# hAhr_test: Test restrictions on coefficients of MIDAS regression using... In midasr: Mixed Data Sampling Regression

## Description

Perform a test whether the restriction on MIDAS regression coefficients holds.

## Usage

 `1` ```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)`

## Details

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.

## Value

a `htest` object

## Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

## References

Kvedaras V., Zemlys, V. The statistical content and empirical testing of the MIDAS restrictions

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44``` ```##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) ```