makewpstRO: Make a wavelet packet regression object from a dependent and...
In wavethresh: Wavelets Statistics and Transforms
makewpstRO R Documentation
Make a wavelet packet regression object from a dependent and independent
time series variable.
Description
The idea here is to try and build facilities to enable
a transfer function model along
the lines of that described by Nason and Sapatinas 2002 in
Statistics and Computing. The idea is to turn the
timeseries variable into a set of nondecimated wavelet packets
which are already pre-selected to have some semblance of relationship
to the response time series. The function does not actually
perform any regression, in contrast to the related makewpstDO
but returns a data frame which the user can use to build their own models.
Usage
makewpstRO(timeseries, response, filter.number = 10,
family = "DaubExPhase", trans = logabs, percentage = 10)
Arguments
timeseries
The dependent variable time series. This series is decomposed
using the wpst function into nondecimated
wavelet packets, need to be a power of two length.
response
The independent or response time series.
filter.number
The type of wavelet used within family, see
filter.select.
family
The family of wavelet, see filter.select
trans
A transform to apply to the nondecimated wavelet packet
coefficients before any selection
percentage
The top percentage of nondecimated wavelet packets
that correlated best with the response series will
be preselected.
Details
The idea behind this methodology is that a response
time series might not be directly related to the dependent
timeseries time series, but it might be related to the
nondecimated wavelet packets of the timeseries, these packets
can pick out various features of the timeseries including
certain delays, oscillations and others.
The best packets (the number if controlled by percentage), those
that correlate best with response are selected and returned.
The response and the best nondecimated wavelet packets
are returned in a data frame object and then any convenient form of
statistical modeling can be used to build a model of the response in
terms of the packet variables.
Once a model has been built it can be interpreted in the usual way, but
with respect to nondecimated wavelet packets.
Note that nondecimated wavelet packets are essential, as they are all
of the same length as the original response series. If a decimated
wavelet packet algorithm had been used then it is not clear what to
do with the "gaps"!
If new timeseries data comes along the wpstREGR
function can be used to extract the identical packets as the ones
produced by this function (as the result of this function stores the
identities of these packets). Then the statistical modelling that
build the model from the output of this function, can be used to
predict future values of the response time series from future
values of the timeseries series.
Value
An object of class wpstRO containing the following items
df
A data frame containing the response time series and
a number of columns/variables/packets that correlated with
response series. These are all entitled "Xn" where n is some
integer
ixvec
A packet index vector. After taking the nondecimated wavelet
packet transform, all the packets are stored in a matrix. This
vector indicates those that were preselected
level
The original level from which the preselected vectors came from
pktix
Another index vector, this time referring to the original
wavelet packet object, not the matrix in which they subsequently
got stored
nlevelsWT
The number of resolution levels in the original wavelet
packet object
cv
The correlation vector. These are the values of the correlations
of the packets with the response, then sorted in terms of decreasing
absolute correlation
filter
The wavelet filter details
trans
The transformation function actually used
Author(s)
G P Nason
References
Nason, G.P. and Sapatinas, T. (2002) Wavelet packet transfer function
modeling of nonstationary time series. Statistics and Computing,
12, 45-56.
See Also
makewpstDO, wpst, wpstREGR
Examples
data(BabyECG)
baseseries <- BabyECG[1:256]
#
# Make up a FICTITIOUS response series!
#
response <- BabyECG[6:261]*3+52
#
# Do the modeling
#
BabeModel <- makewpstRO(timeseries=baseseries, response=response)
#Level: 0 ..........
#1 ..........
#2 ..........
#3 ..........
#4 ................
