farforecast: Functional data forecasting through functional principal...

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/farforecast.R

Description

The coefficients from the fitted object are forecasted using a multivariate time-series forecasting method. The forecast coefficients are then multiplied by the functional principal components to obtain a forecast curve.

Usage

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farforecast(object, h = 10, var_type = "const", Dmax_value, Pmax_value, 
	level = 80, PI = FALSE)

Arguments

object

An object of fds.

h

Forecast horizon.

var_type

Type of multivariate time series forecasting method; see VAR for details.

Dmax_value

Maximum number of components considered.

Pmax_value

Maximum order of VAR model considered.

level

Nominal coverage probability of prediction error bands.

PI

When PI = TRUE, a prediction interval will be given along with the point forecast.

Details

1. Decompose the smooth curves via a functional principal component analysis (FPCA).

2. Fit a multivariate time-series model to the principal component score matrix.

3. Forecast the principal component scores using the fitted multivariate time-series models. The order of VAR is selected optimally via an information criterion.

4. Multiply the forecast principal component scores by estimated principal components to obtain forecasts of f_{n+h}(x).

5. Prediction intervals are constructed by taking quantiles of the one-step-ahead forecast errors.

Value

point_fore

Point forecast

order_select

Selected VAR order and number of components

PI_lb

Lower bound of a prediction interval

PI_ub

Upper bound of a prediction interval

Author(s)

Han Lin Shang

References

A. Aue, D. D. Norinho and S. Hormann (2015) "On the prediction of stationary functional time series", Journal of the American Statistical Association, 110(509), 378-392.

J. Klepsch, C. Kl\"uppelberg and T. Wei (2017) "Prediction of functional ARMA processes with an application to traffic data", Econometrics and Statistics, 1, 128-149.

See Also

forecast.ftsm, forecastfplsr

Examples

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sqrt_pm10 = sqrt(pm_10_GR$y)
x = seq(0,23.5, by=.5)
multi_forecast_sqrt_pm10 = farforecast(object = fts(x,sqrt_pm10), h = 10, 
	Dmax_value = 21, Pmax_value = 3)
plot(multi_forecast_sqrt_pm10$point_fore, ylim = c(5.2,8.5))

Example output

Loading required package: forecast
Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 
Loading required package: rainbow
Loading required package: MASS
Loading required package: pcaPP
Loading required package: sde
Loading required package: stats4
Loading required package: fda
Loading required package: splines
Loading required package: Matrix
Loading required package: fds
Loading required package: RCurl

Attaching package:fdaThe following object is masked frompackage:forecast:

    fourier

The following object is masked frompackage:graphics:

    matplot

Loading required package: zoo

Attaching package:zooThe following objects are masked frompackage:base:

    as.Date, as.Date.numeric

sde 2.0.15
Companion package to the bookSimulation and Inference for Stochastic Differential Equations With R ExamplesIacus, Springer NY, (2008)
To check the errata corrige of the book, type vignette("sde.errata")

Attaching package:ftsaThe following objects are masked frompackage:stats:

    sd, var

ftsa documentation built on Jan. 13, 2021, 6:21 p.m.