Curve Linear Regression

Description

clr provides functions for curve linear regression via dimension reduction.

Details

The package implements a new methodology for linear regression with both curve response and curve regressors, which is described in Cho et al. (2013) and Cho et al. (2015). The CLR model performs a data-driven dimension reduction, based on a singular value decomposition in a Hilbert Space, as well as a data transformation so that the relationship between the transformed data is linear and can be captured by simple regression models.

Author(s)

Amandine Pierrot <amandine.m.pierrot@gmail.com>

with contributions and help from Qiwei Yao, Haeran Cho, Yannig Goude and Tony Aldon.

References

These provide details for the underlying clr methods.

Cho, H., Y. Goude, X. Brossat, and Q. Yao (2013) Modelling and Forecasting Daily Electricity Load Curves: A Hybrid Approach. Journal of the American Statistical Association 108: 7-21.

Cho, H., Y. Goude, X. Brossat, and Q. Yao (2015) Modelling and Forecasting Daily Electricity Load via Curve Linear Regression. In Modeling and Stochastic Learning for Forecasting in High Dimension, edited by Anestis Antoniadis and Xavier Brossat, 35-54, Springer.

Curve Linear Regression via dimension reduction

Description

Fits a curve linear regression (CLR) model to data, using dimension reduction based on singular value decomposition.

Usage

clr(Y, X, clust = NULL, qx_estimation = list(method = "pctvar", param =
  0.999), ortho_Y = TRUE, qy_estimation = list(method = "pctvar", param
  = 0.999), d_estimation = list(method = "cor", param = 0.5))

Arguments

Value

An object of class clr, which can be used to compute predictions. This clr object is a list of lists: one list by cluster of data, each list including:

See Also

clr-package, clrdata and predict.clr.

Examples

library(clr)
data(gb_load)
data(clust_train)

clr_load <- clrdata(x = gb_load$ENGLAND_WALES_DEMAND,
                    order_by = gb_load$TIMESTAMP,
                    support_grid = 1:48)

## data cleaning: replace zeros with NA
clr_load[rowSums((clr_load == 0) * 1) > 0, ] <- NA
matplot(t(clr_load), ylab = 'Daily loads', type = 'l')

Y <- clr_load[2:nrow(clr_load), ]
X <- clr_load[1:(nrow(clr_load) - 1), ]

begin_pred <- which(substr(rownames(Y), 1, 4) == '2016')[1]
Y_train <- Y[1:(begin_pred - 1), ]
X_train <- X[1:(begin_pred - 1), ]

## Example without any cluster
model <- clr(Y = Y_train, X = X_train)

## Example with clusters
model <- clr(Y = Y_train, X = X_train, clust = clust_train)

Create an object of clrdata

Description

clrdata is used to create a clrdata object from raw data inputs.

Usage

clrdata(x, order_by, support_grid)

Arguments

Value

An object of class clrdata with one function a row. As it inherits the matrix class, all matrix methods remain valid. If time-dates are missing in x, corresponding NA functions are added by clrdata so that time sequence is preserved between successive rows.

Examples

library(clr)
data(gb_load)

clr_load <- clrdata(x = gb_load$ENGLAND_WALES_DEMAND,
                    order_by = gb_load$TIMESTAMP,
                    support_grid = 1:48)

head(clr_load)
dim(clr_load)
summary(clr_load)

matplot(t(clr_load), ylab = 'Daily loads', type = 'l')
lines(colMeans(clr_load, na.rm = TRUE),
      col = 'black', lwd = 2)


clr_weather <- clrdata(x = gb_load$TEMPERATURE,
                       order_by = gb_load$TIMESTAMP,
                       support_grid = 1:48)
summary(clr_weather)
plot(1:48,
     colMeans(clr_weather, na.rm = TRUE),
     xlab = 'Instant', ylab = 'Mean of temperatures',
     type = 'l', col = 'cornflowerblue')

Electricity load example: clusters on test set

Description

A list with observations by cluster for prediction

Usage

clust_test

Format

A list of length 14:

14 clusters of loads, depending on both daily and seasonal classification, banking holidays being removed

Author(s)

Amandine Pierrot <amandine.m.pierrot@gmail.com>

Electricity load example: clusters on train set

Description

A list with observations by cluster for fitting

Usage

clust_train

Format

A list of length 14:

14 clusters of loads, depending on both daily and seasonal classification, banking holidays being removed

Author(s)

Amandine Pierrot <amandine.m.pierrot@gmail.com>

Electricity load from Great Britain

Description

A dataset containing half-hourly electricity load from Great Britain from 2011 to 2016, together with observed temperatures. Temperatures are computed from weather stations all over the country. It is a weighted averaged temperature depending on population geographical distribution.

Usage

gb_load

Format

A data frame with 105216 rows and 7 variables:

SETTLEMENT_DATE

date, the time zone being Europe/London

SETTLEMENT_PERIOD

time of the day

TIMESTAMP

date-time, the time zone being Europe/London

ENGLAND_WALES_DEMAND

British electric load, measured in MW, on average over the half hour

TEMPERATURE

observed temperature in Celsius

MV

percentage of missing values when averaging over weather stations, depending on the weight of the station

DAY_TYPE

type of the day of the week, from 1 for Sunday to 7 for Saturday, 8 being banking holidays

Author(s)

Amandine Pierrot <amandine.m.pierrot@gmail.com>

Source

National Grid
National Centers for Environmental Information

Prediction from fitted CLR model(s)

Description

Takes a fitted clr object produced by clr() and produces predictions given a new set of functions or the original values used for the model fit.

Usage

## S3 method for class 'clr'
predict(object, newX = NULL, newclust = NULL,
  newXmean = NULL, simplify = FALSE, ...)

Arguments

Value

predicted functions

Examples

library(clr)
data(gb_load)

clr_load <- clrdata(x = gb_load$ENGLAND_WALES_DEMAND,
                    order_by = gb_load$TIMESTAMP,
                    support_grid = 1:48)

# data cleaning: replace zeros with NA
clr_load[rowSums((clr_load == 0) * 1) > 0, ] <- NA

Y <- clr_load[2:nrow(clr_load), ]
X <- clr_load[1:(nrow(clr_load) - 1), ]

begin_pred <- which(substr(rownames(Y), 1, 4) == '2016')[1]
Y_train <- Y[1:(begin_pred - 1), ]
X_train <- X[1:(begin_pred - 1), ]
Y_test <- Y[begin_pred:nrow(Y), ]
X_test <- X[begin_pred:nrow(X), ]


## Example without any cluster
model <- clr(Y = Y_train, X = X_train)

pred_on_train <- predict(model)
head(pred_on_train[[1]])

pred_on_test <- predict(model, newX = X_test)
head(pred_on_test[[1]])


## Example with clusters
model <- clr(Y = Y_train, X = X_train, clust = clust_train)

pred_on_train <- predict(model)
str(pred_on_train)
head(pred_on_train[[1]])

pred_on_test <- predict(model, newX = X_test, newclust = clust_test,
                        simplify = TRUE)
str(pred_on_test)
head(pred_on_test)

# With dates as row names
rownames(pred_on_test) <- rownames(Y_test)[as.numeric(rownames(pred_on_test))]