#5
#6
#7
#
#Contains SWP coefficients
#Original time series length: 256
#Number of bases: 25
#Some basis selection performed
# Level Pkt Index Orig Index Score
#[1,] 5 0 497 0.6729833
#[2,] 4 0 481 0.6120771
#[3,] 6 0 505 0.4550616
#[4,] 3 0 449 0.4309924
#[5,] 7 0 509 0.3779385
#[6,] 1 53 310 0.3275428
#[7,] 2 32 417 -0.3274858
#[8,] 2 59 444 -0.2912863
#[9,] 3 16 465 -0.2649679
#[10,] 1 110 367 0.2605178
#etc. etc.
#
#
# Let's look at the data frame component
#
names(BabeModel$df)
# [1] "response" "X1" "X2" "X3" "X4" "X5"
# [7] "X6" "X7" "X8" "X9" "X10" "X11"
#[13] "X12" "X13" "X14" "X15" "X16" "X17"
#[19] "X18" "X19" "X20" "X21" "X22" "X23"
#[25] "X24" "X25"
#
# Generate a formula including all of the X's (note we could use the .
# argument, but we later want to be more flexible
#
xnam <- paste("X", 1:25, sep="")
fmla1 <- as.formula(paste("response ~ ", paste(xnam, collapse= "+")))
#
# Now let's fit a linear model, the response on all the Xs
#
Babe.lm1 <- lm(fmla1, data=BabeModel$df)
#
# Do an ANOVA to see what's what
#
anova(Babe.lm1)
#Analysis of Variance Table
#
#Response: response
# Df Sum Sq Mean Sq F value Pr(>F)
#X1 1 214356 214356 265.7656 < 2.2e-16 ***
#X2 1 21188 21188 26.2701 6.289e-07 ***
#X3 1 30534 30534 37.8565 3.347e-09 ***
#X4 1 312 312 0.3871 0.5344439
#X5 1 9275 9275 11.4999 0.0008191 ***
#X6 1 35 35 0.0439 0.8343135
#X7 1 195 195 0.2417 0.6234435
#X8 1 94 94 0.1171 0.7324600
#X9 1 331 331 0.4103 0.5224746
#X10 1 0 0 0.0006 0.9810560
#X11 1 722 722 0.8952 0.3450597
#X12 1 0 0 0.0004 0.9850243
#X13 1 77 77 0.0959 0.7570769
#X14 1 2770 2770 3.4342 0.0651404 .
#X15 1 6 6 0.0072 0.9326155
#X16 1 389 389 0.4821 0.4881649
#X17 1 44 44 0.0544 0.8157015
#X18 1 44 44 0.0547 0.8152640
#X19 1 4639 4639 5.7518 0.0172702 *
#X20 1 490 490 0.6077 0.4364469
#X21 1 389 389 0.4823 0.4880660
#X22 1 85 85 0.1048 0.7463860
#X23 1 1710 1710 2.1198 0.1467664
#X24 1 12 12 0.0148 0.9033427
#X25 1 82 82 0.1019 0.7498804
#Residuals 230 185509 807
#---
#Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#
# Looks like X1, X2, X3, X5, X14 and X19 are "significant". Also throw in
# X4 as it was a highly ranked preselected variable, and refit
#
fmla2 <- response ~ X1 + X2 + X3 + X4 + X5 + X14 + X19
Babe.lm2 <- lm(fmla2, data=BabeModel$df)
#
# Let's see the ANOVA table for this
#
anova(Babe.lm2)
#Analysis of Variance Table
#
#Response: response
# Df Sum Sq Mean Sq F value Pr(>F)
#X1 1 214356 214356 279.8073 < 2.2e-16 ***
#X2 1 21188 21188 27.6581 3.128e-07 ***
#X3 1 30534 30534 39.8567 1.252e-09 ***
#X4 1 312 312 0.4076 0.5238034
#X5 1 9275 9275 12.1075 0.0005931 ***
#X14 1 3095 3095 4.0405 0.0455030 *
#X19 1 4540 4540 5.9259 0.0156263 *
#Residuals 248 189989 766
#---
#Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#
# So, let's drop X4, refit, and then do ANOVA
#
Babe.lm3 <- update(Babe.lm2, . ~ . -X4)
anova(Babe.lm3)
#
# After viewing this, drop X14
#
Babe.lm4 <- update(Babe.lm3, . ~ . -X14)
anova(Babe.lm4)
#
# Let's plot the original series, and the "fitted" one
#
## Not run: ts.plot(BabeModel$df[["response"]])
## Not run: lines(fitted(Babe.lm4), col=2)
#
# Let's plot the wavelet packet basis functions associated with the model
#
## Not run: oldpar <- par(mfrow=c(2,2))
## Not run: z <- rep(0, 256)
## Not run: zwp <- wp(z, filter.number=BabeModel$filter$filter.number,
family=BabeModel$filter$family)
