hAhr_test | R Documentation |
Perform a test whether the restriction on MIDAS regression coefficients holds.
hAhr_test(x, PHI = vcovHAC(x$unrestricted, sandwich = FALSE))
x |
MIDAS regression model with restricted coefficients, estimated with |
PHI |
the "meat" covariance matrix, defaults to |
Given MIDAS regression:
y_t=∑_{j=0}^k∑_{i=0}^{m-1}θ_{jm+i} x_{(t-j)m-i}+u_t
test the null hypothesis that the following restriction holds:
θ_h=g(h,λ),
where h=0,...,(k+1)m.
a htest
object
Virmantas Kvedaras, Vaidotas Zemlys
Kvedaras V., Zemlys, V. The statistical content and empirical testing of the MIDAS restrictions
hAh_test
##The parameter function theta_h0 <- function(p, dk, ...) { i <- (1:dk-1) (p[1] + p[2]*i)*exp(p[3]*i + p[4]*i^2) } ##Generate coefficients theta0 <- theta_h0(c(-0.1,0.1,-0.1,-0.001),4*12) ##Plot the coefficients plot(theta0) ##Generate the predictor variable set.seed(13) xx <- ts(arima.sim(model = list(ar = 0.6), 600 * 12), frequency = 12) ##Simulate the response variable y <- midas_sim(500, xx, theta0) x <- window(xx, start=start(y)) ##Fit restricted model mr <- midas_r(y~fmls(x,4*12-1,12,theta_h0)-1, list(y=y,x=x), start=list(x=c(-0.1,0.1,-0.1,-0.001))) ##The gradient function theta_h0_gradient <-function(p, dk,...) { i <- (1:dk-1) a <- exp(p[3]*i + p[4]*i^2) cbind(a, a*i, a*i*(p[1]+p[2]*i), a*i^2*(p[1]+p[2]*i)) } ##Perform test (the expected result should be the acceptance of null) hAhr_test(mr) mr <- midas_r(y~fmls(x,4*12-1,12,theta_h0)-1, list(y=y,x=x), start=list(x=c(-0.1,0.1,-0.1,-0.001)), weight_gradients=list()) ##Use exact gradient. Note the hAhr_test(mr)
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