| Title: | Trend Estimation of Univariate and Bivariate Time Series with Controlled Smoothness |
|---|---|
| Description: | It performs the smoothing approach provided by penalized least squares for univariate and bivariate time series, as proposed by Guerrero (2007) and Gerrero et al. (2017). This allows to estimate the time series trend by controlling the amount of resulting (joint) smoothness. --- Guerrero, V.M (2007) <DOI:10.1016/j.spl.2007.03.006>. Guerrero, V.M; Islas-Camargo, A. and Ramirez-Ramirez, L.L. (2017) <DOI:10.1080/03610926.2015.1133826>. |
| Authors: | L. Leticia Ramirez-Ramirez [aut, cre], Alejandro Islas-Camargo [aut], Victor M. Guerrero [aut] |
| Maintainer: | L. Leticia Ramirez-Ramirez <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2025-02-11 03:26:11 UTC |
| Source: | https://github.com/cran/TSsmoothing |
Computes the correlation given a covariance matrix of a bivariate variable.
corrmvc(mat)corrmvc(mat)
mat |
is a 2x2 covariace matrix |
The empirical correlation fo the two series
Dataset of the
emp_agremp_agr
A ts vector a length of 25 observations from 1991 to 2015.
https://databank.worldbank.org/source/jobs#
It plots the univariate or bivariate. This function is not intended for users but to be called by trend_estimate.
graph_trend(dat, N, tau, dvar, label = NULL, jump = 1:N, bands = TRUE, las, bivariate = TRUE)graph_trend(dat, N, tau, dvar, label = NULL, jump = 1:N, bands = TRUE, las, bivariate = TRUE)
dat |
is a 2x2 covariace matrix |
N |
the number of observations |
tau |
the smoothed time series |
dvar |
the estimated variance for tau |
label |
the vectors of caracters associated to the time points to appear in the axis |
jump |
if label is too long, jump thin them on the axis |
bands |
is TRUE to draw the approximately 95% confidence bands around tau |
las |
is 1 and 2 if the asis should appear vertical and horizontal, respectively |
bivariate |
is FALSE if dat is a univariate time series |
The empirical correlation fo the two series
Obtains the lambda value for specific values of the smoothing level, correlation and length.
lambda_value(s, rho, N)lambda_value(s, rho, N)
s |
is a scalar that specifies the smoothing level. |
rho |
is the estimated correlation of the two time series. If the time series is univariate rho should be 0. |
N |
the length of the bivariate time series. |
The value of lambda lambda_value that corresponds to a smoothing level s
A flag to indicate if the lambda value was read from ltable
An array that presents the lambda values according to time series (N), the smoothing value (s), and the ts correlation (rho).
ltableltable
A 3d array with dimension 393 x 12 x 11, where dimensions are:
with values from 8 to 400
with smoothing values c(0.5, 0.6, 0.7, 0.75, 0.8, 0.825, 0.85, 0.875, 0.9, 0.925, 0.95, 0.975)
with values c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95)
3d array of float number that correspond to the lambda values that correspond to the specified values of the length of the
It plots the univariate or bivariate time series and its smoothed version (trend) using ggplot. It directly uses the output of trend_estimate.
plot_trend(smoothedTS, title = NULL, xlab = "Time", ylab = names(dat)[1:2])plot_trend(smoothedTS, title = NULL, xlab = "Time", ylab = names(dat)[1:2])
smoothedTS |
Is an object generated by the function trend_estimate |
title |
Main title of the graph |
xlab |
Common x label |
ylab |
A 2-length vector of characters. |
The ggplot of the original time series, their treind and its approximated 95
Checks if a squared matrix is positive definite and turn it to positive definied if necessary
positive_definite(m, c = NULL)positive_definite(m, c = NULL)
m |
Is a 2x2 matrix. |
c |
Is a small nonegative number. |
The same matrix (if positive definite) or its modification that is positive definite.
Obtains the preliminar smoothed series, based on the preliminar lambda value and empirical estimates for Sigma_eta and Sigma_epsilon. This function is called by trend_estimate as part of the smoothing process.
preliminar(dat)preliminar(dat)
dat |
is a 2-column matrix with the observations of a bivariate time series. Each row correspond to the values at a given time. |
The preliminary smoothen series ptau.
