GNSSseg: Homogeneization of GNSS series

In arq16/GNSSseg: Homogeneization of GNSS series

Description

fit a segmentation in the mean model by taken into account for a functional part (estimated with a Fourier decomposition) and a heterogeneous variance (monthly variance)

Usage

GNSSseg(Data, lyear = 365.25, lmin = 1, Kmax = NULL,
  selection.K = "mBIC", S = 0.75, f = TRUE, selection.f = FALSE,
  threshold = 0.05, tol = 1e-04)

Arguments

Data	a data frame, with size [n x 2], containing the signal (e.g. the daily GPS-ERAI series for GNSS) and the dates (in format yyyy-mm-dd of type "calendar time" (class POSIXct))
lyear	the length of the year in the signal. Defalut is 365.25
lmin	the minimum length of the segments. Default is 1
Kmax	the maximal number of segments (must be lower than n). Default is [n/2 log(n)]
selection.K	a name indicating the model selection criterion to select the number of segments K (mBIC, ML, BM_BJ or BM_slope). "none" indicates that no selection is claimed and the procedure considers Kmax segments or Kmax-1 changes. If selection.K="All", the results for the four possible criteria are given. Default is "mBIC"
S	the threshold used in the ML criterion. Default is 0.75
f	a boolean indicating if the functional part is taking into account for in the model. Default is FALSE
selection.f	a boolean indicating if a selection on the functions of the Fourier decomposition of order 4 is performed. Default is FALSE
threshold	a numeric value lower than 1. Default is 0.05
tol	the stopping rule for the iterative procedure. Default is 1e-4

Details

The function performs homogeneization of GNSS series. The considered model is a segmentation in the mean model (detection of abrupt changes model) in which a functional part is added and with heterogeneous variances on fixed intervals. On GNSS series, the latter intervals corresponds to the month. The inference procedure consists for a fixed number of segments K in first estimating robustly the variances and second estimating the segmentation and the functional parts using an iterative procedure. The solution is obtained for k=1,...,Kmax segments. Then the "best k" is chosen using model selection criteria. The possible criteria are mBIC the modified BIC criterion REFEREF, ML the criterion proposed by REFEF, BM_BJ and BM_slope the criteria proposed by REFEF where the penalty constant is calibrated using the Biggest Jump and the slope respectively REFERF.

• The data is a data frame with 2 columns: $signal is the signal to be homogeneized (a daily series) and $date is the date. The date will be in format yyyy-mm-dd of type "calendar time" (class POSIXct).

• The function part is estimated using a Fourier decomposition of order 4 with selection.f=FALSE. selection.f=TRUE consists in selecting twice functions of the Fourier decomposition of order 4, first by using a stepwise procedure using AIC and second by considering among them the signficative ones (for which p.values are lower than threshold)

• If selection.K="none" the procedure is performed with Kmax segments.

• Missing data in the signal are accepted.

Note that if f=FALSE, only a segmentation is performed.

Value

A file containing

• selected.K that corresponds to the selected number of segments. If selection.K="none", the number of segments is fixed to Kmax

• segmentation that corresponds to the estimation of the segmentation parameters (the begin and the end positions of each segment with the estimated mean)

• functional that corresponds to the estimation of the functional part

• loglik that corresponds to the log-likelihood for k=1,...,Kmax. If selection.K="none", it contains only the log-likelihood for Kmax segments

• variances that corresponds to the estimated variances for each fixed interval (e.g. the months).

• mBIC that corresponds to the values of the mBIC criterion for k=1,...,Kmax if it is required (selection.K="mBIC" or selection.K="All")

If selection.K="All", the outputs selected.K, segmentation and functional are each a list containing the corresponding result for the four model selection criteria

Examples

data(Data)
lyear=365.25
Kmax=8
lmin=1
result=GNSSseg(Data,lyear,Kmax=Kmax)
plot_GNSS(Data,result$segmentation,result$functional)

arq16/GNSSseg documentation built on Dec. 6, 2019, 1:38 a.m.