Package {MAPA}

MAPA: Multiple Aggregation Prediction Algorithm

Description

Functions and wrappers for using the Multiple Aggregation Prediction Algorithm (MAPA) for time series forecasting. MAPA models and forecasts time series at multiple temporal aggregation levels, thus strengthening and attenuating the various time series components for better holistic estimation of its structure. For details see Kourentzes et al. (2014) doi:10.1016/j.ijforecast.2013.09.006.

Wrapper functions

These estimate MAPA and produce forecasts in a single call.

mapa

Estimate MAPA and produce in- and out-of-sample forecasts, with optional prediction intervals. This is the recommended function for most uses.

mapasimple

Estimate MAPA and produce out-of-sample forecasts, together with the forecasted components at each aggregation level.

Estimation and forecasting

These separate estimation from forecasting, so that a fitted MAPA can be reused, for example to forecast with new xreg values.

mapaest

Estimate the exponential smoothing model at each aggregation level, using ets from the forecast package or es from the smooth package, optionally with exogenous variables (MAPAx).

mapafor

Produce in- and out-of-sample forecasts from a fitted MAPA, with optional prediction intervals and in-sample errors.

mapacalc

Produce out-of-sample forecasts from a fitted MAPA, together with the forecasted components at each aggregation level.

Methods for MAPA outputs

The outputs of the functions above have the classes mapa.fit (mapaest), mapa.calc (mapacalc and mapasimple), and mapa.for (mapafor and mapa), with the following methods.

plot.mapa.fit

Plot the components of the model fitted at each aggregation level.

plot.mapa.calc

Plot the forecasts and, optionally, the forecasted components at each aggregation level.

plot.mapa.for

Plot the in- and out-of-sample forecasts and the prediction intervals.

print and summary.mapa.fit

Print and summarise each of the outputs: the fitted model and parameters at each aggregation level; the combined components for each horizon; and the in-sample errors for each horizon.

Utilities

tsaggr

Non-overlapping temporal aggregation of a time series to one or more aggregation levels.

Data

admissions

Monthly UK NHS total non-elective G&A admissions, April 2008 to June 2013.

Compatibility with earlier versions

These are provided only for compatibility and will be removed in a later version of the package.

mapafit.old

Transform a fitted MAPA to the structure of versions <= 2.0.6, for code that depends on the earlier indexing.

plotmapa

Plot a fitted MAPA. This is deprecated, use plot instead.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com; Fotios Petropoulos.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

Useful links:

• https://kourentzes.com/forecasting/2014/04/19/multiple-aggregation-prediction-algorithm-mapa/

• Report bugs at https://github.com/trnnick/mapa/issues

Total Non-elective G&A Admissions (FFCEs)

Description

UK NHS Total Non-elective G&A Admissions (FFCEs). April 2008 – June 2013.

Usage

admissions

Format

Time series data

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com.

Source

UK Department of Health: Monthly Activity Return

Examples

forecast::tsdisplay(admissions)

Multiple Aggregation Prediction Algorithm (Wrapper)

Description

Wrapper to estimate and produce MAPA in- and out-of-sample forecasts. Uses mapaest and mapafor.

Usage

mapa(
  y,
  ppy = NULL,
  fh = NULL,
  ifh = 1,
  minimumAL = 1,
  maximumAL = ppy,
  comb = c("w.mean", "w.median", "mean", "median", "wght"),
  paral = c(0, 1, 2),
  display = c(0, 1),
  outplot = c(0, 1),
  hybrid = c(TRUE, FALSE),
  model = "ZZZ",
  type = c("ets", "es"),
  conf.lvl = NULL,
  xreg = NULL,
  pr.comp = 0,
  cl = NULL,
  ...
)

Arguments

Details

This function calls mapaest and mapafor internally.

Use type="es" for the es function of the smooth package, instead of the default ets function of the forecast package. See mapaest for details on the differences between the two and on the use of xreg.

Value

The output is of class mapa.for, which also stores the time series and the settings used. See mapafor and plot.mapa.for.

