, Hartmut Hebbel [aut]| Title: | The Generalized Berlin Method for Time Series Decomposition |
|---|---|
| Description: | Time series decomposition for univariate time series using the "Verallgemeinerte Berliner Verfahren" (Generalized Berlin Method) as described in 'Kontinuierliche Messgrößen und Stichprobenstrategien in Raum und Zeit mit Anwendungen in den Natur-, Umwelt-, Wirtschafts- und Finanzwissenschaften', by Hebbel and Steuer, Springer Berlin Heidelberg, 2022 <doi:10.1007/978-3-662-65638-9>, or 'Decomposition of Time Series using the Generalised Berlin Method (VBV)' by Hebbel and Steuer, in Jan Beran, Yuanhua Feng, Hartmut Hebbel (Eds.): Empirical Economic and Financial Research - Theory, Methods and Practice, Festschrift in Honour of Prof. Siegfried Heiler. Series: Advanced Studies in Theoretical and Applied Econometrics. Springer 2014, p. 9-40. |
| Authors: | Detlef Steuer [aut, cre]
, Hartmut Hebbel [aut] |
| Maintainer: | Detlef Steuer <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.6.2 |
| Built: | 2024-10-31 22:08:00 UTC |
| Source: | https://github.com/cran/VBV |
decomposition - decompose a time series with VBV
decomposition(t.vec, p, q.vec, base.period, lambda1, lambda2)decomposition(t.vec, p, q.vec, base.period, lambda1, lambda2)
t.vec |
vector of observation points. |
p |
maximum exponent in polynomial for trend |
q.vec |
vector containing frequencies to use for seasonal component, given as integers, i.e. c(1, 3, 5) for 1/2pi, 3/2pi, 5/2*pi (times length of base period) |
base.period |
base period in number of observations, i.e. 12 for monthly data with yearly oscillations |
lambda1 |
penalty weight for smoothness of trend |
lambda2 |
penalty weight for smoothness of seasonal component (lambda1 == lambda2 == Inf result in estimations of the original Berliner Verfahren) |
list with the following components:
trendA function which returns the appropriate weights if applied to a point in time
saisonA function which returns the appropriate weights if applied to a point in time
A, G1, G2Some matrices that allow to calclate SSE etc. Exposed only to reuse their calculation. See the referenced paper for details.
### Usage of decomposition t <- 1:121 # equidistant time points, i.e. 5 days p <- 2 # maximally quadratic q <- c(1, 3, 5) # 'seasonal' components within the base period base.period <- 24 # i.e. hourly data with daily cycles l1 <- 1 l2 <- 10 dec <- decomposition( t, p, q, base.period, l1, l2) ### Note: decomosition is independent of data, only depends on time### Usage of decomposition t <- 1:121 # equidistant time points, i.e. 5 days p <- 2 # maximally quadratic q <- c(1, 3, 5) # 'seasonal' components within the base period base.period <- 24 # i.e. hourly data with daily cycles l1 <- 1 l2 <- 10 dec <- decomposition( t, p, q, base.period, l1, l2) ### Note: decomosition is independent of data, only depends on time
estimation – estimate trend and seasonal components statically
estimation(t.vec, y.vec, p, q.vec, base.period, lambda1, lambda2)estimation(t.vec, y.vec, p, q.vec, base.period, lambda1, lambda2)
t.vec |
vector of points in time as integers |
y.vec |
vector of data |
p |
maximum exponent in polynomial for trend |
q.vec |
vector containing frequencies to use for seasonal component, given as integers, i.e. c(1, 3, 5) for 1/2pi, 3/2pi, 5/2*pi (times length of base period) |
base.period |
base period in number of observations, i.e. 12 for monthly data with yearly oscillations |
lambda1 |
penalty weight for smoothness of trend |
lambda2 |
penalty weight for smoothness of seasonal component (lambda1 == lambda2 == Inf result in estimations of the original Berliner Verfahren) |
