farforecast: Functional data forecasting through functional principal... In ftsa: Functional Time Series Analysis

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

 ```1 2``` ```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

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.

`forecast.ftsm`, `forecastfplsr`

Examples

 ```1 2 3 4 5``` ```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

Attaching package: ‘fda’

The following object is masked from ‘package:forecast’:

fourier

The following object is masked from ‘package:graphics’:

matplot

Attaching package: ‘zoo’

The following objects are masked from ‘package:base’:

as.Date, as.Date.numeric

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

Attaching package: ‘ftsa’

The following objects are masked from ‘package:stats’:

sd, var
```

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