| Title: | Time Series Cointegrated System |
|---|---|
| Description: | A set of functions to implement Time Series Cointegrated System (TSCS) spatial interpolation and relevant data visualization. |
| Authors: | Tianjian Yang [aut, cre] |
| Maintainer: | Tianjian Yang <[email protected]> |
| License: | GPL (>= 2.0) |
| Version: | 0.1.1 |
| Built: | 2024-11-13 06:35:59 UTC |
| Source: | CRAN |
Two appraisal indexes used for evaluating the result of interpolation/prediction - RMSE and standard deviation of error.
appraisal_index(est, true)appraisal_index(est, true)
est |
a numeric vector; estimations. |
true |
a numeric vector; true values. |
The first appraisal index is RMSE, abbr. of root-mean-square error. It is used for measuring the differences between estimated values by a method and the values actually observed. Smaller RMSE means more accurate interpolation/prediction.
The second appraisal index is standard deviation of error, which is used for measuring how far the errors are spread out from their mean, namely, stability of errors. Smaller value means greater stability of errors, suggesting that errors would not fluctuate heavily due to difference of data.
A list of 2 is returned, including:
RMSEnumeric; RMSE.
stdnumeric; standard deviation of error.
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)
Provided that you have the true values of missing observations, you can compare them
with the results of interpolation. plot_compare visualizes the comparison
between estimates and true values. (NB: this plotting function can also be used
in other similar situations involving comparison between estimates and true values.)
plot_compare(est, true, cex = 1, width = 1, P = 6/7, AI = TRUE)plot_compare(est, true, cex = 1, width = 1, P = 6/7, AI = TRUE)
est |
a numeric vector; estimations. |
true |
a numeric vector; true values. |
cex |
numeric; size of point to be plotted. (default: 1) |
width |
numeric; width of fitted straight line. (default: 1) |
P |
numeric, between 0 and 1; position for superimposing values of appraisal indexes. (default: 6/7) |
AI |
logical; |
Attentions:
The values in est and true vectors should be arranged in the same order,
in correspondence with the sequence of observations.
If the maximum value of either est or true is greater than 1000, or the
minimum is smaller than -1000, please make appropriate transformation that limits your data
to bound [-1000,1000].
In the plot:
The big red point is the origin.
The red line stands for straight line y = x.
The blue line stands for fitted straight line.
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01) # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1) # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01) # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1) # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)
plot_dif differentiates boundary and interior spatial locations in a spatial domain (a collection of
spatial locations with their coordinates). Since TSCS method is only capable of interpolation but not
extrapolation, it is necessary to highlight the difference between interior spatial locations and system boundary.
plot_dif(coords, h, v, xlab = NULL, ylab = NULL, title = NULL, cex = 1)plot_dif(coords, h, v, xlab = NULL, ylab = NULL, title = NULL, cex = 1)
coords |
data frame; should only contain the two variables: X coordinate and Y coordinate. Each row uniquely denotes a spatial location. (coordinates must be numeric) |
h |
numeric; side length of the unit grid in X coordinate direction. |
v |
numeric; side length of the unit grid in Y coordinate direction. |
xlab |
a label for the x axis, defaults to the name of X coordinate. |
ylab |
a label for the y axis, defaults to the name of Y coordinate. |
title |
a main title for the plot. |
cex |
numeric; size of plotting point for each spatial location. (default: 1) |
plot_dif is exclusive to 2D rectangular grid system. Similarly, if you want to fathom how this package
handles 3D rectangular grid system, please refer to plot3D_dif.
