td: Temporal Disaggregation of Time Series
In christophsax/tempdisagg: Methods for Temporal Disaggregation and Interpolation of Time Series
td R Documentation
Temporal Disaggregation of Time Series
Description
Perform temporal disaggregation or interpolation of low frequency to high
frequency time series. td can be used with objects of class
"ts", with numeric vectors or with any
ts-boxable time series object.
Usage
td(
formula,
conversion = "sum",
to = "quarterly",
method = "chow-lin-maxlog",
truncated.rho = 0,
fixed.rho = 0.5,
criterion = "proportional",
h = 1,
start = NULL,
end = NULL,
...
)
Arguments
formula
an object of class "formula": a symbolic
description of the the temporal disaggregation model. The details of model
specification are given under 'Details'.
conversion
type of conversion: "sum", "mean" (or: "average"),
"first" or "last".
to
high-frequency destination frequency as a character string
("quarter" (or "quarterly"), "month" (or "monthly"), "day",
"hour", "minute", "second", or "year")
or as a scalar (e.g. 2, 4, 7, 12). Required if no right hand side
indicator series is provided. The tsbox package must
be installed to deal with frequencies other than monthly or quarterly. If
the input series are numeric, to is a scalar indicating the
frequency ratio.
method
method of temporal disaggregation:
"chow-lin-maxlog", "chow-lin-minrss-ecotrim",
"chow-lin-minrss-quilis", "chow-lin-fixed",
"dynamic-maxlog" (experimental), "dynamic-minrss" (experimental), "dynamic-fixed" (experimental),
"fernandez", "litterman-maxlog", "litterman-minrss",
"litterman-fixed", "denton-cholette", "denton", "fast",
"uniform" or "ols". See 'Details'.
truncated.rho
lower bound for the autoregressive parameter
\rho. If set to 0 (default), no negative values are allowed.
If set to -1, truncation is disabled.
fixed.rho
set a predefined autoregressive parameter \rho. Only
works with the methods "chow-lin-fixed" and
"litterman-fixed".
criterion
minimzation criterion for Denton methods:
"proportional" or "additive". See 'Details'.
h
degree of differencing for Denton methods. See 'Details'.
start
(optional) start date. Similar to pre-processing the input
series with window().
end
(optional) end date. Similar to pre-processing the input
series with window().
...
additional arguments to be passed to the low level
subfunctions.
Details
td is used to disaggregate or interpolate a low frequency to a higher
frequency time series, while either the sum, the average, the first or the
last value of the resulting high-frequency series is consistent with the low
frequency series. Disaggregation can be performed with or without the help of
one or more right hand side indicator series. It can deal with both with
a regular disaggregation setting (e.g. quarters to months) but also with
an irregular disaggregation setting (e.g. months to days), where it respects
the the different lengths of the months.
If the high-frequency indicator(s) cover(s) a longer time span than the
low-frequency series, an extrapolation or retropolation (Wei, 1994, p. 138)
is performed, using the same model as for interpolation.
The selection of a temporal disaggregation model is similar to the selection
of a linear regression model. Thus, td closely mirrors the working of
the lm() function. The left hand side of the
formula() denotes the low-frequency series, the right hand side
the indicators. If no indicator is specified, the right hand side must be set
equal to 1 (see examples). Unlike lm, td handles
ts() and mts time-series objects, as a typical application
involves the use of these objects. Alternatively, If used with basic vectors,
the to argument specifies the ratio between the high and the low
frequency series.
For the generalized least squares (GLS) methods "chow-lin-maxlog",
"chow-lin-minrss-ecotrim", "chow-lin-minrss-quilis",
"litterman-maxlog" and "litterman-minrss", an autoregressive
parameter \rho is estimated. Default (and recommended) method is
chow-lin-maxlog. With truncated.rho = 0 (default), it produces
good results for a wide range of applications.