## End(Not run)
## Not run: draw(zwp, level=BabeModel$level[1], index=BabeModel$pktix[1], main="", sub="")
## Not run: draw(zwp, level=BabeModel$level[2], index=BabeModel$pktix[2], main="", sub="")
## Not run: draw(zwp, level=BabeModel$level[3], index=BabeModel$pktix[3], main="", sub="")
## Not run: draw(zwp, level=BabeModel$level[5], index=BabeModel$pktix[5], main="", sub="")
## Not run: par(oldpar)
#
# Now let's do some prediction of future values of the response, given
# future values of the baseseries
#
newseries <- BabyECG[257:512]
#
# Get the new data frame
#
newdfinfo <- wpstREGR(newTS = newseries, wpstRO=BabeModel)
#
# Now use the best model (Babe.lm4) with the new data frame (newdfinfo)
# to predict new values of response
#
newresponse <- predict(object=Babe.lm4, newdata=newdfinfo)
#
# What is the "true" response, well we made up a response earlier, so let's
# construct the true response for this future data (in your case you'll
# have a separate genuine response variable)
#
trucfictresponse <- BabyECG[262:517]*3+52
#
# Let's see them plotted on the same plot
#
## Not run: ts.plot(trucfictresponse)
## Not run: lines(newresponse, col=2)
#
# On my plot they look tolerably close!
#
wavethresh documentation built on Nov. 16, 2022, 5:16 p.m.
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| makewpstRO | R Documentation |
Make a wavelet packet regression object from a dependent and independent time series variable.
Description
The idea here is to try and build facilities to enable
a transfer function model along
the lines of that described by Nason and Sapatinas 2002 in
Statistics and Computing. The idea is to turn the
timeseries variable into a set of nondecimated wavelet packets
which are already pre-selected to have some semblance of relationship
to the response time series. The function does not actually
perform any regression, in contrast to the related makewpstDO
but returns a data frame which the user can use to build their own models.
Usage
makewpstRO(timeseries, response, filter.number = 10,
family = "DaubExPhase", trans = logabs, percentage = 10)
Arguments
timeseries |
The dependent variable time series. This series is decomposed
using the |
response |
The independent or response time series. |
filter.number |
The type of wavelet used within |
family |
The family of wavelet, see |
trans |
A transform to apply to the nondecimated wavelet packet coefficients before any selection |
percentage |
The top |
Details
The idea behind this methodology is that a response
time series might not be directly related to the dependent
timeseries time series, but it might be related to the
nondecimated wavelet packets of the timeseries, these packets
can pick out various features of the timeseries including
certain delays, oscillations and others.
The best packets (the number if controlled by percentage), those
that correlate best with response are selected and returned.
The response and the best nondecimated wavelet packets
are returned in a data frame object and then any convenient form of
statistical modeling can be used to build a model of the response in
terms of the packet variables.
Once a model has been built it can be interpreted in the usual way, but with respect to nondecimated wavelet packets.
Note that nondecimated wavelet packets are essential, as they are all of the same length as the original response series. If a decimated wavelet packet algorithm had been used then it is not clear what to do with the "gaps"!
