Description Usage Arguments Details Value References Examples

It applies the required kernel smoothing to the moment function in order for the GEL estimator to be valid. It is used by the `gel`

function.

1 2 3 |

`x` |
a |

`bw` |
The method to compute the bandwidth parameter. By default, it uses the bandwidth proposed by Andrews(1991). As an alternative, we can choose bw=bwNeweyWest (without "") which is proposed by Newey-West(1996). |

`prewhite` |
logical or integer. Should the estimating functions
be prewhitened? If |

`ar.method` |
character. The |

`weights` |
The smoothing weights can be computed by |

`approx` |
a character specifying the approximation method if the
bandwidth has to be chosen by |

`tol` |
numeric. Weights that exceed |

`kernel` |
The choice of kernel |

The sample moment conditions *∑_{t=1}^n g(θ,x_t)* is replaced by:
*∑_{t=1}^n g^k(θ,x_t)*, where *g^k(θ,x_t)=∑_{i=-r}^r k(i) g(θ,x_{t+i})*,
where *r* is a truncated parameter that depends on the bandwidth and *k(i)* are normalized weights so that they sum to 1.

If the vector of weights is provided, it gives only one side weights. For exemple, if you provide the vector (1,.5,.25), *k(i)* will become *(.25,.5,1,.5,.25)/(.25+.5+1+.5+.25) = (.1,.2,.4,.2,.1)*

smoothx: A *q \times q* matrix containing an estimator of the asymptotic variance of *√{n} \bar{x}*, where *\bar{x}* is *q\times 1*vector with typical element *\bar{x}_i = \frac{1}{n}∑_{j=1}^nx_{ji}*. This function is called by `gel`

but can also be used by itself.

`kern_weights`

: Vector of weights used for the smoothing.

Anatolyev, S. (2005), GMM, GEL, Serial Correlation, and Asymptotic Bias. *Econometrica*, **73**, 983-1002.

Andrews DWK (1991),
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation.
*Econometrica*, **59**,
817–858.

Kitamura, Yuichi (1997), Empirical Likelihood Methods With Weakly Dependent Processes.
*The Annals of Statistics*, **25**, 2084-2102.

Zeileis A (2006), Object-oriented Computation of Sandwich Estimators.
*Journal of Statistical Software*, **16**(9), 1–16.
URL http://www.jstatsoft.org/v16/i09/.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
g <- function(tet, x)
{
n <- nrow(x)
u <- (x[7:n] - tet[1] - tet[2]*x[6:(n-1)] - tet[3]*x[5:(n-2)])
f <- cbind(u, u*x[4:(n-3)], u*x[3:(n-4)], u*x[2:(n-5)], u*x[1:(n-6)])
return(f)
}
n = 500
phi<-c(.2, .7)
thet <- 0.2
sd <- .2
x <- matrix(arima.sim(n = n, list(order = c(2, 0, 1), ar = phi, ma = thet, sd = sd)), ncol = 1)
gt <- g(c(0, phi), x)
sgt <- smoothG(gt)$smoothx
plot(gt[,1])
lines(sgt[,1])
``` |

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