Testing for Serial Correlation in Autoregressive Exogenous Models with Possible GARCH Errors

Abstract

Autoregressive exogenous, hereafter ARX, models are widely adopted in time series-related domains as they can be regarded as the combination of an autoregressive process and a predictive regression. Within a more complex structure, extant diagnostic checking methods face difficulties in remaining validity in many conditions existing in real applications, such as heteroscedasticity and error correlations exhibited between the ARX model itself and its exogenous processes. For these reasons, we propose a new serial correlation test method based on the profile empirical likelihood. Simulation results, as well as two real data examples, show that our method has a good performance in all mentioned conditions.

Variants of Chaotic Grey Wolf Heuristic for Robust Identification of Control Autoregressive Model

“…The ARX structure effectively model various engineering and applied sciences problems such as time series prediction, pneumatic positioning system, wheeled robots, MIMO systems, and behavior modeling [ 78 , 79 , 80 , 81 , 82 ]. The block diagram of the ARX model is presented in Figure 2 , where and are polynomials with a degree and respectively, and given in (1) and (2).…”

“…The autoregressive exogenous model (ARX) is used in different engineering problems such as time series data prediction [ 78 ], pneumatic positioning systems [ 79 ], wheeled robots [ 80 ], multiple-input–multiple-output (MIMO) systems [ 81 ], and human driving behavior modeling [ 82 ]. Various identification techniques were proposed for the parameter estimation of ARX.…”

Mildly Explosive Autoregression with Strong Mixing Errors

“…The -mixing sequence is a weakly dependent sequence and several linear and nonlinear time series models satisfy the mixing properties. For more works on -mixing and applications of regression, we refer the reader to Hall and Heyde [ 13 ], Györfi et al [ 14 ], Lin and Lu [ 15 ], Fan and Yao [ 16 ], Jinan et al [ 17 ], Escudero et al [ 18 ], Li et al [ 19 ], and the references therein. Many researchers have studied mildly explosive models.…”