Real time prediction of irregular periodic time series data

• Published date: 01 April 2020
• DOI: http://doi.org/10.1002/for.2637
• Date: 01 April 2020
• Author: Myung Hwan Na,Kaimeng Zhang,Chi Tim Ng

Received: 17 June 2019 Revised: 8 October 2019 Accepted: 20 November 2019

DOI: 10.1002/for.2637

RESEARCH ARTICLE

Real time prediction of irregular periodic time series data

Kaimeng Zhang Chi Tim Ng Myung Hwan Na

Department of Statistics, Chonnam

National University,Gwangju, South

Korea

Correspondence

Chi Tim Ng, Department of Statistics,

Chonnam National University,Gwangju,

South Korea.

Email: easterlyng@gmail.com

Funding information

National Research Foundation of Korea,

Grant/AwardNumber:

NRF-2017R1C1B2011652

By means of a novel time-dependent cumulated variation penalty function, a

new class of real-time prediction methods is developed to improve the predic-

tion accuracy of time series exhibiting irregular periodic patterns: in particular,

the breathing motion data of the patients during robotic radiation therapy. It

is illustrated that for both simulated and empirical data involving changes in

mean, trend, and amplitude, the proposed methods outperform existing fore-

casting methods based on support vector machines and artificial neural network

in terms of prediction accuracy. Moreover, the proposed methods are designed

so that real-time updates can be done efficiently with O(1)computational com-

plexity upon the arrival of a new signal without scanning the old data repeatedly.

KEYWORDS

periodic time series data, real-time prediction, respiratory motion data, robotic radiation therapy,

time-varying parameters

1INTRODUCTION

Accurate prediction of tumor motion during respiration

is of paramount importance in robotic radiation therapy,

where a robot arm chases the tumor actively according to

the prediction generated from a computer program. There

are two main challenges. First, as noted in Benchetrit

(2000), human breathing pattern can be irregular. This

suggests that the parameters of the prediction model

should not be considered constant and should be updated

during the treatment session. Failure to update the param-

eters results in large prediction errors. Second, radiation

therapy requiresthat predictions are generated fast enough

to capture the motion of the tumor. For example, the res-

piratory motion data used in Choi et al. (2014) and White

et al. (2011) contain 30 and 100 signals per second respec-

tively. If 30 or 100 predictions haveto be made per second,

it would be too time consuming to recalculate the parame-

ters using the full historical data upon the arrival of a new

signal. Moreover,if there is a change in the parameters, the

full historical data contain obsolete data, giving bias in the

prediction. Therefore, it is necessary to devise an updating

strategy for the parameters so that both bias in prediction

and computational complexity are mitigated.

In the literature, a variety of the so-called “adaptive”

methods (Choi et al., 2014) have been developed to reduce

the computational complexity in updating the parame-

ters. For example, Rout, Majhi, Majhi, and Panda (2014)

proposed an “adaptive” parameter updating method for

the autoregressive moving average model (Box, Jenkins,

& Rinsel, 1994). Cauwenberghs and Poggio (2001) devel-

oped a similar parameter updating method for the support

vector regression machine model (Smola & Vapnik,1997).

The NN toolbox provided by MATLABcontains a function

for the “adaptive” training of an artificial neural network

model (Adya & Collopy, 1998). Upon the arrival of a new

signal, only O(1)computational time is required to update

the parameter. However, it is important to note that all

these methods assume time-constant parameter models

and, at time T, the estimated parameter ̂

𝜗(T)is obtained

from the data up to time Tas if the true parameters fulfill

𝜗1=𝜗2=…=𝜗T. Obviously, a change in the param-

eter at time 0 <t<Tgives biased prediction. White

et al. (2011) applied the autoregressive moving average

model to the respiratory motion data. However, as men-

tioned by the authors on page 1588, the method “failed

to account for breathing irregularities.” This is because

the parameters are estimated from the data in the first 30

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