Note

The calculation of the prediction intervals is based on the empirical multiple step ahead MSE. To speed up calculations set conf.lvl=NULL. If very long forecast horizons are requested then once no more t+h MSE can be calculated the following approximation is used: \sqrt{MSE_{t+1}}*\sqrt{h} for the error.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com; Fotios Petropoulos.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

mapaest, mapafor, mapasimple.

Examples

# MAPA with ets from the forecast package (default), forecasting 18 steps 
# ahead, with in-sample forecasts up to 3 steps ahead and prediction intervals
out <- mapa(admissions, fh=18, ifh=3, conf.lvl=c(0.8,0.95))
print(out)
summary(out)
plot(out)

# MAPAx with es from the smooth package. xreg must contain the in-sample 
# observations and the fh future values
set.seed(1)
fh <- 12
x <- matrix(rnorm((length(admissions)+fh)*2), ncol=2)
out <- mapa(admissions, fh=fh, type="es", xreg=x)


# es with a different combination operator and without hybrid forecasts
out <- mapa(admissions, type="es", comb="median", hybrid=FALSE)

# Non-seasonal models only, at aggregation levels 1 to 6
out <- mapa(admissions, model="ZZN", maximumAL=6)

# MAPAx with xreg preprocessed by principal components, selecting the number
# of components automatically, and plotting the output
out <- mapa(admissions, fh=fh, type="es", xreg=x, pr.comp=-1, conf.lvl=0.9, outplot=1)

# Only in-sample forecasts
out <- mapa(admissions, fh=0, ifh=6)

MAPA Internal Calculation of Forecasts

Description

The following function produces a simple MAPA forecast from a given origin. This is meant to be an internal function. Use mapafor instead.

Usage

mapacalc(
  y,
  mapafit,
  fh = NULL,
  comb = c("w.mean", "w.median", "mean", "median", "wght"),
  outplot = c(0, 1, 2),
  hybrid = c(TRUE, FALSE),
  xreg = NULL
)

Arguments

Details

If mapafit was estimated with xreg, then xreg must also be provided here, with the same variables and at least length(y) + fh observations, so that the values for the forecast horizon are available. See mapaest for details on the use of xreg.

mapafit can also have the structure of earlier versions (<= 2.0.6), for example a fitted MAPA saved with an earlier version, or produced by mapafit.old. Note that mapafit.old is provided only for compatibility and will be removed in a later version of the package.

Value

The output is of class mapa.calc, which also stores the time series and the settings used. It has print, summary, and plot methods, see plot.mapa.calc.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com; Fotios Petropoulos.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

mapafor, mapa.

Examples

mapafit <- mapaest(admissions)

# Forecast a full season ahead (default)
out <- mapacalc(admissions, mapafit)
print(out)

# Forecast 18 steps ahead, and plot the forecasts and the components
out <- mapacalc(admissions, mapafit, fh=18, outplot=2)
summary(out)
plot(out, components=c("level","season"), main="Admissions")

# Different combination operators, with and without the hybrid forecasts
out.mean <- mapacalc(admissions, mapafit, comb="mean")
out.wght <- mapacalc(admissions, mapafit, comb="wght", hybrid=FALSE)

# The same works for MAPA estimated with es from the smooth package
mapafit.es <- mapaest(admissions, type="es")
out.es <- mapacalc(admissions, mapafit.es, fh=18)

# MAPAx: xreg is needed both in estimation and forecasting. For forecasting 
# it must contain the in-sample observations and the fh future values.
set.seed(1)
fh <- 12
x <- rnorm(length(admissions)+fh)
mapafit.x <- mapaest(admissions, type="es", xreg=x)
out.x <- mapacalc(admissions, mapafit.x, fh=fh, xreg=x)
plot(out.x, components=TRUE)

MAPA Estimation

Description

The following function estimates MAPA and saves all fitted model.

Usage

mapaest(
  y,
  ppy = NULL,
  minimumAL = 1,
  maximumAL = ppy,
  paral = c(0, 1, 2),
  display = c(0, 1),
  outplot = c(0, 1, 2),
  model = "ZZZ",
  type = c("ets", "es"),
  xreg = NULL,
  pr.comp = 0,
  cl = NULL,
  ...
)

Arguments

Details

MAPA can use two implementations of exponential smoothing at each aggregation level. With type="ets" the ets function of the forecast package is used, which supports seasonal periods up to 24. With type="es" the es function of the smooth package is used, which supports any seasonal period, the model codes "X" and "Y", and exogenous variables (xreg). Additional arguments are passed to ets or es through ..., for example the information criterion used for model selection (ic="bic" for ets, or ic="BIC" for es).

