Generalized autoregressive and moving average models: multicollinearity, interpretation and a new modified model

ABSTRACT

In this paper, we call attention of two observed features in practical applications of the Generalized Autoregressive Moving Average (GARMA) model due to the structure of its linear predictor. One is the multicollinearity which may lead to a non-convergence of the maximum likelihood, using iteratively reweighted least squares, and the inflation of the estimator's variance. The second is that the inclusion of the same lagged observations into the autoregressive and moving average components confounds the interpretation of the parameters. A modified model, GAR-M, is presented to reduce the multicollinearity and to improve the interpretation of the parameters. The expectation and variance under stationarity conditions are presented for the identity and logarithm link function. In a general sense, simulation studies show that the maximum likelihood estimators based on the GARMA and GAR-M models are equivalent but the GAR-M estimators presented a little lower standard errors and some restrictions in the parametric space are imposed to guarantee the stationarity of the process. Also, a real data analysis illustrates the GAR-M fit for daily hospitalization rates of elderly people due to respiratory diseases from October 2012 to April 2015 in São Paulo city, Brazil.

Keywords:

• Hospilatization rates
• count time series
• exponential family distribution
• ILRS algorithm
• GARMA model

2010 Mathematics Subject Classifications:

• 62M10. Time series
• auto-correlation
• regression

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Orlando Albarracinhttp://orcid.org/0000-0001-6037-6518

Airlane Pereira Alencar  http://orcid.org/0000-0002-0779-0426

LindaLee Ho  http://orcid.org/0000-0001-9984-8711

Additional information

Funding

The authors would like to acknowledge CNPq, CAPES and FAPESP (Grant number 2018/04654-9) for the financial support.