A Methodology for Selecting Subset Autoregressive Time Series Models

Abstract

In time series modelling, subset models are often desirable, especially when the data exhibit some form of periodic behaviour with a range of different natural periods in terms of days, weeks, months and years. Recently, Hokstad proposed a method based on personal judgement for selecting the first tentative model to obtain the best subset autoregressive model. The subjective approach adopted in the Hokstad method is a disadvantage in building up a computer program which could automatically select the appropriate model of a given time series. In this paper, we propose overcoming this disadvantage by employing the inverse autocorrelation function to select the first tentative model. In addition to sets of synthetic data, some well-known real series such as the D, E and F series of Box and Jenkins and the Canadian lynx data are analysed to validate the proposed method. The results indicate that the method can successfully detect the true model for a given time series.

Projection Modulus: A New Direction for Selecting Subset Autoregressive Models

“…The comparison shows that, although the success rate for the proposed method in identifying the true model is dependent on the maximum lag of the model and the sample size, the proposed method is always better than the method suggested by Yu and Lin (1991), for each of the four different models with six different sample sizes, when is chosen between 1=5 and 1=3. Yu and Lin's method is very sensitive to sample size, which is easily seen if we compare the variation of W % with the ratio L for a given model.…”

“…Haggan and Oyetunji (1984) developed an algorithm to calculate all possible models efficiently. Yu and Lin (1991) argue that the Haggan-Oyetunji method will be less efficient when k is large because the number of possible SAR models increases exponentially with k. They developed an iterative model-building approach to find the optimal model without checking all possible models. The first tentative model is chosen with a lag which has the most significant absolute value in the inverse autocorrelation function (IACF).…”

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).…”

“…In addition the unknown parameter k p should be carefully selected before modelling. Yu and Lin (1991) modi®ed the Haggan±Oyetunji method to overcome these disadvantages. Their proposal is to use an iterative model-building approach.…”

A delay damage model selection algorithm for NARX neural networks

“…Various methods have been suggested for the determination of the orders in the linear case [45], [69]. In designing the nonlinear sparse models, we can determine the memory order by applying the delay damage algorithm, which is described in the next section.…”