MAPAx: exogenous variables are provided with xreg, as a vector or as a matrix with one column per variable. These are aggregated in the same way as y at each aggregation level. Including xreg forces type="es". For estimation xreg must have at least as many observations as y, and any additional observations are ignored. For forecasting, with mapacalc, mapafor, mapa, and mapasimple, xreg must also contain the values for the forecast horizon, so it must have at least length(y) + fh observations. The same xreg variables must be used in estimation and forecasting. When pr.comp is not 0, xreg is preprocessed with principal components. These are calculated in estimation and stored in the fitted MAPA, so that the same components are used in forecasting.

Since version 2.1.0 the fitted MAPA is a list, as described in Value. Earlier versions (<= 2.0.6) returned a list-matrix with one row per aggregation level. Code that depends on the earlier structure, for example indexing as mapafit[,"use"] or mapafit[[1,14]], can transform the fitted MAPA to the earlier structure with mapafit.old. This is provided only for compatibility and will be removed in a later version of the package. Such code should be updated to use the current structure, for example mapafit$use or mapafit$models[[1]]$components.

Value

Estimated MAPA model structure, of class mapa.fit. This is a list containing:

Earlier versions (<= 2.0.6) stored the fitted models in a list-matrix. Such objects are still accepted by mapacalc, mapafor, and the methods for mapa.fit.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com; Fotios Petropoulos.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

mapa, mapafor.

Examples

# Estimate MAPA using ets from the forecast package (default)
mapafit <- mapaest(admissions)
print(mapafit)
summary(mapafit)
plot(mapafit)

# Use es from the smooth package instead
mapafit.es <- mapaest(admissions, type="es")

# Restrict the model at each aggregation level. With type="es" the codes "X"
# and "Y" can be used, here to select between no and additive trend and 
# seasonality, with additive errors
mapafit.es <- mapaest(admissions, type="es", model="AXX")

# Use only non-seasonal models, at aggregation levels 2 to 6
mapafit <- mapaest(admissions, model="ZZN", minimumAL=2, maximumAL=6)

# If y is not a ts object, then ppy must be provided
mapafit <- mapaest(as.numeric(admissions), ppy=12)

# MAPAx: estimate with exogenous variables, here 3 simulated ones. Only 
# type="es" accepts xreg. Observations beyond the length of y are ignored 
# in estimation, so the same xreg can be used later for forecasting
set.seed(1)
x <- matrix(rnorm((length(admissions)+12)*3), ncol=3)
mapafit.x <- mapaest(admissions, type="es", xreg=x)
summary(mapafit.x)
plot(mapafit.x)


# Preprocess xreg with principal components, retaining 2 components, or
# selecting the number of components automatically
mapafit.pc <- mapaest(admissions, type="es", xreg=x, pr.comp=2)
mapafit.pc <- mapaest(admissions, type="es", xreg=x, pr.comp=-1)
summary(mapafit.pc)

# Pass additional arguments to ets or es, here the information criterion
mapafit <- mapaest(admissions, ic="bic")
mapafit.es <- mapaest(admissions, type="es", ic="BIC")

# Parallel processing with an existing cluster
library(parallel)
cl <- makeCluster(2)
mapafit <- mapaest(admissions, paral=1, cl=cl)
stopCluster(cl)


# Code that depends on the structure of earlier versions can use mapafit.old.
# This will be removed in a later version of the package.
mapafit.prev <- suppressWarnings(mapafit.old(mapafit))
mapafit.prev[,"use"]

Transform MAPA fit to the structure of earlier versions

Description

Since version 2.1.0 the fitted MAPA model returned by mapaest is a list that keeps the complete fitted model at each aggregation level. Earlier versions (<= 2.0.6) stored it as a list-matrix, with one row per aggregation level. This function transforms the current structure to the earlier one, so that code that depends on the old indexing of the fitted MAPA keeps working.

