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.
farforecast(object, h = 10, var_type = "const", Dmax_value, Pmax_value,
level = 80, PI = FALSE)
Point forecast
Selected VAR order and number of components
Lower bound of a prediction interval
Upper bound of a prediction interval
An object of fds
.
Forecast horizon.
Type of multivariate time series forecasting method; see VAR
for details.
Maximum number of components considered.
Maximum order of VAR model considered.
Nominal coverage probability of prediction error bands.
When PI = TRUE
, a prediction interval will be given along with the point forecast.
Han Lin Shang
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.
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
sqrt_pm10 = sqrt(pm_10_GR$y)
multi_forecast_sqrt_pm10 = farforecast(object = fts(seq(0, 23.5, by = 0.5), sqrt_pm10),
h = 1, Dmax_value = 5, Pmax_value = 3)
Run the code above in your browser using DataLab