There are two variants of the chow-lin-minrss approach that lead to
different results: Ecotrim by Barcellan (2003) uses a correlation matrix
instead of the variance covariance matrix (implemented in
"chow-lin-minrss-ecotrim"), the Matlab library by Quilis (2009)
multiplies the correlation matrix with 1/(1-\rho^2) (implemented in
"chow-lin-minrss-quilis").
The methods "dynamic-maxlog", "dynamic-minrss" and
"dynamic-fixed" are dynamic extensions of Chow-Lin (Santos Silva and
Cardoso, 2001). If the autoregressive parameter \rho is equal to 0, no
truncation remainder is added.
The Denton methods "denton" and "denton-cholette" can be
specified with one or without an indicator. The parameter h can be set
equal to 0, 1, or 2. Depending on the value, the
denton procedure minimizes the sum of squares of the deviations
between the levels (0), the first differences (1) or the second
differences (2) of the indicator and the resulting series.
Additionally, criterion can be set equal to "proportional" or
"additive", depending on whether the proportional or the absolute
deviations should be considered for minimzation. "denton-cholette"
removes the transient movement of the original "denton" method at the
beginning of the resulting series. "fast" is a shortcut for
"chow-lin-fixed" with fixed.rho = 0.99999. It returns approximately the
same results as "denton-cholette" with h = 1, but is much faster.
"uniform" is a special case of the "denton" approach, with
h equals 0 and criterion equals "additive".
It distributes the residuals uniformly. If no indicator is used, this leads
to a step-shaped series.
"ols" performs an ordinary least squares regression (OLS) and
distributes the residuals uniformly. It is especially useful for comparing
the estimators of GLS and OLS regressions.
Value
td returns an object of class "td".
The function predict() computes the interpolated
high frequency series. If the high-frequency indicator series are longer
than the low-frequency series, the resulting series will be extrapolated.
The function coefficients extracts the coefficients. The function
residuals extracts the low frequency residuals. The function
summary() prints a summary of the estimation.
An object of class "td" is a list containing the following
components:
values
disaggregated or interpolated (and extrapolated)
high frequency series
fitted.values
low frequency fitted values of
the regression; low frequency indicator for the Denton methods.
p
preliminary high frequency series
residuals
low-frequency
residuals
rho
autoregressive parameter, \rho
truncated
logical, whether \rho has been truncated
coefficients
a named vector of coefficients
se
standard
errors of the coefficients
s_2
ML-estimator of the variance of the
high-frequency residuals
s_2_gls
GLS-estimator of the variance of
the high-frequency residuals
tss
weighted (low frequency) total sum
of squares
rss
weighted (low frequency) residual sum of squares
r.squared
R squared
adj.r.squared
adjusted R squared
logl
log-likelihood
aic
Akaike information criterion
bic
Schwarz information criterion
rank
number of right hand
variables (including intercept)
df
degrees of freedom
method
method of temporal disaggregation
call
function call
name
name of the low frequency variable
fr
the ratio of high
to low-frequency series
conversion
type of temporal conversion
actual
actual values of the low frequeny series
model
a
matrix containing the indicators (and a constant if present)
criterion
minimization criterion in Denton methods
h
order
of differencing in Denton methods
References
Chow, G. C., & Lin, A. L. (1971). Best linear unbiased
interpolation, distribution, and extrapolation of time series by related
series. The review of Economics and Statistics, 372-375.
Denton, F. T. (1971). Adjustment of monthly or quarterly series to annual
totals: an approach based on quadratic minimization. Journal of the
American Statistical Association, 66(333), 99-102.
Santos Silva, J. M. C. & Cardoso, F. N. (2001). The Chow-Lin method using
dynamic models. Economomic Modelling, 18, 269-280.
Wei, W. W. S. (1994). Time series analysis. Addison-Wesley publ.
Sax, C. und Steiner, P. (2013). Temporal Disaggregation of Time Series.
The R Journal, 5(2), 80-88. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.32614/RJ-2013-028")}
See Also
ta() for temporal aggregation, the inverse function of
td.
summary() is used to obtain and print a summary of
the results.
predict() is used to extract the disaggregated or
interpolated high frequency series.
plot() is used to plot the fitted and actual low
frequency series, as well as the residuals.