This function is provided only for compatibility and will be removed in a later version of the package. A warning is given every time it is used.

Usage

mapafit.old(mapafit)

Arguments

Value

Fitted MAPA model as a list-matrix of class mapa.fit, with one row per aggregation level, as in MAPA <= 2.0.6. For type="ets" the columns are the 18 elements of the ets fit that were stored previously, followed by use, AL, original.ppy, etstype, and pr.comp. For type="es" the columns are the elements of the es fit that were stored previously, followed by smoothLength, use, AL, original.ppy, etstype, and pr.comp. The output is still accepted by mapacalc, mapafor, and the methods of mapa.fit.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com.

See Also

mapaest.

Examples

mapafit <- mapaest(admissions)

# Transform to the structure of earlier versions. A warning is given, as this 
# function will be removed in a later version of the package.
mapafit.prev <- suppressWarnings(mapafit.old(mapafit))

# Old style indexing
mapafit.prev[,"use"]
mapafit.prev[[1,"method"]]

# The equivalent with the current structure
mapafit$use
mapafit$models[[1]]$method

# The earlier structure is still accepted for forecasting
mapacalc(admissions, mapafit.prev)

MAPA Forecast

Description

The following function produces in- and out-of-sample MAPA forecasts, for multiple steps ahead. This is the recommended function to use in forecasting with MAPA.

Usage

mapafor(
  y,
  mapafit,
  fh = NULL,
  ifh = 1,
  comb = c("w.mean", "w.median", "mean", "median", "wght"),
  outplot = c(0, 1),
  hybrid = c(TRUE, FALSE),
  conf.lvl = NULL,
  xreg = NULL,
  paral = c(0, 1, 2),
  cl = NULL
)

Arguments

Details

If mapafit was estimated with xreg, then xreg must also be provided here, with the same variables and at least length(y) + fh observations, so that the values for the forecast horizon are available. See mapaest for details on the use of xreg.

mapafit can also have the structure of earlier versions (<= 2.0.6), for example a fitted MAPA saved with an earlier version, or produced by mapafit.old. Note that mapafit.old is provided only for compatibility and will be removed in a later version of the package.

Value

If y is a ts object, then outfor is also a ts object. The output is of class mapa.for, which also stores the time series and the settings used. It has print, summary, and plot methods, see plot.mapa.for. The summary reports in-sample errors for each horizon.

Note

The calculation of the prediction intervals is based on the empirical multiple step ahead MSE. To speed up calculations set conf.lvl=NULL. If very long forecast horizons are requested then once no more t+h MSE can be calculated the following approximation is used: \sqrt{MSE_{t+1}}*\sqrt{h} for the error.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com; Fotios Petropoulos.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

mapa, mapaest, mapacalc.

Examples

mapafit <- mapaest(admissions)

# Out-of-sample forecasts a full season ahead and in-sample 1-step ahead forecasts
out <- mapafor(admissions, mapafit)

# Forecast 18 steps ahead, with in-sample forecasts up to 3 steps ahead and
# 80% and 95% prediction intervals
out <- mapafor(admissions, mapafit, fh=18, ifh=3, conf.lvl=c(0.8,0.95))
print(out)
summary(out)
plot(out, main="Admissions", col.PI="lightblue")

# Only in-sample forecasts, for example to evaluate the fit up to 12 steps ahead
out <- mapafor(admissions, mapafit, fh=0, ifh=12)
summary(out)


# With es from the smooth package and the w.median combination
mapafit.es <- mapaest(admissions, type="es")
out.es <- mapafor(admissions, mapafit.es, comb="w.median")

# MAPAx: xreg must contain the in-sample observations and the fh future values
set.seed(1)
fh <- 12
x <- rnorm(length(admissions)+fh)
mapafit.x <- mapaest(admissions, type="es", xreg=x)
out.x <- mapafor(admissions, mapafit.x, fh=fh, xreg=x, conf.lvl=0.9)
plot(out.x)

# Parallel processing for the in-sample forecasts, with an existing cluster
library(parallel)
cl <- makeCluster(2)
out <- mapafor(admissions, mapafit, ifh=3, paral=1, cl=cl)
stopCluster(cl)

MAPA Single Origin Forecast (Wrapper)

Description

The following function estimates MAPA and produces out-of-sample forecasts. It is not suggested, unless only simple single origin forecasts are required.

