Variance Estimator

Variance Estimator

Usage

var_estimator(x, coef, ...)

Arguments

x

input time series.

coef

vector of coefficients or a moving-average (moving_average()).

...

other arguments passed to the function moving_average() to convert coef to a "moving_average" object.

Details

Let \((\theta_i)_{-p\leq i \leq q}\) be a moving average of length \(p+q+1\) used to filter a time series \((y_i)_{1\leq i \leq n}\). It is equivalent to a local regression and the associated error variance \(\sigma^2\) can be estimated using the normalized residual sum of squares, which can be simplified as: $$ \hat\sigma^2=\frac{1}{n-(p+q)}\sum_{t=p+1}^{n-q} \frac{(y_t-\hat \mu_t)^2}{1-2w_0^2+\sum_{i=-p}^q w_i^2} $$

References

Loader, Clive. 1999. Local regression and likelihood. New York: Springer-Verlag.