If new timeseries data comes along the wpstREGR
function can be used to extract the identical packets as the ones
produced by this function (as the result of this function stores the
identities of these packets). Then the statistical modelling that
build the model from the output of this function, can be used to
predict future values of the response time series from future
values of the timeseries series.
Value
An object of class wpstRO containing the following items
df |
A data frame containing the |
ixvec |
A packet index vector. After taking the nondecimated wavelet packet transform, all the packets are stored in a matrix. This vector indicates those that were preselected |
level |
The original level from which the preselected vectors came from |
pktix |
Another index vector, this time referring to the original wavelet packet object, not the matrix in which they subsequently got stored |
nlevelsWT |
The number of resolution levels in the original wavelet packet object |
cv |
The correlation vector. These are the values of the correlations of the packets with the response, then sorted in terms of decreasing absolute correlation |
filter |
The wavelet filter details |
trans |
The transformation function actually used |
Author(s)
G P Nason
References
Nason, G.P. and Sapatinas, T. (2002) Wavelet packet transfer function modeling of nonstationary time series. Statistics and Computing, 12, 45-56.
See Also
makewpstDO, wpst, wpstREGR
Examples
data(BabyECG)
baseseries <- BabyECG[1:256]
#
# Make up a FICTITIOUS response series!
#
response <- BabyECG[6:261]*3+52
#
# Do the modeling
#
BabeModel <- makewpstRO(timeseries=baseseries, response=response)
#Level: 0 ..........
#1 ..........
#2 ..........
#3 ..........
#4 ................
#5
#6
#7
#
#Contains SWP coefficients
#Original time series length: 256
#Number of bases: 25
#Some basis selection performed
# Level Pkt Index Orig Index Score
#[1,] 5 0 497 0.6729833
#[2,] 4 0 481 0.6120771
#[3,] 6 0 505 0.4550616
#[4,] 3 0 449 0.4309924
#[5,] 7 0 509 0.3779385
#[6,] 1 53 310 0.3275428
#[7,] 2 32 417 -0.3274858
#[8,] 2 59 444 -0.2912863
#[9,] 3 16 465 -0.2649679
#[10,] 1 110 367 0.2605178
#etc. etc.
#
#
# Let's look at the data frame component
#
names(BabeModel$df)
# [1] "response" "X1" "X2" "X3" "X4" "X5"
# [7] "X6" "X7" "X8" "X9" "X10" "X11"
#[13] "X12" "X13" "X14" "X15" "X16" "X17"
#[19] "X18" "X19" "X20" "X21" "X22" "X23"
#[25] "X24" "X25"
#
# Generate a formula including all of the X's (note we could use the .
# argument, but we later want to be more flexible
#
xnam <- paste("X", 1:25, sep="")
fmla1 <- as.formula(paste("response ~ ", paste(xnam, collapse= "+")))
#
# Now let's fit a linear model, the response on all the Xs
#
Babe.lm1 <- lm(fmla1, data=BabeModel$df)
#
# Do an ANOVA to see what's what
#
anova(Babe.lm1)
#Analysis of Variance Table
#
#Response: response
# Df Sum Sq Mean Sq F value Pr(>F)
#X1 1 214356 214356 265.7656 < 2.2e-16 ***
#X2 1 21188 21188 26.2701 6.289e-07 ***
#X3 1 30534 30534 37.8565 3.347e-09 ***
#X4 1 312 312 0.3871 0.5344439
#X5 1 9275 9275 11.4999 0.0008191 ***
#X6 1 35 35 0.0439 0.8343135
#X7 1 195 195 0.2417 0.6234435
#X8 1 94 94 0.1171 0.7324600
#X9 1 331 331 0.4103 0.5224746
#X10 1 0 0 0.0006 0.9810560
#X11 1 722 722 0.8952 0.3450597
#X12 1 0 0 0.0004 0.9850243
#X13 1 77 77 0.0959 0.7570769
#X14 1 2770 2770 3.4342 0.0651404 .