Usage

mapasimple(
  y,
  ppy = NULL,
  fh = NULL,
  minimumAL = 1,
  maximumAL = ppy,
  comb = c("w.mean", "w.median", "mean", "median", "wght"),
  paral = c(0, 1, 2),
  display = c(0, 1),
  outplot = c(0, 1, 2),
  hybrid = c(TRUE, FALSE),
  model = "ZZZ",
  type = c("ets", "es"),
  xreg = NULL,
  pr.comp = 0,
  cl = NULL,
  ...
)

Arguments

Details

This function calls mapaest and mapacalc internally.

Use type="es" for the es function of the smooth package, instead of the default ets function of the forecast package. See mapaest for details on the differences between the two and on the use of xreg.

Value

The output is of class mapa.calc. See mapacalc and plot.mapa.calc.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com; Fotios Petropoulos.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

mapa.

Examples

# MAPA forecasts with ets from the forecast package (default)
out <- mapasimple(admissions)
print(out)

# With es from the smooth package, 24 steps ahead, plotting forecasts and components
out <- mapasimple(admissions, fh=24, type="es", outplot=2)

# Weighted combination, without the hybrid forecasts
out <- mapasimple(admissions, comb="wght", hybrid=FALSE)

# MAPAx: xreg must contain the in-sample observations and the fh future values
set.seed(1)
x <- rnorm(length(admissions)+12)
out <- mapasimple(admissions, fh=12, type="es", xreg=x)
summary(out)

Plot MAPA forecasts and components

Description

The following function plots the forecasts produced by mapacalc or mapasimple, and optionally the forecasted components at each aggregation level. The black line in each component panel is the combination of the component across aggregation levels, as used for the forecasts. The plot is the same as the one that can be produced optionally by mapacalc.

Usage

## S3 method for class 'mapa.calc'
plot(x, components = c(FALSE, TRUE), col = NULL, col.AL = NULL, ...)

Arguments

Note

If y is a ts object, its time index is used for the horizontal axis. When only the forecasts are plotted the current graphical layout is respected, so the plot can be placed in a user defined grid. When components are plotted the layout is restored on exit.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• You can find more information about MAPA at Nikos' blog.

See Also

mapacalc, mapasimple.

Examples

mapafit <- mapaest(admissions)
out <- mapacalc(admissions, mapafit, fh=18)
plot(out)
plot(out, components=TRUE)
plot(out, components="season", main="Admissions", col=c("black","red"))

# Custom colours for the aggregation levels
plot(out, components=c("level","trend"), col.AL=rainbow(12))

# Place the forecast plot in a user defined layout
par(mfrow=c(1,2))
plot(out, xlim=c(2012,2015), main="Zoomed")
plot(mapafit)
par(mfrow=c(1,1))

Produce estimated MAPA fit plot

Description

The following function plots the fitted components at each aggregation level of an estimated MAPA. The plot is the same as the one that can be produced optionally by mapaest. Aggregation levels for which seasonality cannot be estimated are in grey and levels that were not estimated due to insufficient sample are marked with '-'.

Usage

## S3 method for class 'mapa.fit'
plot(x, xreg.plot = c(TRUE, FALSE), col = NULL, ...)

Arguments

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

mapaest, mapa.

Examples

mapafit <- mapaest(admissions)
plot(mapafit)
plot(mapafit, main="Admissions")

# With es and xreg, the number of xreg variables is shown at each level
set.seed(1)
x <- rnorm(length(admissions))
mapafit.x <- mapaest(admissions, type="es", xreg=x)
plot(mapafit.x)
plot(mapafit.x, xreg.plot=FALSE, col=heat.colors(5))

Plot MAPA in- and out-of-sample forecasts

Description

The following function plots the in- and out-of-sample forecasts and prediction intervals produced by mapafor or mapa. The plot is the same as the one that can be produced optionally by mapafor.