Examples
data(tempdisagg)
# one indicator, no intercept
mod1 <- td(sales.a ~ 0 + exports.q)
summary(mod1) # summary statistics
plot(mod1) # residual plot of regression
plot(predict(mod1))
# interpolated quarterly series
# temporally aggregated series is equal to the annual value
all.equal(window(
ta(predict(mod1), conversion = "sum", to = "annual"),
start = 1975), sales.a)
# several indicators, including an intercept
mod2 <- td(sales.a ~ imports.q + exports.q)
# no indicator (Denton-Cholette)
mod3 <- td(sales.a ~ 1, to = "quarterly", method = "denton-cholette")
# no indicator (uniform)
mod4 <- td(sales.a ~ 1, to = "quarterly", method = "uniform")
# Dynamic Chow-Lin (Santos Silva and Cardoso, 2001)
# (no truncation parameter added, because rho = 0)
mod5 <- td(sales.a ~ exports.q, method = "dynamic-maxlog")
# Example from Denton (1971), see references.
d.q <- ts(rep(c(50, 100, 150, 100), 5), frequency = 4)
d.a <- ts(c(500, 400, 300, 400, 500))
a1 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "additive", h = 0))
a2 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "additive", h = 1))
a3 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "additive", h = 2))
a4 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "additive", h = 3))
p1 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "proportional", h = 0))
p2 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "proportional", h = 1))
p3 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "proportional", h = 2))
p4 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "proportional", h = 3))
# Table in Denton (1971), page 101:
round(cbind(d.q, a1, a2, a3, a4, p1, p2, p3, p4))
## Not run:
# Using altvernative time series classes (see https://docs.ropensci.org/tsbox/)
library(tsbox)
sales.a.xts <- ts_xts(window(sales.a, start = 2000))
exports.q.xts <- ts_xts(window(exports.q, start = 2000))
mod1b <- td(sales.a.xts ~ 0 + exports.q.xts)
predict(mod1b) # class 'xts'
# non-standard frequencies: decades to years
predict(td(ts_xts(uspop) ~ 1, "mean", to = "year", method = "fast"))
# quarter to daily (no indicator)
m.d.noind <- td(gdp.q ~ 1, to = "daily", method = "fast")
predict(m.d.noind)
# quarter to daily (one indicator)
m.d.stocks <- td(gdp.q ~ spi.d, method = "chow-lin-fixed", fixed.rho = 0.9)
predict(m.d.stocks)
## End(Not run)
christophsax/tempdisagg documentation built on Aug. 19, 2023, 9:07 p.m.
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| td | R Documentation |
Temporal Disaggregation of Time Series
Description
Perform temporal disaggregation or interpolation of low frequency to high
frequency time series. td can be used with objects of class
"ts", with numeric vectors or with any
ts-boxable time series object.
Usage
td(
formula,
conversion = "sum",
to = "quarterly",
method = "chow-lin-maxlog",
truncated.rho = 0,
fixed.rho = 0.5,
criterion = "proportional",
h = 1,
start = NULL,
end = NULL,
...
)
Arguments
formula |
an object of class |
conversion |
type of conversion: |
to |
high-frequency destination frequency as a character string
( |
method |
method of temporal disaggregation:
|
truncated.rho |
lower bound for the autoregressive parameter
|
fixed.rho |
set a predefined autoregressive parameter |
criterion |
minimzation criterion for Denton methods:
|
h |
degree of differencing for Denton methods. See 'Details'. |
start |
(optional) start date. Similar to pre-processing the input
series with |
end |
(optional) end date. Similar to pre-processing the input
series with |
... |
additional arguments to be passed to the low level subfunctions. |
Details
td is used to disaggregate or interpolate a low frequency to a higher
frequency time series, while either the sum, the average, the first or the
last value of the resulting high-frequency series is consistent with the low
frequency series. Disaggregation can be performed with or without the help of
one or more right hand side indicator series. It can deal with both with
a regular disaggregation setting (e.g. quarters to months) but also with
an irregular disaggregation setting (e.g. months to days), where it respects
the the different lengths of the months.
