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This R package implements our novel method to supplement the classical HP filter with jumps and, possibly, regressors. The method is based 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 time series, \(\mu_t\) is the level component, \(\nu_t\) is the slope component, \(\varepsilon_t\) and \(\zeta_t\) are white noise sequences with variances \(\sigma^2_\varepsilon\) and \(\sigma^2_\zeta\), respectively. The smoother, that is, the linear projection of \(\mu_t\) on the span of the observations \(\{y_1,\ldots,y_n\}\), coincides with the HP filter, where the smoothing constant \(\lambda\) is given by \(\sigma^2_\varepsilon / \sigma^2_\zeta\). Finally, \(x_t\) is a vector of regressors, and \(\beta\) is a vector of regression coefficients. These regressors are mainly used to model seasonal patterns in the data and should have a zero mean to not alter the interpretation of the HP filter as a trend extractor.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.