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)
plot_map draws a two-dimensional spatial map. It is plotted based on the cross-section data
of a given time point, which is also often extracted from spatio-temporal data.
plot_map(newdata, xlab = NULL, ylab = NULL, title = NULL, cex = 2, shape = 15, low = "blue", mid = "yellow", high = "red", na.value = "white", midpoint = NULL)plot_map(newdata, xlab = NULL, ylab = NULL, title = NULL, cex = 2, shape = 15, low = "blue", mid = "yellow", high = "red", na.value = "white", midpoint = NULL)
newdata |
data frame; should only contain the three variables in order: X coordinate, Y coordinate and observation. This is the cross-section data or pure spatial data of a particular time point you have selected, with missing observations that you want to predict. (coordinates must be numeric) |
xlab |
a label for the x axis, defaults to the name of X coordinate. |
ylab |
a label for the y axis, defaults to the name of Y coordinate. |
title |
a main title for the plot. |
cex |
numeric; size of plotting point for each spatial locations. (default: 2) |
shape |
either an integer specifying a symbol or a single character to be used as the default in plotting points. (default: 15) |
low, high
|
colours for low and high ends of the gradient. (default: "blue","red") |
mid |
colour for midpoint of the gradient. (default: "yellow") |
na.value |
colour for missing values/observations. (default: "white") |
midpoint |
numeric; the midpoint of the gradient scale, defaults to the midpoint value of index presented. |
plot_map is exclusive to 2D rectangular grid system. Similarly, if you want to fathom how this package
handles 3D rectangular grid system, please refer to plot3D_map.
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)
plot_NA shows spatial locations with or without missing observation. It is plotted based on
the cross-section data of a given time point, which is also often extracted from spatio-temporal data.
plot_NA(newdata, xlab = NULL, ylab = NULL, title = NULL, cex = 1)plot_NA(newdata, xlab = NULL, ylab = NULL, title = NULL, cex = 1)
newdata |
data frame; should only contain the three variables in order: X coordinate, Y coordinate and observation. This is the cross-section data or pure spatial data of a particular time point you have selected, with missing observations that you want to predict. (coordinates must be numeric) |
xlab |
a label for the x axis, defaults to the name of X coordinate. |
ylab |
a label for the y axis, defaults to the name of Y coordinate. |
title |
a main title for the plot. |
cex |
numeric; size of plotting point for each spatial location. (default: 1) |
plot_NA is exclusive to 2D rectangular grid system. Similarly, if you want to fathom how this package
handles 3D rectangular grid system, please refer to plot3D_NA.
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)
plot3D_dif differentiates boundary and interior spatial locations in a spatial domain (a collection of
spatial locations with their coordinates). Since TSCS method is only capable of interpolation but not
extrapolation, it is necessary to highlight the difference between interior spatial locations and system boundary.
plot3D_dif(coords, h1, h2, v, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 3)plot3D_dif(coords, h1, h2, v, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 3)
coords |
data frame; should only contain the three variables: X coordinate, Y coordinate and Z coordinate. Each row uniquely denotes a spatial location. (coordinates must be numeric) |
h1 |
numeric; side length of the unit cubic grid in X coordinate direction (horizontal). |
h2 |
numeric; side length of the unit cubic grid in Y coordinate direction (horizontal). |
v |
numeric; side length of the unit cubic grid in Z coordinate direction (vertical). |
xlab |
a label for the x axis, defaults to the name of X coordinate. |
ylab |
a label for the y axis, defaults to the name of Y coordinate. |
zlab |
a label for the z axis, defaults to the name of Z coordinate. |
title |
a main title for the plot. |
cex |
numeric; size of point to be plotted for each spatial location. (default: 3) |
The resulting plot is interactive, where the red points are interior spatial locations while the black points denote system boundary.
plot3D_dif is exclusive to 3D rectangular grid system. Similarly, if you want to fathom how
this package handles 2D rectangular grid system, please refer to plot_dif.
plot_dif, plot3D_NA, plot3D_map
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)
plot_map draws a three-dimensional spatial map. It is plotted based on the cross-section data
of a given time point, which is also often extracted from spatio-temporal data.
plot3D_map(newdata, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 9, colorNA = "white")plot3D_map(newdata, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 9, colorNA = "white")
newdata |
data frame; should only contain the four variables in order: X coordinate, Y coordinate, Z coordinate and observation. This is the cross-section data or pure spatial data of a particular time point you have selected, with missing observations that you want to predict. (coordinates must be numeric) |
xlab |
a label for the x axis, defaults to the name of X coordinate. |
ylab |
a label for the y axis, defaults to the name of Y coordinate. |
zlab |
a label for the z axis, defaults to the name of Z coordinate. |
title |
a main title for the plot. |
cex |
numeric; size of plotting point for each spatial locations. (default: 9) |
colorNA |
colour for missing values/observations. (default: "white") |
The resulting plot is interactive.
