Periodogram Test for Assessing Equality of Spectral Densities

\(\varphi_n^p\) is an adaption of the test \(T_3\) from the work by Scaccia and Martin (2005). The test compares individual deviations of the periodogram ordinates \(I_x\) and \(I_y\) from the total amplitude of \(I_x + I_y\). We define \(G(\omega_{kl})\) as the comparison value: $$G(\omega_{kl}) = \frac{I_x(\omega_{kl})-I_y(\omega_{kl})}{I_x(\omega_{kl}) + I_y(\omega_{kl})}$$ The test statistic \(PT_3\) is then given by: $$PT_3 = \sqrt{12n}(\overline{|G|-1/2}) \overset d\longrightarrow \mathcal N(0,1)$$ Critical values are drawn from the standard normal distirbution.

Usage

test.periodo(x, y, alpha)

Arguments

x

Numeric matrix of dims N, M with no NA values (representing the first lattice data sample)

y

Numeric matrix of dims N, M with no NA values (representing the second lattice data sample)

alpha

Numeric value in \((0,1]\)

Value

An object of type periodoTestResult

Examples

set.seed(1)
K0 <- MA_coef_all(0.3)
x <- gridMA(8, 8, K0)
y <- gridMA(8, 8, K0)
test.periodo(x, y, 0.05)
#> Periodogram Test for equality Hypothesis. 
#> 
#> 
#> Results 
#> -----------------------------------------
#> Tn: -0.06621311 
#> p: 0.5263959 
#> Decision: Accepted H0