ontario | R Documentation |
Real dataset employed Benatia et al. (2017). Contains the hourly electricity consumption and air temperature curves in the province of Ontario (Canada). It features a set of daily curves during the summer months of 2010–2014.
ontario
A list with the following entries:
an fdata
with 368 smoothed
daily temperature (in Celsius degrees) curves of the Ontario province,
discretized on 73 equispaced grid points on [-24, 48]
(see examples).
an fdata
with the daily
electricity consumption (in gigawatts) curves of the Ontario province.
Discretized on 25 equispaced grid points on [0, 24]
.
a dataframe with time metadata for each curve:
date
: the date of the observation, a POSIXct
object.
weekday
: the weekday of the observation.
The summer months correspond to June 1st to September 15th. Weekend days and holidays are disregarded.
The smoothed temperature curves are constructed by a weighted average of the temperatures of 41 Ontarian cities that is afterwards smoothed with a local polynomial regression. The curves correspond to a 3-days window of the temperature (see examples). The temperature is standardized such that its original minimum, 6 ºC, is subtracted.
The electricity consumption curves are discretized on the interval
[0, 24]
. That means that the last observation of the
i
-th curve is the same as the first observation of the
(i + 1)
-th curve if the curves correspond to consecutive days.
See more details about the construction of the dataset in Benatia et al. (2017).
Data gathered and processed by David Benatia, Marine Carrasco, and Jean-Pierre Florens. Javier Álvarez-Liébana and Eduardo García-Portugués imported the dataset and added temporal metadata.
The dataset comes from the companion data to Benatia et al. (2017), which was retrieved from the first author's website. The source of the electricity consumption data is the System operator's website. The source of the preprocessed temperature values is the Environment Canada's website.
Benatia, D., Carrasco, M. and Florens, J. P. (2017) Functional linear regression with functional response. Journal of Econometrics, 201(2):269–291. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jeconom.2017.08.008")}
## Show data
# Load data
data("ontario")
# Plot
old_par <- par(mfrow = c(1, 2))
plot(ontario$temp)
plot(ontario$elec)
par(old_par)
# Observe the 3-day windows for each observation
plot(ontario$temp$argvals, ontario$temp$data[2, ], type = "o",
xlim = c(-48, 72), ylim = c(7, 13), xlab = "Hours",
ylab = "Electricity consumption", pch = 16)
points(ontario$temp$argvals - 24, ontario$temp$data[1, ], col = 3, pch = 2)
points(ontario$temp$argvals + 24, ontario$temp$data[3, ], col = 2, cex = 1.5)
abline(v = 24 * -2:3, lty = 2)
legend("top", legend = c("Curve 1", "Curve 2", "Curve 3"), col = c(3, 1, 2),
pt.cex = c(1, 1, 1.5), pch = c(2, 16, 1))
# If the days are not consecutive, then the electricity consumptions at the
# end of one day and the beginning of the next do not match
head(abs(ontario$elec$data[-368, 25] - ontario$elec$data[-1, 1]))
head(diff(ontario$df$date))
## Test the linear model with functional response and predictor
(comp_flmfr <- flm_test(X = ontario$temp, Y = ontario$elec,
est_method = "fpcr_l1s"))
(simp_flmfr <- flm_test(X = ontario$temp, Y = ontario$elec,
beta0 = 0, est_method = "fpcr_l1s"))
# Visualize estimation
filled.contour(x = ontario$temp$argvals, y = ontario$elec$argvals,
z = comp_flmfr$fit_flm$Beta_hat,
color.palette = viridisLite::viridis, nlevels = 20)
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