plot3D_map is exclusive to 3D rectangular grid system. Similarly, if you want to fathom how
this package handles 2D rectangular grid system, please refer to plot_map.
plot_map, plot3D_NA, plot3D_dif
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)
plot3D_NA shows spatial locations with or without missing observation. It is plotted based on
the cross-section data of a given time point, which is also often extracted from spatio-temporal data.
plot3D_NA(newdata, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 3, color = "orange", colorNA = "blue")plot3D_NA(newdata, xlab = NULL, ylab = NULL, zlab = NULL, title = NULL, cex = 3, color = "orange", colorNA = "blue")
newdata |
data frame; should only contain the four variables in order: X coordinate, Y coordinate, Z coordinate and observation. This is the cross-section data or pure spatial data of a particular time point you have selected, with missing observations that you want to predict. (coordinates must be numeric) |
xlab |
a label for the x axis, defaults to the name of X coordinate. |
ylab |
a label for the y axis, defaults to the name of Y coordinate. |
zlab |
a label for the z axis, defaults to the name of Z coordinate. |
title |
a main title for the plot. |
cex |
numeric; size of plotting point for each spatial location. (default: 3) |
color |
colour to be used to fill the spatial locations. (default: "orange") |
colorNA |
colour for denoting missing values/observations. (default: "blue") |
The resulting plot is interactive.
plot3D_NA is exclusive to 3D rectangular grid system. Similarly, if you want to fathom how
this package handles 2D rectangular grid system, please refer to plot_NA.
plot_NA, plot3D_map, plot3D_dif
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)
This package provides functions to implement TSCS spatial interpolation and relevant data visualization. For TSCS method, the current version is only able to make use of spatio-temporal data whose spatial domain is a 2D or 3D rectangular grid system.
TSCS (abbr. of Time Series Cointegrated System) method is a spatial interpolation method based on analysis of historical spatio-temporal data. It can be regarded as a desirable alternative to spatio-temporal interpolation in some cases where we merely intend to interpolate a series of cross-section data at each observed time point for a given spatial domain.
The basic assumption of TSCS method is that, for any spatial location within the spatial domain of spatio-temporal data, its time series and the time series of its adjacent spatial locations are cointegrated (long-term equilibrium relationships).
As to TSCS method, package of the current version is only able to make use of spatio-temporal data whose spatial domain is a 2D or 3D rectangular grid system.
tscsRegression, tscsRegression3D : obtains regression coefficient matrix, the first step of
TSCS for 2D and 3D rectangular grid system respectively.
tscsEstimate, tscsEstimate3D : estimates the missing observations within a cross-section data
(pure spatial data) of a particular time point you have selected, the second step of TSCS for 2D and 3D
rectangular grid system respectively.
plot_dif, plot3D_dif : differentiates boundary and interior spatial locations in a spatial domain.
plot_NA, plot3D_NA : shows spatial locations with or without missing observation in a spatial domain.
plot_map, plot3D_map : draws the spatial map for a cross-section data.
plot_compare : visualizes the comparison between estimates and true values (if you have).
appraisal_index : computes the two appraisal indexes used for evaluating the result of
interpolation/prediction - RMSE and standard deviation of error. (if you have the true values)
Tianjian Yang <[email protected]>
tscsEstimate estimates the missing observations within the cross-section data (pure spatial data)
of a particular time point you have selected, namely, the interpolation process.
tscsEstimate(matrix, newdata, h, v)tscsEstimate(matrix, newdata, h, v)
matrix |
data frame; the first return value |
newdata |
data frame; should only contain the three variables in order: X coordinate, Y coordinate and observation. This is the cross-section data or pure spatial data of a particular time point you have selected, with missing observations that you want to predict. (coordinates must be numeric) |
h |
numeric; side length of the unit grid in X coordinate direction. |
v |
numeric; side length of the unit grid in Y coordinate direction. |
The first step of TSCS spatial interpolation should be carried out by function tscsRegression,
which is the prerequisite of tscsEstimate.
