| Type: | Package |
| Title: | Trend Estimation of Univariate and Bivariate Time Series with Controlled Smoothness |
| Version: | 0.1.0 |
| 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>. |
| Depends: | R (≥ 3.5.0) |
| Imports: | ggplot2(≥ 3.2.0), MASS (≥ 7.3.0), gridExtra (≥ 2.3.0), Matrix (≥ 1.2.0) |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2019-07-10 15:32:03 UTC; hp |
| Author: | L. Leticia Ramirez-Ramirez [aut, cre], Alejandro Islas-Camargo [aut], Victor M. Guerrero [aut] |
| Maintainer: | L. Leticia Ramirez-Ramirez <leticia.ramirez@cimat.mx> |
| Repository: | CRAN |
| Date/Publication: | 2019-07-15 10:50:03 UTC |
Correlation from a 2d covariance matrix.
Description
Computes the correlation given a covariance matrix of a bivariate variable.
Usage
corrmvc(mat)
Arguments
mat |
is a 2x2 covariace matrix |
Value
The empirical correlation fo the two series
Employment in agriculture
Description
Dataset of the
Usage
emp_agr
Format
A ts vector a length of 25 observations from 1991 to 2015.
Source
https://databank.worldbank.org/source/jobs#
Plot of original and smoothed time series.
Description
It plots the univariate or bivariate. This function is not intended for users but to be called by trend_estimate.
Usage
graph_trend(dat, N, tau, dvar, label = NULL, jump = 1:N,
bands = TRUE, las, bivariate = TRUE)
Arguments
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 |
Value
The empirical correlation fo the two series
Calculation of the lambda value.
Description
Obtains the lambda value for specific values of the smoothing level, correlation and length.
Usage
lambda_value(s, rho, N)
Arguments
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. |
Value
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
Lambda values table.
Description
An array that presents the lambda values according to time series (N), the smoothing value (s), and the ts correlation (rho).
Usage
ltable
Format
A 3d array with dimension 393 x 12 x 11, where dimensions are:
- N
with values from 8 to 400
- s
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)
- rho
with values c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95)
Details
3d array of float number that correspond to the lambda values that correspond to the specified values of the length of the
Source
Plot fo the time series and its smoothed version in ggplo
Description
It plots the univariate or bivariate time series and its smoothed version (trend) using ggplot. It directly uses the output of trend_estimate.
Usage
plot_trend(smoothedTS, title = NULL, xlab = "Time",
ylab = names(dat)[1:2])
Arguments
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. |
Value
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
Description
Checks if a squared matrix is positive definite and turn it to positive definied if necessary
Usage
positive_definite(m, c = NULL)
Arguments
m |
Is a 2x2 matrix. |
c |
Is a small nonegative number. |
Value
The same matrix (if positive definite) or its modification that is positive definite.
Preliminar smoothing
Description
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.
Usage
preliminar(dat)
Arguments
dat |
is a 2-column matrix with the observations of a bivariate time series. Each row correspond to the values at a given time. |
Value
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.
Preliminar estimates
Description
It computes the preliminary estimates of Sigma_epsilon and Sigma_eta
Usage
psigma_estimates(dat)
Arguments
dat |
is a 2 column matrix with for the bivariate time series observations. Each column correspond to the values at a given time. |
Value
Sigma epsilon
Sigma eta
Empirical cross-covarinace.
Description
Function that calculates the empirical cross-covariance of order h for a bivariate time series.
Usage
sigma_zf(h, vec1, vec2, N)
Arguments
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. |
Value
The value of lambda that corresponds to a smoothing level s.
Smoothing value
Description
Function that reports the smoothing level for a given value of lambda, N and rho (=0 if univariate).
Usage
smoothing_level(lambda, rho, N)
Arguments
lambda |
a nonegative number. |
rho |
the correlation of the time series. |
N |
the length of the observations. |
Value
S
Annual Trade for USA and Mexico
Description
A dataset (matrix) containing the annual trade (
Usage
trade
Format
An object of class matrix with 49 rows and 2 columns.
Source
https://databank.worldbank.org/source/world-development-indicators#
Trend estimation with controlled smoothing.
Description
This is the main function that estimates the trend for univariate or bivariate time series for a specified smoothing level.
Usage
trend_estimate(dat, smoothing_level = NULL, lambda = NULL,
plot = TRUE, label = time(dat), jump = NULL, las = 2,
bands = TRUE)
Arguments
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. |
Value
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.
Examples
# 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")