td: Temporal Disaggregation of Time Series

View source: R/td.R

tdR 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.