For 3D rectangular grid system, the procedure of TSCS stays the same.
Please see tscsRegression3D and tscsEstimate3D.
Attentions: Since TSCS is only capable of interpolation but not extrapolation, please make sure that the missing observations in a given spatial domain are all located at interior spatial locations. Otherwise, extrapolation would occur with an error following.
A list of 3 is returned, including:
estimatedata frame; estimate of missing observations which contains the 3 variables in order: X coordinate, Y coordinate and estimation.
completedata frame; an updated version of the cross-section data (pure spatial data) newdata,
with all of its missing observations interpolated.
NA_idan integer vector; reveals the instance ID, in data frame newdata,
of spatial locations with missing observation.
tscsRegression, tscsEstimate3D, plot_NA, plot_map
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)
tscsEstimate estimates the missing observations within the cross-section data (pure spatial data)
of a particular time point you have selected, namely, the interpolation process.
tscsEstimate3D(matrix, newdata, h1, h2, v)tscsEstimate3D(matrix, newdata, h1, h2, v)
matrix |
data frame; the first return value |
newdata |
data frame; should only contain the four variables in order: X coordinate, Y coordinate, Z coordinate and observation. This is the cross-section data or pure spatial data of a particular time point you have selected, with missing observations that you want to predict. (coordinates must be numeric) |
h1 |
numeric; side length of the unit cubic grid in X coordinate direction (horizontal). |
h2 |
numeric; side length of the unit cubic grid in Y coordinate direction (horizontal). |
v |
numeric; side length of the unit cubic grid in Z coordinate direction (vertical). |
The first step of TSCS spatial interpolation should be carried out by function tscsRegression3D,
which is the prerequisite of tscsEstimate3D.
For 2D rectangular grid system, the procedure of TSCS stays the same.
Please see tscsRegression and tscsEstimate.
Attentions: Since TSCS is only capable of interpolation but not extrapolation, please make sure that the missing observations in a given spatial domain are all located at interior spatial locations. Otherwise, extrapolation would occur with an error following.
A list of 3 is returned, including:
estimatedata frame; estimate of missing observations which contains the 4 variables in order: X coordinate, Y coordinate, Z coordinate and estimation.
completedata frame; an updated version of the cross-section data (pure spatial data) newdata,
with all of its missing observations interpolated.
NA_idan integer vector; reveals the instance ID, in data frame newdata,
of spatial locations with missing observation.
tscsRegression3D, tscsEstimate, plot3D_NA, plot3D_map
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)
To implement TSCS spatial interpolation for a spatial domain that is a 2D rectangular grid system,
the first step is obtaining regression coefficient matrix, which can be done
by function tscsRegression. It is the prerequisite of TSCS interpolation process
because the 'matrix' derived from historical spatio-temporal data is the initial value of
the second step - estimating missing observations.
tscsRegression(data, h, v, alpha = 0.05)tscsRegression(data, h, v, alpha = 0.05)
data |
data frame; should contain these variables in order: X coordinate, Y coordinate and observations
as time goes on. That is to say, each row should include X and Y coordinate first, and then a time series.
This is the historical spatio-temporal data that you intend to analyze as the basis for
interpolation later on in |
h |
numeric; side length of the unit grid in X coordinate direction. |
v |
numeric; side length of the unit grid in Y coordinate direction. |
alpha |
numeric; specify the significance level for ADF test, to test if the time series of a group of spatial locations are cointegrated. (default: 0.05) |
The second step of TSCS spatial interpolation should be carried out by function tscsEstimate,
where you have to input the cross-section data or pure spatial data of a particular time point
you have selected, with missing observations that you want to predict.
For 3D rectangular grid system, the procedure of TSCS stays the same.
Please see tscsRegression3D and tscsEstimate3D.
Attentions:
(1) Since TSCS is only capable of interpolation but not extrapolation, it is necessary to highlight the
difference between interior spatial locations and system boundary. Function plot_dif can help.
(2) NA value in historical spatio-temporal data data is not allowed. Please handle them beforehand
(such as filling these NA values through spatio-temporal kriging).
