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The stationarity of generalized STAR(2;λ1, λ2) process through the invers of autocovariance matrix
a Statistics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]In this paper, we apply the Invers of Autocovariance Matrix (IAcM) to investigate the process stationarity of the Generalized STAR model. In particular, we consider the second order of Generalized STAR (GSTAR(2;λ1,λ2)) processes. For that purpose, we derive the use of IAcM for the first order of GSTAR (GSTAR(1;λ1)) processes briefly. We move forward to the second order by following two important steps i.e. investigate the relevance between the sum square of errors and IAcM, and formulate the elements of IAcM as the function of autoregressive parameters and spatial weights. We obtain a definite positive IAcM whose size is twice the IAcM’s size of GSTAR(1;λ 1). We acquire the GSTAR(2;λ1,λ2) process is stationary if all determinants of the IAcM’s leading principal submatrices are positive. Furthermore we find that the stationary condition obtained from the IAcM is stronger than from the characteristic polynomial of parameter matrix. © 2014 AIP Publishing LLC.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Auto-regressive,Autocovariance matrices,Autoregressive parameters,Characteristic polynomials,Principal submatrices,spatial weight,Stationarity,Stationary conditions[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]autoregressive,invers of autocovariance matrix,spatial weight,stationarity,sum square of errors[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1063/1.4868849[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]