The final estimate for sigma.eta
The time series correlation given by sigma.eta, rho.eta.
The preliminary estimation for sigma_epsilon, sigma.epsilon,
A suggested value for lambda given by the empirical estimations.
The empirical time series correlation (preliminar to rho.eta), emp_rho.
The time series length N.
It computes the preliminary estimates of Sigma_epsilon and Sigma_eta
psigma_estimates(dat)psigma_estimates(dat)
dat |
is a 2 column matrix with for the bivariate time series observations. Each column correspond to the values at a given time. |
Sigma epsilon
Sigma eta
Function that calculates the empirical cross-covariance of order h for a bivariate time series.
sigma_zf(h, vec1, vec2, N)sigma_zf(h, vec1, vec2, N)
h |
the lag value. |
vec1 |
observations for the first variable of the bivariate time series. |
vec2 |
observations for the second variable of the bivariate time series. |
N |
the common length of vec1 and vec2. |
The value of lambda that corresponds to a smoothing level s.
Function that reports the smoothing level for a given value of lambda, N and rho (=0 if univariate).
smoothing_level(lambda, rho, N)smoothing_level(lambda, rho, N)
lambda |
a nonegative number. |
rho |
the correlation of the time series. |
N |
the length of the observations. |
S
A dataset (matrix) containing the annual trade (
tradetrade
An object of class matrix with 49 rows and 2 columns.
https://databank.worldbank.org/source/world-development-indicators#
This is the main function that estimates the trend for univariate or bivariate time series for a specified smoothing level.
trend_estimate(dat, smoothing_level = NULL, lambda = NULL, plot = TRUE, label = time(dat), jump = NULL, las = 2, bands = TRUE)trend_estimate(dat, smoothing_level = NULL, lambda = NULL, plot = TRUE, label = time(dat), jump = NULL, las = 2, bands = TRUE)
dat |
is a 2x2 matrix with the two time series. Each column correspond to the values at a given time. |
smoothing_level |
is a scalar between 0 and 1 that specifies the smoothing of the resulting time series tau. |
lambda |
Alternative, the function directly accepts the lambda value that corresponds to the desired smoothing level. |
plot |
is TRUE when we cant to plot of the original agaist the resulting series. |
label |
vector of characters that corresponds to the labels for each time point in the serie. |
jump |
is a vector of integers that specifies which values of labels should appear in the x labels. |
las |
is 1(2) if the x labels should be vertical (horizontal). |
bands |
is TRUE tolo include 95% confidence bands in the plots. |
The smoothed series tau.
The orginal data dat.
The estimation for sigma_eta, sigma.eta
The length of the time series N.
The lambda value corresponding to the smoothing level.
The diagonal values of the estimated variance of tau, diag.var.tau
A flag that indicates if data is a bivariate time series.
# Employment in agriculture (\% of total employment) (modeled ILO estimate) in OCDE members data(emp_agr) #It is a ts object with one single time series sts<-trend_estimate(emp_agr,0.70) plot_trend(sts, title="Employment in agriculture in OCDE members", xlab = "Years") # Data Trade (\% of GDP) for USA and Mexico downloaded from data(trade) #It is a numeric matrix with two columns sts<-trend_estimate(trade,0.7) plot_trend(sts, title="Trade in% of GDP",xlab="years") ts_trade<-ts(trade, start=1969,end=2017) #We transform tade to a ts object sts<-trend_estimate(ts_trade,0.7) plot_trend(sts, title="Trade in% of GDP",xlab="years")# Employment in agriculture (\% of total employment) (modeled ILO estimate) in OCDE members data(emp_agr) #It is a ts object with one single time series sts<-trend_estimate(emp_agr,0.70) plot_trend(sts, title="Employment in agriculture in OCDE members", xlab = "Years") # Data Trade (\% of GDP) for USA and Mexico downloaded from data(trade) #It is a numeric matrix with two columns sts<-trend_estimate(trade,0.7) plot_trend(sts, title="Trade in% of GDP",xlab="years") ts_trade<-ts(trade, start=1969,end=2017) #We transform tade to a ts object sts<-trend_estimate(ts_trade,0.7) plot_trend(sts, title="Trade in% of GDP",xlab="years")