Compute quality criteria for asymmetric filters — diagnostic

Function du compute a diagnostic matrix of quality criteria for asymmetric filters

Usage

diagnostic_matrix(x, lags, passband = pi/6, sweights, ...)

Arguments

x: Weights of the asymmetric filter (from -lags to m).
lags: Lags of the filter (should be positive).
passband: passband threshold.
sweights: Weights of the symmetric filter (from 0 to lags or -lags to lags). If missing, the criteria from the functions mse are not computed.
...: optional arguments to mse.

Details

For a moving average of coefficients $\theta=(\theta_i)_{-p\le i\le q}$ diagnostic_matrix returns a list with the following ten criteria:

b_c Constant bias (if $b_c=0$, $\theta$ preserve constant trends) $$\sum_{i=-p}^q\theta_i - 1$$
b_l Linear bias (if $b_c=b_l=0$, $\theta$ preserve constant trends) $$\sum_{i=-p}^q i \theta_i$$
b_q Quadratic bias (if $b_c=b_l=b_q=0$, $\theta$ preserve quadratic trends) $$\sum_{i=-p}^q i^2 \theta_i$$
F_g Fidelity criterium of Grun-Rehomme et al (2018) $$$$
S_g Smoothness criterium of Grun-Rehomme et al (2018)
T_g Timeliness criterium of Grun-Rehomme et al (2018)
A_w Accuracy criterium of Wildi and McElroy (2019)
S_w Smoothness criterium of Wildi and McElroy (2019)
T_w Timeliness criterium of Wildi and McElroy (2019)
R_w Residual criterium of Wildi and McElroy (2019)

References

Grun-Rehomme, Michel, Fabien Guggemos, and Dominique Ladiray (2018). “Asymmetric Moving Averages Minimizing Phase Shift”. In: Handbook on Seasonal Adjustment.

Wildi, Marc and McElroy, Tucker (2019). “The trilemma between accuracy, timeliness and smoothness in real-time signal extraction”. In: International Journal of Forecasting 35.3, pp. 1072–1084.