Projection Modulus: A New Direction for Selecting Subset Autoregressive Models

Abstract

Selecting a parsimonious subset autoregressive time series model is a valuable objective particularly where there is or may be evidence that a time series may have some form of periodic or quasi-periodic behaviour. An efficient model selection procedure is essential because of the large number of possible alternative models involved. The explanation of an increase in residual variance due to excluding a lag is examined in Hilbert space. As a result, a new statistic, the projection modulus, and its derivatives are developed to assess the significance of any lag in a model. The impact of deleting a lag, as measured by these statistics, helps to produce a selection procedure where true lags have less chance of being removed. We then assess an efficient subset autoregressive model selection procedure employing these statistics. The success of the proposed procedure is illustrated by its efficiency in identifying the true model for simulated and real data.

Subset ARMA Model Identification for Monthly Electricity Consumption Data

“…As Zhang and Terrell (1997) inform a new statistic and a new algorithm for selecting the optimal SAR, there may always be preference for using automatic model choice techniques (see Brockwell and Davis, 1996). The model space in the subset model selection of high-order AR may be quiet big hence, the usual AIC/BIC criteria might choose over parameterized models.…”

Partial autocorrelation parameterization for subset autoregression

“…Although an admissible model may not be needed for short-term forecasting, it is required for spectral estimation or data simulation in engineering design (Hipel and McLeod, 1994, §9.7.3). Zhang and Terrell (1997) have suggested a new criterion, the projection modulus, which is computationally more efficient but their method is based on Yule-Walker estimates that are known to be less accurate than some alternatives (Tjøstheim and Paulsen, 1983;Percival and Walden, A.T, 1993, p.414 and p.453;Zhang and McLeod, 2005). Bayesian methods of variable selection in regression were introduced by George and McCulloch (1993) and Bayesian methods for subset autoregression have been developed by Chen (1999) and Unnikrishnan (2004).…”

Subset ARMA Model Identification Using Genetic Algorithms

“…Recentlly, a class of subset autoregressive (SAR) models has been proposed by several reseachers, such as McClave (1975), Penm and Terrell (1982), Haggan and Oyetunji (1984), Yu and Lin (1991) and Zhang and Terrell (1997).…”

“…More recently, Zhang and Terrell (1997) introduced a new statistic, the projection modulus, and developed a new algorithm for selecting the optimal SAR that is considerably more ef®cient than the McClave algorithm, in the sense that fewer SAR models need to be included to ®nd the optimal one. Moreover it is more accurate than the Yu±Lin method in the sense of a true model being identi®ed with higher probability.…”