Home
This Title All WIREs
WIREs RSS Feed
How to cite this WIREs title:
WIREs Comp Stat

Periodic autoregressive moving average methods based on Fourier representation of periodic coefficients

Full article on Wiley Online Library:   HTML PDF

Can't access this content? Tell your librarian.

Methods for estimating parameters of periodic autoregressive moving average PARMA systems when the periodic coefficients are represented by Fourier series remain to be employed in practice and still offer problem areas for future research. As pointed out by early writers on the subject, such as Hannan (1955) and Jones and Brelsford (1967), if the periodic variations are smooth within the fundamental period, as might be expected in many physical time series, a substantial reduction in the number of estimated parameters may be realized by setting many of the Fourier coefficients to be zero; this restricts the estimated solutions to a subspace. The identification problem becomes the determination of lags and frequencies with significant amplitudes. While progress has been made in this area, improvements and new methods are needed. In reviewing the development of Fourier‐PARMA methods, we naturally view many of the main advances in PARMA time series analysis under the usual parameterization. Two simulations are presented that demonstrate further potential and open problems associated with the Fourier methods. WIREs Comput Stat 2016, 8:130–149. doi: 10.1002/wics.1380 This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Histogram for coefficient a21 = 0.25; and , P value ≥ 0.5 for NSAMP = 100, NLEN = 600.
[ Normal View | Magnified View ]
Logo of UE Comission.
[ Normal View | Magnified View ]
Boxplots of parmsef parameter estimates, NSAMP = 100 realizations, N = ν = 1024, 17 parameters estimated; the only non‐null parameters those with indices 1, 2, 10, 11, 13.
[ Normal View | Magnified View ]
The dependence of on NLEN for parameter a1,2 (solid) and ordinary least squares fit ( (dashed). NSAMP = 500 realizations.
[ Normal View | Magnified View ]
The dependence of on NLEN for parameter a1,1 (solid) and ordinary least squares fit ( (dashed). NSAMP = 500 realizations.
[ Normal View | Magnified View ]
Empirical distributions of parmsef parameter estimates, NSAMP = 500 realizations, N = ν = 4096 for a1,2 = 0.6; , , Lilliefors P value ≥ 0.5
[ Normal View | Magnified View ]
Empirical distributions of parmsef parameter estimates, NSAMP = 500 realizations, N = ν = 4096 for a1,1 = 1.1; , , Lilliefors P value ≥ 0.5
[ Normal View | Magnified View ]
Boxplots of parameter estimates for simulation using NSAMP = 100 and NLEN = 600. Parameter identifiers correspond to rows of Table , where true values may be found.
[ Normal View | Magnified View ]
The dependence of on NLEN for parameter b21; NLEN = 300, 600, 1200, 2400 with NSAMP = 100 (solid) and ordinary least squares fit (dashed).
[ Normal View | Magnified View ]
The dependence of on NLEN for parameter a21; NLEN = 300, 600, 1200, 2400 with NSAMP = 100 (solid) and ordinary least squares fit (dashed).
[ Normal View | Magnified View ]
Histogram for coefficient b21 = 0.15; and , P value ≥ 0.5 for NSAMP = 100, NLEN = 600.
[ Normal View | Magnified View ]

Browse by Topic

Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods
Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data

Access to this WIREs title is by subscription only.

Recommend to Your
Librarian Now!

The latest WIREs articles in your inbox

Sign Up for Article Alerts