goffda (version 0.1.2)

ontario: Ontario temperature and electricity consumption during 2010--2014

Description

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.

Usage

ontario

Format

A list with the following entries:

temp

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).

elec

an fdata with the daily electricity consumption (in gigawatts) curves of the Ontario province. Discretized on 25 equispaced grid points on \([0, 24]\).

df

a dataframe with time metadata for each curve:

• date: the date of the observation, a POSIXct object.

• weekday: the weekday of the observation.

Author

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.

Details

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).

References

Benatia, D., Carrasco, M. and Florens, J. P. (2017) Functional linear regression with functional response. Journal of Econometrics, 201(2):269--291. tools:::Rd_expr_doi("10.1016/j.jeconom.2017.08.008")

Examples

## 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))
# \donttest{
## 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)
# }