1d:T71a,# Wald Test and Confidence Band for Equality of Granger-Causality in Two Samples This function computes Wald test and confidence band for equality of Granger-causality in two samples using bootstrap samples generated by `sar.eq.bootstrap()` based on the spline autoregression (SAR) models of quantile series (QSER). ```r sar.eq.test(A1, A1.sim, A2, A2.sim, sel.lag = NULL, sel.tau = NULL) ``` ## Arguments - `A1`: matrix of selected SAR coefficients for sample 1 - `A1.sim`: simulated bootstrap samples from `sar.eq.bootstrap()` for sample 1 - `A2`: matrix of selected SAR coefficients for sample 2 - `A2.sim`: simulated bootstrap samples from `sar.eq.bootstrap()` for sample 2 - `sel.lag`: indices of time lags for Wald test (default = `NULL`: all lags) - `sel.tau`: indices of quantile levels for Wald test (default = `NULL`: all quantiles) ## Returns a list with the following elements: - **test**: list of Wald test result containing `wald` and `p.value` - **D.u**: matrix of upper limits of 95% confidence band for `A1 - A2` - **D.l**: matrix of lower limits of 95% confidence band for `A1 - A2` ## Examples ```r y11 <- stats::arima.sim(list(order=c(1,0,0), ar=0.5), n=64) y21 <- stats::arima.sim(list(order=c(1,0,0), ar=-0.5), n=64) y12 <- stats::arima.sim(list(order=c(1,0,0), ar=0.5), n=64) y22 <- stats::arima.sim(list(order=c(1,0,0), ar=-0.5), n=64) tau <- seq(0.1,0.9,0.05) y1.sar <- qspec.sar(cbind(y11,y21),tau0=tau,p=1) y2.sar <- qspec.sar(cbind(y12,y22),tau0=tau,p=1) A1.sim <- sar.eq.bootstrap(y1.sar$qser,y1.sar$fit,y2.sar$fit,index=c(1,2),nsim=5) A2.sim <- sar.eq.bootstrap(y2.sar$qser,y2.sar$fit,y1.sar$fit,index=c(1,2),nsim=5) A1 <- sar.gc.coef(y1.sar$fit,index=c(1,2)) A2 <- sar.gc.coef(y2.sar$fit,index=c(1,2)) test <- sar.eq.test(A1,A1.sim,A2,A2.sim,sel.lag=NULL,sel.tau=NULL) ```1e:T49a,M7.49933 0.25C3.49635 0.25 0.25 3.49593 0.25 7.50024C0.25 10.703 2.32715 13.4206 5.2081 14.3797C5.57084 14.446 5.70302 14.2222 5.70302 14.0299C5.70302 13.8576 5.69679 13.4019 5.69323 12.797C3.67661 13.235 3.25112 1

sar.eq.test function