If the high-frequency indicator(s) cover(s) a longer time span than the low-frequency series, an extrapolation or retropolation (Wei, 1994, p. 138) is performed, using the same model as for interpolation.
The selection of a temporal disaggregation model is similar to the selection
of a linear regression model. Thus, td closely mirrors the working of
the lm() function. The left hand side of the
formula() denotes the low-frequency series, the right hand side
the indicators. If no indicator is specified, the right hand side must be set
equal to 1 (see examples). Unlike lm, td handles
ts() and mts time-series objects, as a typical application
involves the use of these objects. Alternatively, If used with basic vectors,
the to argument specifies the ratio between the high and the low
frequency series.
For the generalized least squares (GLS) methods "chow-lin-maxlog",
"chow-lin-minrss-ecotrim", "chow-lin-minrss-quilis",
"litterman-maxlog" and "litterman-minrss", an autoregressive
parameter \rho is estimated. Default (and recommended) method is
chow-lin-maxlog. With truncated.rho = 0 (default), it produces
good results for a wide range of applications.
There are two variants of the chow-lin-minrss approach that lead to
different results: Ecotrim by Barcellan (2003) uses a correlation matrix
instead of the variance covariance matrix (implemented in
"chow-lin-minrss-ecotrim"), the Matlab library by Quilis (2009)
multiplies the correlation matrix with 1/(1-\rho^2) (implemented in
"chow-lin-minrss-quilis").
The methods "dynamic-maxlog", "dynamic-minrss" and
"dynamic-fixed" are dynamic extensions of Chow-Lin (Santos Silva and
Cardoso, 2001). If the autoregressive parameter \rho is equal to 0, no
truncation remainder is added.
The Denton methods "denton" and "denton-cholette" can be
specified with one or without an indicator. The parameter h can be set
equal to 0, 1, or 2. Depending on the value, the
denton procedure minimizes the sum of squares of the deviations
between the levels (0), the first differences (1) or the second
differences (2) of the indicator and the resulting series.
Additionally, criterion can be set equal to "proportional" or
"additive", depending on whether the proportional or the absolute
deviations should be considered for minimzation. "denton-cholette"
removes the transient movement of the original "denton" method at the
beginning of the resulting series. "fast" is a shortcut for
"chow-lin-fixed" with fixed.rho = 0.99999. It returns approximately the
same results as "denton-cholette" with h = 1, but is much faster.
"uniform" is a special case of the "denton" approach, with
h equals 0 and criterion equals "additive".
It distributes the residuals uniformly. If no indicator is used, this leads
to a step-shaped series.
"ols" performs an ordinary least squares regression (OLS) and
distributes the residuals uniformly. It is especially useful for comparing
the estimators of GLS and OLS regressions.
Value
td returns an object of class "td".
The function predict() computes the interpolated
high frequency series. If the high-frequency indicator series are longer
than the low-frequency series, the resulting series will be extrapolated.
The function coefficients extracts the coefficients. The function
residuals extracts the low frequency residuals. The function
summary() prints a summary of the estimation.
An object of class "td" is a list containing the following
components:
values |
disaggregated or interpolated (and extrapolated) high frequency series |
fitted.values |
low frequency fitted values of the regression; low frequency indicator for the Denton methods. |
p |
preliminary high frequency series |
residuals |
low-frequency residuals |
rho |
autoregressive parameter, |
truncated |
logical, whether |
coefficients |
a named vector of coefficients |
se |
standard errors of the coefficients |
s_2 |
ML-estimator of the variance of the high-frequency residuals |
s_2_gls |
GLS-estimator of the variance of the high-frequency residuals |
tss |
weighted (low frequency) total sum of squares |
rss |
weighted (low frequency) residual sum of squares |
r.squared |
R squared |
adj.r.squared |
adjusted R squared |
logl |
log-likelihood |
aic |
Akaike information criterion |
bic |
Schwarz information criterion |
rank |
number of right hand variables (including intercept) |
df |
degrees of freedom |
method |
method of temporal disaggregation |
call |
function call |
name |
name of the low frequency variable |
fr |
the ratio of high to low-frequency series |
conversion |
type of temporal conversion |
actual |
actual values of the low frequeny series |
model |
a matrix containing the indicators (and a constant if present) |
criterion |
minimization criterion in Denton methods |
h |
order of differencing in Denton methods |
References
Chow, G. C., & Lin, A. L. (1971). Best linear unbiased interpolation, distribution, and extrapolation of time series by related series. The review of Economics and Statistics, 372-375.