Usage

## S3 method for class 'mapa.for'
plot(
  x,
  insample = c(TRUE, FALSE),
  PI = c(TRUE, FALSE),
  col = NULL,
  col.PI = NULL,
  ...
)

Arguments

Note

If y is a ts object, its time index is used for the horizontal axis. The current graphical layout is respected, so the plot can be placed in a user defined grid.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• You can find more information about MAPA at Nikos' blog.

See Also

mapafor, mapa.

Examples

out <- mapa(admissions, ifh=3, conf.lvl=c(0.8,0.95))
plot(out)
plot(out, insample=FALSE, main="Admissions", ylab="Patients", col.PI="lightblue")
plot(out, PI=FALSE, lwd=2, col=c("grey50","blue"))

# The prediction intervals are shaded from the forecast colour, unless col.PI is given
plot(out, col=c("grey30","darkgreen"))

Produce estimated MAPA fit plot (OBSOLETE!)

Description

The following function plots the fitted components at each aggregation level of an estimated MAPA. The plot is the same as the one that can be produced optionally by mapaest.

Usage

plotmapa(mapafit)

Arguments

Note

The function 'plotmapa' is deprecated. Use plot() instead.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com; Fotios Petropoulos.

References

• Kourentzes N., Petropoulos F., Trapero J.R. (2014) Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302.

• Kourentzes N., Petropoulos F. (2015) Forecasting with multivariate temporal aggregation: The case of promotional modelling. International Journal of Production Economics.

• You can find more information about MAPA at Nikos' blog.

See Also

mapaest, mapa.

Examples

mapafit <- mapaest(admissions,outplot=0)
# plotmapa is deprecated, use plot instead
plot(mapafit)

Summaries of MAPA estimation and forecasts

Description

Print and summary methods for the outputs of mapaest, mapacalc, mapasimple, mapafor, and mapa.

Usage

## S3 method for class 'mapa.fit'
print(x, ...)

## S3 method for class 'mapa.fit'
summary(object, ...)

## S3 method for class 'mapa.calc'
print(x, ...)

## S3 method for class 'mapa.calc'
summary(object, ...)

## S3 method for class 'mapa.for'
print(x, ...)

## S3 method for class 'mapa.for'
summary(object, ...)

Arguments

Details

The summary of mapa.fit reports for each aggregation level: the aggregated sample size, the seasonal periods, the fitted model, the smoothing parameters, and the number of xreg variables. Levels that could not be estimated due to insufficient sample are marked.

The summary of mapa.calc reports the combined level, trend, season, and xreg components for each horizon, alongside the forecasts.

The summary of mapa.for reports the in-sample errors (ME, MAE, and RMSE) for each in-sample forecast horizon, and the out-of-sample forecasts with any prediction intervals.

The summaries are returned as objects, so their contents can be used directly, for example summary(fit)$table.

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com.

See Also

mapaest, mapacalc, mapafor.

Examples

mapafit <- mapaest(admissions)
summary(mapafit)
summary(mapafit)$table

# Summary of a MAPAx with principal component preprocessing of xreg
set.seed(1)
x <- matrix(rnorm(length(admissions)*3), ncol=3)
summary(mapaest(admissions, type="es", xreg=x, pr.comp=-1))

# Summaries of forecasts
summary(mapacalc(admissions, mapafit))
out <- mapafor(admissions, mapafit, ifh=3, conf.lvl=0.9)
summary(out)
summary(out)$errors

Non-overlapping temporal aggregation

Description

Non-overlapping temporal aggregation.

Usage

tsaggr(
  y,
  fout,
  fmean = c(FALSE, TRUE),
  outplot = c(FALSE, TRUE),
  col.AL = NULL,
  ...
)

Arguments

Value

Author(s)

Nikolaos Kourentzes, nikolaos@kourentzes.com.

Examples

# Aggregate to quarterly and annual series, using sums
out <- tsaggr(admissions, fout=c(3,12))
out$out$AL12

# All aggregation levels from 2 to 12, using means, with a plot
out <- tsaggr(admissions, fout=2:12, fmean=TRUE, outplot=TRUE, main="Admissions")

# User defined colours for the aggregated series
out <- tsaggr(admissions, fout=c(3,12), fmean=TRUE, outplot=TRUE, col.AL=c("blue","red"))