Direct Filter Approach

Usage

dfa_filter(
  horizon = 6,
  degree = 0,
  density = c("uniform", "rw"),
  targetfilter = lp_filter(horizon = horizon)[, 1],
  passband = 2 * pi/12,
  accuracy.weight = 1/3,
  smoothness.weight = 1/3,
  timeliness.weight = 1/3
)

Arguments

horizon: horizon (bandwidth) of the symmetric filter.
degree: degree of polynomial.
density: hypothesis on the spectral density: "uniform" (= white woise, the default) or "rw" (= random walk).
targetfilter: the weights of the symmetric target filters (by default the Henderson filter).
passband: passband threshold.
accuracy.weight, smoothness.weight, timeliness.weight: the weight used for the optimisation. The weight associated to the residual is derived so that the sum of the four weights are equal to 1.

Details

Moving average computed by a minimisation of a weighted mean of three criteria under polynomials constraints. The criteria come from the decomposition of the mean squared error between th trend-cycle

Let \(\boldsymbol \theta=(\theta_{-p},\dots,\theta_{f})'\) be a moving average where \(p\) and \(f\) are two integers defined by the parameter lags and leads. The three criteria are:

Examples

dfa_filter(horizon = 6, degree = 0)
#>             q=6          q=5           q=4         q=3         q=2         q=1
#> t-6 -0.01934985 -0.030012305 -0.0408092039 -0.04068978 -0.03622977 -0.03672904
#> t-5 -0.02786378 -0.033359743 -0.0411977083 -0.04106306 -0.03072500 -0.01681858
#> t-4  0.00000000  0.001617955  0.0031630124  0.00320233  0.01204228  0.04093710
#> t-3  0.06549178  0.071870402  0.0795170526  0.07941604  0.08550769  0.12220301
#> t-2  0.14735651  0.154367848  0.1632402190  0.16312197  0.16726498  0.20144314
#> t-1  0.21433675  0.218278871  0.2226926829  0.22264487  0.22680122  0.25014591
#> t    0.24005716  0.238829368  0.2358094694  0.23588451  0.24196319  0.24750757
#> t+1  0.21433675  0.207944469  0.1985282507  0.19868118  0.20515234  0.19131090
#> t+2  0.14735651  0.138054450  0.1272631817  0.12741087  0.12822306  0.00000000
#> t+3  0.06549178  0.057433857  0.0513680901  0.05139107  0.00000000  0.00000000
#> t+4  0.00000000 -0.002016302  0.0004249535  0.00000000  0.00000000  0.00000000
#> t+5 -0.02786378 -0.023008869  0.0000000000  0.00000000  0.00000000  0.00000000
#> t+6 -0.01934985  0.000000000  0.0000000000  0.00000000  0.00000000  0.00000000
#>             q=0
#> t-6 -0.02675707
#> t-5  0.01420277
#> t-4  0.08880802
#> t-3  0.17595533
#> t-2  0.24508791
#> t-1  0.26838604
#> t    0.23431701
#> t+1  0.00000000
#> t+2  0.00000000
#> t+3  0.00000000
#> t+4  0.00000000
#> t+5  0.00000000
#> t+6  0.00000000
dfa_filter(horizon = 6, degree = 2)
#>             q=6          q=5         q=4         q=3         q=2          q=1
#> t-6 -0.01934985 -0.031105441 -0.04888338 -0.05764640 -0.04948784 -0.007961043
#> t-5 -0.02786378 -0.030840929 -0.03722806 -0.04096008 -0.03686433 -0.036884447
#> t-4  0.00000000  0.005553125  0.01509948  0.02043095  0.01419427 -0.019710732
#> t-3  0.06549178  0.075680118  0.09443554  0.10664294  0.09370622  0.043998864
#> t-2  0.14735651  0.157683962  0.17753428  0.18829824  0.17738803  0.138819404
#> t-1  0.21433675  0.221376079  0.23306525  0.23716685  0.23398281  0.237104542
#> t    0.24005716  0.241802252  0.23989975  0.23478728  0.24355756  0.308924895
#> t+1  0.21433675  0.210178737  0.19487115  0.18311315  0.20164062  0.335708518
#> t+2  0.14735651  0.138186344  0.11635204  0.10287717  0.12188266  0.000000000
#> t+3  0.06549178  0.054026865  0.03459332  0.02528989  0.00000000  0.000000000
#> t+4  0.00000000 -0.009233115 -0.01973936  0.00000000  0.00000000  0.000000000
#> t+5 -0.02786378 -0.033307998  0.00000000  0.00000000  0.00000000  0.000000000
#> t+6 -0.01934985  0.000000000  0.00000000  0.00000000  0.00000000  0.000000000
#>             q=0
#> t-6  0.13737578
#> t-5 -0.08485848
#> t-4 -0.16654786
#> t-3 -0.10200794
#> t-2  0.09325916
#> t-1  0.38573469
#> t    0.73704465
#> t+1  0.00000000
#> t+2  0.00000000
#> t+3  0.00000000
#> t+4  0.00000000
#> t+5  0.00000000
#> t+6  0.00000000