size {acrt}  R Documentation 
This function provides an implementation of Algorithm 2 in Pötscher and Preinerstorfer (2016), which we here abbreviate as (A2). The user is referred to this article for definitions, a detailed description of the problem solved by (A2), and for a detailed description of the algorithm itself.
size(C, ar.order.max, bandwidth, ker, R, X, N0, N1, N2, Mp, M1, M2, Eicker = FALSE, opt.method.1 = "NelderMead", opt.method.2 = "NelderMead", control.1 = list("reltol" = N1^(.5), "maxit" = dim(X)[1]*20), control.2 = list("reltol" = N2^(.5), "maxit" = dim(X)[1]*30), cores = 1, margin = rep(1, length = ar.order.max))
C 
Critical value. A positive real number (for negative critical values the size of the test equals 1). 
ar.order.max 
Maximal order of the stationary autoregressive
error process. A nonnegative integer.
If 
bandwidth 
Bandwidth parameter used in the construction of the test statistic. A positive real number. 
ker 
Kernel function used in the construction of the test statistic.

R 
The restriction matrix. 
X 
The design matrix. 
N0 
A positive integer. Corresponds to N_0 in the description of (A2) in Pötscher and Preinerstorfer (2016). 
N1 
A positive integer. Corresponds to N_1 in the description of (A2) in Pötscher and Preinerstorfer (2016). N1 should be greater than N0. 
N2 
A positive integer. Corresponds to N_2 in the description of (A2) in Pötscher and Preinerstorfer (2016). N2 should be greater than N1. 
Mp 
A positive integer.

M1 
A positive integer. Corresponds to M_1 in the description of (A2) in Pötscher and Preinerstorfer (2016). M1 must not exceed Mp. 
M2 
A positive integer. Corresponds to M_2 in the description of (A2) in Pötscher and Preinerstorfer (2016). M2 must not exceed M1. 
Eicker 
Determines the test for which the size is computed. If

opt.method.1 
The optimization method chosen in Stage 1
of (A2). Any optimization routine implemented in 
opt.method.2 
The optimization method chosen in Stage 2
of (A2). Any optimization routine implemented in 
control.1 
Control parameters passed to the 
control.2 
Control parameters passed to the 
cores 
The number of CPU cores used in the (parallelized) computation of the MonteCarlo approximations in (A2). Default is 1. Parallelized computation is enabled only if the compiler used to build acrt supports OpenMP. 
margin 
The restrictions imposed on the partial autocorrelation
coefficients. 
For details see the relevant sections in Pötscher and Preinerstorfer (2016), in particular the description of Algorithm 2 in the Appendix.
The output of size
depends on ar.order.max
. If
ar.order.max
is zero, the function size
returns a list consisting of:
size 
The size obtained by drawing a pseudorandom sample of size 
If ar.order.max
is greater than zero, the function size
returns a list consisting of:
starting.parameters 
The rows of this matrix are the initial values (partial autocorrelation coefficient vectors) that were used in Stage 1 of (A2), and which were chosen from the pool of randomly generated initial values in Stage 0. The rows correspond to ρ_{1:M_0}, ..., ρ_{M_1:M_0}, respectively, in the description of (A2). 
starting.rejection.probs 
Monte Carlo approximations of the nullrejection probabilities corresponding to the initial values used in Stage 1 of (A2). The coordinates of this vector correspond to \tilde{p}_{1:M_0}, ..., \tilde{p}_{M_1:M_0} in the description of (A2). 
first.stage.parameters 
The rows of this matrix are the parameters (partial autocorrelation coefficients) that were obtained in Stage 1 of (A2). The rows correspond to ρ^*_{1}, ..., ρ^*_{M_1}, respectively, in the description of (A2). 
first.stage.rejection.probs 
Monte Carlo approximations of the
nullrejection
probabilities corresponding to the 
second.stage.parameters 
The rows of this matrix are the parameters (partial autocorrelation coefficients) that were obtained in Stage 2 of (A2). The rows correspond to ρ^{**}_{1}, ..., ρ^{**}_{M_2}, respectively, in the description of (A2). 
second.stage.rejection.probs 
Monte Carlo approximations of the null
rejection probabilities
corresponding to the 
convergence 
Convergence codes returned from 
size 
The size computed by (A2), i.e., the maximum of \bar{\bar{p}}_{j, ρ_j^{**}} for j = 1, ..., M_2. 
Jones, M. C. (1987). Randomly choosing parameters from the stationarity and invertibility region of autoregressivemoving average models. Applied Statistics, 36 134138
Pötscher, B.M. and Preinerstorfer, D. (2016). Controlling the size of autocorrelation robust tests. https://arxiv.org/abs/1612.06127/
## Not run: n < 100 C < 2.260568^2 ar.order.max < n1 bandwidth < n/10 ker < "Bartlett" R < matrix(c(0, 1), nrow = 1, ncol = 2) X < cbind(rep(1, length = n), rnorm(n)) N0 < 1000 N1 < 10000 N2 < 50000 Mp < 5000 M1 < 10 M2 < 2 size(C, ar.order.max, bandwidth, ker, R, X, N0, N1, N2, Mp, M1, M2) ## End(Not run)