Artificial bandwidth extension (ABE) algorithms have been developed to improve speech quality when wideband devices are used in conjunction with narrowband devices or infrastructure. While past work points to the benefit of using contextual information or memory for ABE, an understanding of the relative benefit of explicit memory inclusion, rather than just dynamic information, calls for a comparative, quantitative analysis. The need for practical ABE solutions calls further for the inclusion of memory without significant increases to latency or computational complexity. The paper reports the use of an information theoretic approach to show the potential of benefit of memory inclusion. Findings are validated through objective and subjective assessments of an ABE system which uses memory with only negligible increases to latency and computational complexity. Listening tests show that narrowband signals whose bandwidth is artificially extended with, rather than without the inclusion of memory, are of consistently improved quality.