ftsa: dynamic_FLR – R documentation

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dynamic_FLR

Dynamic updates via functional linear regression

Description

A functional linear regression is used to address the problem of dynamic updating, when partial data in the most recent curve are observed.

Usage

dynamic_FLR(dat, newdata, holdoutdata, order_k_percent = 0.9, order_m_percent = 0.9, 
    pcd_method = c("classical", "M"), robust_lambda = 2.33, bootrep = 100, 
    	pointfore, level = 80)

Arguments

`dat`	An object of class `sfts`.
`newdata`	A data vector of newly arrived observations.
`holdoutdata`	A data vector of holdout sample to evaluate point forecast accuracy.
`order_k_percent`	Select the number of components that explains at least 90 percent of the total variation.
`order_m_percent`	Select the number of components that explains at least 90 percent of the total variation.
`pcd_method`	Method to use for principal components decomposition. Possibilities are "M", "rapca" and "classical".
`robust_lambda`	Tuning parameter in the two-step robust functional principal component analysis, when `pcdmethod = "M"`.
`bootrep`	Number of bootstrap samples.
`pointfore`	If `pointfore = TRUE`, point forecasts are produced.
`level`	Nominal coverage probability.

Details

This function is designed to dynamically update point and interval forecasts, when partial data in the most recent curve are observed.

Value

`update_forecast`	Updated forecasts.
`holdoutdata`	Holdout sample.
`err`	Forecast errors.
`order_k`	Number of principal components in the first block of functions.
`order_m`	Number of principal components in the second block of functions.
`update_comb`	Bootstrapped forecasts for the dynamically updating time period.
`update_comb_lb_ub`	By taking corresponding quantiles, obtain lower and upper prediction bounds.
`err_boot`	Bootstrapped in-sample forecast error for the dynamically updating time period.

Author(s)

Han Lin Shang

References

H. Shen and J. Z. Huang (2008) "Interday forecasting and intraday updating of call center arrivals", Manufacturing and Service Operations Management, 10(3), 391-410.

H. Shen (2009) "On modeling and forecasting time series of curves", Technometrics, 51(3), 227-238.

H. L. Shang and R. J. Hyndman (2011) "Nonparametric time series forecasting with dynamic updating", Mathematics and Computers in Simulation, 81(7), 1310-1324.

J-M. Chiou (2012) "Dynamical functional prediction and classification with application to traffic flow prediction", Annals of Applied Statistics, 6(4), 1588-1614.

H. L. Shang (2013) "Functional time series approach for forecasting very short-term electricity demand", Journal of Applied Statistics, 40(1), 152-168.

H. L. Shang (2015) "Forecasting Intraday S&P 500 Index Returns: A Functional Time Series Approach", Journal of Forecasting, 36(7), 741-755.

H. L. Shang (2017) "Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentration", Econometrics and Statistics, 1, 184-200.

Examples

dynamic_FLR_point = dynamic_FLR(dat = ElNino_ERSST_region_1and2$y[,1:68], 
	newdata = ElNino_ERSST_region_1and2$y[1:4,69], 
	holdoutdata = ElNino_ERSST_region_1and2$y[5:12,69], pointfore = TRUE)

dynamic_FLR_interval = dynamic_FLR(dat = ElNino_ERSST_region_1and2$y[,1:68], 
	newdata = ElNino_ERSST_region_1and2$y[1:4,69], 
	holdoutdata = ElNino_ERSST_region_1and2$y[5:12,69], pointfore = FALSE)

ftsa

Functional Time Series Analysis

v6.0

GPL-3

Authors

Rob Hyndman [aut] (<https://orcid.org/0000-0002-2140-5352>), Han Lin Shang [aut, cre, cph] (<https://orcid.org/0000-0003-1769-6430>)

Initial release

2020-11-29