Movatterモバイル変換

This R package implements our novel method to supplement theclassical HP filter with jumps and, possibly, regressors. The method isbased on the following state-space representation

\[y_t = x_t^\top \beta + \mu_t +\varepsilon_t\]

\[\mu_{t+1} = \mu_t + \nu_t\]

\[\nu_{t+1} = \nu_t +\zeta_t,\]

where\(y_t\) is the observable timeseries,\(\mu_t\) is the levelcomponent,\(\nu_t\) is the slopecomponent,\(\varepsilon_t\) and\(\zeta_t\) are white noise sequences withvariances\(\sigma^2_\varepsilon\) and\(\sigma^2_\zeta\), respectively. Thesmoother, that is, the linear projection of\(\mu_t\) on the span of the observations\(\{y_1,\ldots,y_n\}\), coincides withthe HP filter, where the smoothing constant\(\lambda\) is given by\(\sigma^2_\varepsilon / \sigma^2_\zeta\).Finally,\(x_t\) is a vector ofregressors, and\(\beta\) is a vectorof regression coefficients. These regressors are mainly used to modelseasonal patterns in the data and should have a zero mean to not alterthe interpretation of the HP filter as a trend extractor.