Denton, F. T. (1971). Adjustment of monthly or quarterly series to annual totals: an approach based on quadratic minimization. Journal of the American Statistical Association, 66(333), 99-102.
Santos Silva, J. M. C. & Cardoso, F. N. (2001). The Chow-Lin method using dynamic models. Economomic Modelling, 18, 269-280.
Wei, W. W. S. (1994). Time series analysis. Addison-Wesley publ.
Sax, C. und Steiner, P. (2013). Temporal Disaggregation of Time Series. The R Journal, 5(2), 80-88. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.32614/RJ-2013-028")}
See Also
ta() for temporal aggregation, the inverse function of
td.
summary() is used to obtain and print a summary of
the results.
predict() is used to extract the disaggregated or
interpolated high frequency series.
plot() is used to plot the fitted and actual low
frequency series, as well as the residuals.
Examples
data(tempdisagg)
# one indicator, no intercept
mod1 <- td(sales.a ~ 0 + exports.q)
summary(mod1) # summary statistics
plot(mod1) # residual plot of regression
plot(predict(mod1))
# interpolated quarterly series
# temporally aggregated series is equal to the annual value
all.equal(window(
ta(predict(mod1), conversion = "sum", to = "annual"),
start = 1975), sales.a)
# several indicators, including an intercept
mod2 <- td(sales.a ~ imports.q + exports.q)
# no indicator (Denton-Cholette)
mod3 <- td(sales.a ~ 1, to = "quarterly", method = "denton-cholette")
# no indicator (uniform)
mod4 <- td(sales.a ~ 1, to = "quarterly", method = "uniform")
# Dynamic Chow-Lin (Santos Silva and Cardoso, 2001)
# (no truncation parameter added, because rho = 0)
mod5 <- td(sales.a ~ exports.q, method = "dynamic-maxlog")
# Example from Denton (1971), see references.
d.q <- ts(rep(c(50, 100, 150, 100), 5), frequency = 4)
d.a <- ts(c(500, 400, 300, 400, 500))
a1 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "additive", h = 0))
a2 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "additive", h = 1))
a3 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "additive", h = 2))
a4 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "additive", h = 3))
p1 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "proportional", h = 0))
p2 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "proportional", h = 1))
p3 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "proportional", h = 2))
p4 <- predict(td(d.a ~ 0 + d.q, method = "denton",
criterion = "proportional", h = 3))
# Table in Denton (1971), page 101:
round(cbind(d.q, a1, a2, a3, a4, p1, p2, p3, p4))
## Not run:
# Using altvernative time series classes (see https://docs.ropensci.org/tsbox/)
library(tsbox)
sales.a.xts <- ts_xts(window(sales.a, start = 2000))
exports.q.xts <- ts_xts(window(exports.q, start = 2000))
mod1b <- td(sales.a.xts ~ 0 + exports.q.xts)
predict(mod1b) # class 'xts'
# non-standard frequencies: decades to years
predict(td(ts_xts(uspop) ~ 1, "mean", to = "year", method = "fast"))
# quarter to daily (no indicator)
m.d.noind <- td(gdp.q ~ 1, to = "daily", method = "fast")
predict(m.d.noind)
# quarter to daily (one indicator)
m.d.stocks <- td(gdp.q ~ spi.d, method = "chow-lin-fixed", fixed.rho = 0.9)
predict(m.d.stocks)
## End(Not run)
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