`	The `h`-function used in the calculation of the test statistic. The default value is `h(x) = x^2`.
`S`	The integration area for the test statistic. Must be a logical function that accepts an n x 2 matrix and returns TRUE if a row is in S.
`bootstrap_type`	The bootstrap method. Choose "plain" for the ordinary nonparametric bootstrap valid for independence test for iid data and for serial dependence within a time series. Choose "stationary" or "block" for a test for cross dependence between two time series.
`block_length`	Block length if using block bootstrap for the cross dependence test. Calculated by `np::b.star()` if not supplied.
`n_rep`	Number of bootstrap replications.

Implementation of three independence tests: For iid data (Berentsen et al., 2014), for serial dependence within a time series (Lacal and Tjøstheim, 2017a), and for serial cross-dependence between two time series (Lacal and Tjøstheim, 2017b). The first test has a different theoretical foundation than the latter two, but the implementations are similar and differ only in the bootstrap procedure. For the time series applications, the user must lag the series to his/her convenience before making the lg_object and calling this function.

A list containing the test result as well as various parameters. The elements are:

lg_object The lg-object supplied by the user.
observed The observed value of the test statistic.
replicated The replicated values of the test statistic.
bootstrap_type The bootstrap type.
block_length The block length used for the block bootstrap.
p_value The p-value of the test.

Berentsen, Geir Drage, and Dag Tjøstheim. "Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation." Statistics and Computing 24.5 (2014): 785-801.

Lacal, Virginia, and Dag Tjøstheim. "Local Gaussian autocorrelation and tests for serial independence." Journal of Time Series Analysis 38.1 (2017a): 51-71.

Lacal, Virginia, and Dag Tjøstheim. "Estimating and testing nonlinear local dependence between two time series." Journal of Business & Economic Statistics just-accepted (2017b).

    # Remember to increase the number of bootstrap samplesin preactical
    # implementations.

    ## Not run: 

    # Test for independence between two vectors, iid data.
    x1 <- cbind(rnorm(100), rnorm(100))
    lg_object1 <- lg_main(x1)
    test_result1 = ind_test(lg_object1,
                            bootstrap_type = "plain",
                            n_rep = 20)

    # Test for serial dependence in time series, lag 1
    data(EuStockMarkets)
    logreturns <- apply(EuStockMarkets, 2, function(x) diff(log(x)))
    x2 <- cbind(logreturns[1:100,1], logreturns[2:101, 1])
    lg_object2 <- lg_main(x2)
    test_result2 = ind_test(lg_object2,
                            bootstrap_type = "plain",
                            n_rep = 20)

    # Test for cross-dependence, lag 1
    x3 <- cbind(logreturns[1:100,1], logreturns[2:101, 2])
    lg_object3 <- lg_main(x3)
    test_result3 = ind_test(lg_object3,
                            bootstrap_type = "block",
                            n_rep = 20)
    
## End(Not run)