A dataframe with the following components:
dataoriginal data y.vec
trendvector of estimated trend of length length(y.vec)
seasonvector of estimated season of length length(y.vec)
### using of estimation t <- 1:121 # equidistant time points, i.e. 5 days y <- 0.1*t + sin(t) + rnorm(length(t)) p <- 2 # maximally quadratic q <- c(1, 3, 5) # 'seasonal' components within the base period base.period <- 24 # i.e. hourly data with daily cycles l1 <- 1 l2 <- 10 est <- estimation( t, y, p, q, base.period, l1, l2) plot(est$data) lines(est$trend + est$season)### using of estimation t <- 1:121 # equidistant time points, i.e. 5 days y <- 0.1*t + sin(t) + rnorm(length(t)) p <- 2 # maximally quadratic q <- c(1, 3, 5) # 'seasonal' components within the base period base.period <- 24 # i.e. hourly data with daily cycles l1 <- 1 l2 <- 10 est <- estimation( t, y, p, q, base.period, l1, l2) plot(est$data) lines(est$trend + est$season)
moving.decomposition – decompose a times series into locally estimated trend and season figures
moving.decomposition(n, p, q.vec, m, base.period, lambda1, lambda2)moving.decomposition(n, p, q.vec, m, base.period, lambda1, lambda2)
n |
number of observation points (must be odd!). Internally this will be transformed to seq( -(n-1)/2, (n-1)/2, 1) |
p |
maximum exponent in polynomial for trend |
q.vec |
vector containing frequencies to use for seasonal component, given as integers, i.e. c(1, 3, 5) for 1/2pi, 3/2pi, 5/2*pi (times length of base period) |
m |
width of moving window |
base.period |
base period in number of observations, i.e. 12 for monthly data with yearly oscillations |
lambda1 |
penalty weight for smoothness of trend |
lambda2 |
penalty weight for smoothness of seasonal component |
list with the following components:
W1nxn matrix of weights. Trend is estimated as W1 %% y, if y is the data vector
W2nxn matrix of weights. Season is estimated as W2 %% y, if y is the data vector
lambda1 == lambda2 == Inf result in estimations of the original Berliner Verfahren
### Usage of moving.decomposition t <- 1:121 # equidistant time points, i.e. 5 days m <- 11 p <- 2 # maximally quadratic q <- c(1, 3, 5) # 'seasonal' components within the base period base.period <- 24 # i.e. hourly data with daily cycles l1 <- 1 l2 <- 1 m.dec <- moving.decomposition( length(t), p, q, m, base.period, l1, l2)### Usage of moving.decomposition t <- 1:121 # equidistant time points, i.e. 5 days m <- 11 p <- 2 # maximally quadratic q <- c(1, 3, 5) # 'seasonal' components within the base period base.period <- 24 # i.e. hourly data with daily cycles l1 <- 1 l2 <- 1 m.dec <- moving.decomposition( length(t), p, q, m, base.period, l1, l2)
moving.estimation – estimate locally optimized trend and season figures
moving.estimation(t.vec, y.vec, p, q.vec, m, base.period, lambda1, lambda2)moving.estimation(t.vec, y.vec, p, q.vec, m, base.period, lambda1, lambda2)
t.vec |
vector of points in time as integers |
y.vec |
vector of data |
p |
maximum exponent in polynomial for trend |
q.vec |
vector containing frequencies to use for seasonal component, given as integers, i.e. c(1, 3, 5) for 1/2pi, 3/2pi, 5/2*pi (times length of base period) |
m |
width of moving window |
base.period |
base period in number of observations, i.e. 12 for monthly data with yearly oscillations |
lambda1 |
penalty weight for smoothness of trend |
lambda2 |
penalty weight for smoothness of seasonal component |
A dataframe with the following components:
dataoriginal data y.vec
trendvector of estimated trend of length length(y.vec)
seasonvector of estimated season of length length(y.vec)
lambda1 == lambda2 == Inf result in estimations of the original Berliner Verfahren