implicit_forecast: Retrieve implicit forecasts corresponding to the asymmetric...

In palatej/rjdfilters: Trend-Cycle Extraction with Linear Filters

Retrieve implicit forecasts corresponding to the asymmetric filters

Description

Function to retrieve the implicit forecasts corresponding to the asymmetric filters

Usage

implicit_forecast(x, coefs)

Arguments

x	a univariate or multivariate time series.
coefs	a matrix or a list that contains all the coefficients of the asymmetric and symmetric filters. (from the symmetric filter to the shortest). See details.

Details

Let h be the bandwidth of the symmetric filter, v_{-h}, \ldots, v_h the coefficients of the symmetric filter and w_{-h}^q, \ldots, w_h^q the coefficients of the asymmetric filter used to estimate the trend when q future values are known (with the convention w_{q+1}^q=\ldots=w_h^q=0). Let denote y_{-h},\ldots, y_0 the las h available values of the input times series. The implicit forecasts, y_{1}*,\ldots, y_h* solve:

\forall q, \quad \sum_{i=-h}^0 v_iy_i + \sum_{i=1}^h v_iy_i* =\sum_{i=-h}^0 w_i^qy_i + \sum_{i=1}^h w_i^qy_i*

which is equivalent to

\forall q, sum_{i=1}^h (v_i- w_i^q) y_i* =\sum_{i=-h}^0 (w_i^q-v_i)y_i.

Note that this is solved numerically: the solution isn't exact.

Examples

x <- retailsa$AllOtherGenMerchandiseStores
ql <- lp_filter(horizon = 6, kernel = "Henderson", endpoints = "QL")
lc <- lp_filter(horizon = 6, kernel = "Henderson", endpoints = "LC")
f_ql <- implicit_forecast(x, ql)
f_lc <- implicit_forecast(x, lc)

plot(window(x, start = 2007),
     xlim = c(2007,2012))
lines(ts(c(tail(x,1), f_ql), frequency = frequency(x), start = end(x)),
      col = "red", lty = 2)
lines(ts(c(tail(x,1), f_lc), frequency = frequency(x), start = end(x)),
      col = "blue", lty = 2)

palatej/rjdfilters documentation built on May 8, 2023, 6:28 a.m.