knitr::opts_chunk$set( collapse = TRUE, fig.width = 7.1, fig.height = 3.5, comment = "#>" )
This is a short introduction to tempdisagg. Our article on temporal disaggregation of time series (\doi{10.32614/RJ-2013-028}) in the R-Journal describes the package and the theory of temporal disaggregation in more detail.
For citation, please see citation("tempdisagg")
.
Suppose we have an annual series and want to create quarterly values that sum up to the annual values. Let us explore the annual sales of the pharmaceutical and chemical industry in Switzerland, from which we want to create a quarterly series.
library(tempdisagg) data(swisspharma) plot(sales.a)
The most simple method is denton-cholette
without an indicator. It
performs a simple interpolation that meets the temporal additivity constraint.
In R, this can be done the following way:
m1 <- td(sales.a ~ 1, to = "quarterly", method = "denton-cholette")
td()
produces an object of class "td"
. The formula, 'sales.a ~ 1'
, indicates
that our low frequency variable will be disaggregated with a constant. The
resulting quarterly values of sales can be extracted with the predict()
function:
predict(m1)
As there is no additional information on quarterly movements, the resulting series is very smooth:
plot(predict(m1))
While this purely mathematical approach is easy to perform and does not need any other data series, the economic value of the resulting series may be limited. There might be a related quarterly series that follows a similar movement than sales. For example, we may use quarterly exports of pharmaceutical and chemical products:
plot(exports.q) m2 <- td(sales.a ~ 0 + exports.q, method = "denton-cholette")
Because we cannot use more than one indicator with the denton-cholette
or
denton
method, the intercept must be specified as missing in the formula
(~ 0
). Contrary to the first example, the to
argument is redundant, because
the destination frequency can be interfered from the time series properties of
exports.q
.
The resulting model leads to a much more interesting series:
plot(predict(m2))
As the indicator series is longer than the annual series, there is an extrapolation period, in which the quarterly sales are forecasted.
With an indicator, the denton-cholette
method simply transfers the movement
of the indicator to the resulting series. Even if in fact there were no
correlation between the two series, there would be a strong similarity between
the indicator and the resulting series.
In contrast, regression based methods transfer the movement only if the indicator series and the resulting series are actually correlated on the annual level. For example, a Chow-Lin regression of the same problem as above can be performed the following way:
m3 <- td(sales.a ~ exports.q)
As chow-lin-maxlog
is the default method, it does not need to be specified.
Like with the corresponding lm
method, summary()
produces an overview of the
regression:
summary(m3)
There is indeed a strong correlation between exports and sales, as it has been
assumed in the example above. The coefficient of exports.q
is highly
significant, and the very high adjusted R-squared points to a strong
relationship between the two variables. The coefficients are the result of a
GLS regression between the annual series.
The estimation of the AR1 parameter, rho, was estimated to be negative; in order to avoid the undesirable side-effects of a negative rho, it has been truncated to 0. This feature can be turned off:
td(sales.a ~ exports.q, truncated.rho = -1)
Again, we can extract the resulting quarterly series of sales:
plot(predict(m3))
Like all regression based methods, chow-lin-maxlog
can also be used with
more than one indicator series (imports.q
is only significant on a 10% level
in the following example, it probably will not help to produce a more accurate
temporal disaggregation):
m4 <- td(formula = sales.a ~ exports.q + imports.q) summary(m4)
In our example, we actually know the true data on quarterly sales, so we can compare the artificial values to the true values:
plot(sales.q) lines(predict(m2), col = "blue") # Denton-Cholette lines(predict(m3), col = "red") # Chow-Lin
With an indicator series, both the Denton method and Chow-Lin produce a series that is close to the true series. This is, of course, due to fact that in this example, exports are a good indicator for sales. If the indicator is less close to the series of interest, the resulting series will be less close to the true series.
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