Economic data can be decomposed into a trend, a seasonal and a remainder component using the Berlin procedure 4.1 (German: Berliner Verfahren 4.1), as used by the National Statistical Office of Germany. Currently with this version of the R package, only the trend and seasonal components can be estimated following BV4.1. All further component estimations, for example the estimation of the calendar component, of the official procedure BV4.1 are not yet implemented. The function supports quarterly and monthly data.
BV4.1(yt, type = NULL)An S4 object with the following elements is returned.
decompAn object of class "mts" that consists of the
decomposed time series data.
frequencythe frequency of the time series.
ts_namethe object name of the initially provided time series object.
a time series object of class ts or an object that can be
converted into such an object with as.ts.
a single character value that indicates, whether the data was
quarterly ("quarterly") or monthly ("monthly") observed; the
default is "monthly"; if a time series object is passed to yt,
the value for this argument will be automatically selected according to the
frequency in yt.
Dominik Schulz (Research Assistant) (Department of Economics, Paderborn
University),
Author and Package Creator
The BV4.1 base model is as follows:
trend and seasonality are estimated based on the additive nonparametric regression model for an equidistant time series $$y_t = m(x_t) + s(x_t) + \epsilon_t,$$ where \(y_t\) is the observed time series with \(t=1,...n\), \(x_t = t / n\) is the rescaled time on the interval \([0, 1]\), \(m(x_t)\) is a smooth trend function, \(s(x_t)\) is a (slowly changing) seasonal component with seasonal period \(p_s\) and \(\epsilon_t\) are stationary errors with \(E(\epsilon_t) = 0\) that are furthermore assumed to be independent but identically distributed (i.i.d.).
It is assumed that \(m\) and \(s\) can be approximated locally by a polynomial of small order and by a trigonometric polynomial, respectively. Through locally weighted regression, \(m\) and \(s\) can therefore be estimated suitably.
The advantage of the Berlin Procedure 4.1 (BV4.1) is that it makes use of
fixed filters based on locally weighted regression (both with a weighted
mixture of local linear and local cubic components for the trend) at all
observation time points. Thus, BV4.1 results in fixed weighting matrices
both for the trend estimation step and for the seasonality estimation step
that can be immediately applied to all economic time series.
Those matrices are saved internally in the package and when applying
BV4.1,
only weighted sums of the observations (with already obtained weights) have
to be obtained at all time points. Thus, this procedure is quite fast.
Permission to include the BV4.1 base model procedure was kindly provided by the Federal Statistical Office of Germany.
Speth, H.-T. (2004). Komponentenzerlegung und Saisonbereinigung ökonomischer Zeitreihen mit dem Verfahren BV4.1. Methodenberichte 3. Statistisches Bundesamt. URL: https://www.destatis.de/DE/Methoden/Saisonbereinigung/BV41-methodenbericht-Heft3_2004.pdf?__blob=publicationFile.
Xt <- log(EXPENDITURES)
est <- BV4.1(Xt)
est
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