onlineforecast (version 1.0.0)

AR: Auto-Regressive (AR) input

Description

Generate auto-regressive (AR) inputs in a model

Usage

AR(lags)

Arguments

lags

integer vector: The lags of the AR to include.

Value

A list of matrices, one for each lag in lags, each with columns according to model$kseq.

Details

The AR function can be used in an onlineforecast model formulation. It creates the input matrices for including AR inputs in a model during the transformation stage. It takes the values from the model output in the provided data does the needed lagging.

The lags must be given according to the one-step ahead model, e.g.:

AR(lags=c(0,1)) will give: Y_t+1|t = \(\phi_1\) y_t-0 + \(\phi_2\) y_t-1 + \(\epsilon\)_t+1

and:

AR(lags=c(0,3,12)) will give: Y_t+1|t = \(\phi\)_1 y_t-0 + \(\phi\)_2 y_t-3 + \(\phi\)_3 y_t-12 + \(\epsilon\)_t+1

Note, that

For k>1 the coefficients will be fitted individually for each horizon, e.g.:

AR(lags=c(0,1)) will be the multi-step AR: Y_t+k|t = \(\phi\)_1,k y_t-0 + \(\phi\)_2,k y_t-1 + \(\epsilon\)_t+k|t

See the details in ??(ref til vignette).

Examples

# NOT RUN {
# Setup data and a model for the example
D <- Dbuilding
model <- forecastmodel$new()
model$output = "heatload"
# Use the AR in the transformation stage
model$add_inputs(AR = "AR(c(0,1))")
# Regression parameters
model$add_regprm("rls_prm(lambda=0.9)")
# kseq must be added
model$kseq <- 1:4
# In the transformation stage the AR input will be generated
# See that it generates two input matrices, simply with the lagged heat load at t for every k
model$transform_data(subset(D, 1:10))

# Fit with recursive least squares (no parameters prm in the model)
fit <- rls_fit(c(lambda=0.99), model, D, returnanalysis=TRUE)

# Plot the result, see "?plot_ts.rls_fit"
plot_ts(fit, xlim=c(ct("2010-12-20"),max(D$t)))
# Plot for a short period with peaks
plot_ts(fit, xlim=c("2011-01-05","2011-01-07"))

# For online updating, see ??ref{vignette, not yet available}:
# the needed lagged output values are stored in the model for next time new data is available
model$yAR
# The maximum lag needed is also kept
model$maxlagAR

# }