1d:T7c5,# Test restrictions on coefficients of MIDAS regression using robust version of the test Perform a test whether the restriction on MIDAS regression coefficients holds. ```r hAhr_test(x, PHI = vcovHAC(x$unrestricted, sandwich = FALSE)) ``` ## Arguments - `x`: MIDAS regression model with restricted coefficients, estimated with `midas_r` - `PHI`: the "meat" covariance matrix, defaults to `vcovHAC(x$unrestricted, sandwich=FALSE)` ## Returns a `htest` object ## Details Given MIDAS regression: $$ y_t=\sum_{j=0}^k\sum_{i=0}^{m-1}\theta_{jm+i} x_{(t-j)m-i}+u_t $$ test the null hypothesis that the following restriction holds: $$ \theta_h=g(h,\lambda), $$ where $h=0,...,(k+1)m$. ## Examples ```r ##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) ``` ## References Kvedaras V., Zemlys, V. **The statistical content and empirical testing of the MIDAS restrictions** ## See Also hAh_test ## Author(s) Virmantas Kvedaras, Vaidotas Zemlys1e:T49a,M7.49933 0.25C3.49635 0.25 0.25 3.49593 0.2

hAhr_test function