#X15 1 6 6 0.0072 0.9326155
#X16 1 389 389 0.4821 0.4881649
#X17 1 44 44 0.0544 0.8157015
#X18 1 44 44 0.0547 0.8152640
#X19 1 4639 4639 5.7518 0.0172702 *
#X20 1 490 490 0.6077 0.4364469
#X21 1 389 389 0.4823 0.4880660
#X22 1 85 85 0.1048 0.7463860
#X23 1 1710 1710 2.1198 0.1467664
#X24 1 12 12 0.0148 0.9033427
#X25 1 82 82 0.1019 0.7498804
#Residuals 230 185509 807
#---
#Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#
# Looks like X1, X2, X3, X5, X14 and X19 are "significant". Also throw in
# X4 as it was a highly ranked preselected variable, and refit
#
fmla2 <- response ~ X1 + X2 + X3 + X4 + X5 + X14 + X19
Babe.lm2 <- lm(fmla2, data=BabeModel$df)
#
# Let's see the ANOVA table for this
#
anova(Babe.lm2)
#Analysis of Variance Table
#
#Response: response
# Df Sum Sq Mean Sq F value Pr(>F)
#X1 1 214356 214356 279.8073 < 2.2e-16 ***
#X2 1 21188 21188 27.6581 3.128e-07 ***
#X3 1 30534 30534 39.8567 1.252e-09 ***
#X4 1 312 312 0.4076 0.5238034
#X5 1 9275 9275 12.1075 0.0005931 ***
#X14 1 3095 3095 4.0405 0.0455030 *
#X19 1 4540 4540 5.9259 0.0156263 *
#Residuals 248 189989 766
#---
#Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#
# So, let's drop X4, refit, and then do ANOVA
#
Babe.lm3 <- update(Babe.lm2, . ~ . -X4)
anova(Babe.lm3)
#
# After viewing this, drop X14
#
Babe.lm4 <- update(Babe.lm3, . ~ . -X14)
anova(Babe.lm4)
#
# Let's plot the original series, and the "fitted" one
#
## Not run: ts.plot(BabeModel$df[["response"]])
## Not run: lines(fitted(Babe.lm4), col=2)
#
# Let's plot the wavelet packet basis functions associated with the model
#
## Not run: oldpar <- par(mfrow=c(2,2))
## Not run: z <- rep(0, 256)
## Not run: zwp <- wp(z, filter.number=BabeModel$filter$filter.number,
family=BabeModel$filter$family)
## End(Not run)
## Not run: draw(zwp, level=BabeModel$level[1], index=BabeModel$pktix[1], main="", sub="")
## Not run: draw(zwp, level=BabeModel$level[2], index=BabeModel$pktix[2], main="", sub="")
## Not run: draw(zwp, level=BabeModel$level[3], index=BabeModel$pktix[3], main="", sub="")
## Not run: draw(zwp, level=BabeModel$level[5], index=BabeModel$pktix[5], main="", sub="")
## Not run: par(oldpar)
#
# Now let's do some prediction of future values of the response, given
# future values of the baseseries
#
newseries <- BabyECG[257:512]
#
# Get the new data frame
#
newdfinfo <- wpstREGR(newTS = newseries, wpstRO=BabeModel)
#
# Now use the best model (Babe.lm4) with the new data frame (newdfinfo)
# to predict new values of response
#
newresponse <- predict(object=Babe.lm4, newdata=newdfinfo)
#
# What is the "true" response, well we made up a response earlier, so let's
# construct the true response for this future data (in your case you'll
# have a separate genuine response variable)
#
trucfictresponse <- BabyECG[262:517]*3+52
#
# Let's see them plotted on the same plot
#
## Not run: ts.plot(trucfictresponse)
## Not run: lines(newresponse, col=2)
#
# On my plot they look tolerably close!
#
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