A list of 2 is returned, including:
coef_matrixdata frame; regression coefficient matrix to be used as input parameter of function
tscsEstimate in the second step of TSCS interpolation.
percentagenumeric; percentage of cointegrated relationships, a measurement of the degree
it satisfies the assumption of cointegrated system. It is highly affected by parameter alpha,
the significance level you have set. Explicitly, smaller alpha results in smaller percentage.
tscsEstimate, tscsRegression3D, plot_dif
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression(data = data, h = 1, v = 1, alpha = 0.01); # regression basis$percentage # see the percentage of cointegrated relationships est <- tscsEstimate(matrix = basis$coef_matrix, newdata = newdata, h = 1, v = 1); # estimation str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,3], true = true) # graphic comparison index <- appraisal_index(est = est$estimate[,3], true = true); # RMSE & std index ## data visualization: plot_dif(data = data[,1:2], h = 1, v = 1) # differentiate boundary and interior spatial locations plot_NA(newdata = newdata) # show spatial locations with missing value, for a cross-section data plot_map(newdata = newdata) # plot the 2D spatial map, for a cross-section data ## End(Not run)
To implement TSCS spatial interpolation for a spatial domain that is a 3D rectangular grid system,
the first step is obtaining regression coefficient matrix, which can be done
by function tscsRegression3D. It is the prerequisite of TSCS interpolation process
because the 'matrix' derived from historical spatio-temporal data is the initial value of
the second step - estimating missing observations.
tscsRegression3D(data, h1, h2, v, alpha = 0.05)tscsRegression3D(data, h1, h2, v, alpha = 0.05)
data |
data frame; should contain these variables in order: X coordinate, Y coordinate, Z coordinate and
observations as time goes on. That is to say, each row should include X, Y and Z coordinate first, and then
a time series. This is the historical spatio-temporal data that you intend to analyze as the basis for
interpolation later on in |
h1 |
numeric; side length of the unit cubic grid in X coordinate direction (horizontal). |
h2 |
numeric; side length of the unit cubic grid in Y coordinate direction (horizontal). |
v |
numeric; side length of the unit cubic grid in Z coordinate direction (vertical). |
alpha |
numeric; specify the significance level for ADF test, to test if the time series of a group of spatial locations are cointegrated. (default: 0.05) |
The second step of TSCS spatial interpolation should be carried out by function tscsEstimate3D,
where you have to input the cross-section data or pure spatial data of a particular time point
you have selected, with missing observations that you want to predict.
For 2D rectangular grid system, the procedure of TSCS stays the same.
Please see tscsRegression and tscsEstimate.
Attentions:
(1) Since TSCS is only capable of interpolation but not extrapolation, it is necessary to highlight the
difference between interior spatial locations and system boundary. Function plot3D_dif can help.
(2) NA value in historical spatio-temporal data data is not allowed. Please handle them beforehand
(such as filling these NA values through spatio-temporal kriging).
A list of 2 is returned, including:
coef_matrixdata frame; regression coefficient matrix to be used as input parameter of function
tscsEstimate in the second step of TSCS interpolation.
percentagenumeric; percentage of cointegrated relationships, a measurement of the degree
it satisfies the assumption of cointegrated system. It is highly affected by parameter alpha,
the significance level you have set. Explicitly, smaller alpha results in smaller percentage.
tscsEstimate3D, tscsRegression, plot3D_dif
## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)## Not run: ## TSCS spatial interpolation procedure: basis <- tscsRegression3D(data = data, h1 = 3.75, h2 = 2.5, v = 5, alpha = 0.01); basis$percentage est <- tscsEstimate3D(matrix = basis$coef_matrix, newdata = newdata, h1 = 3.75, h2 = 2.5, v = 5); str(est) ## comparison of estimates and true values: plot_compare(est = est$estimate[,4], true = true) index <- appraisal_index(est = est$estimate[,4], true = true); index ## data visualization: plot3D_dif(data = data[,1:3], h1 = 3.75, h2 = 2.5, v = 5) plot3D_NA(newdata = newdata) plot3D_map(newdata = newdata) ## End(Not run)