Arrogant bluster is a term that is often used to describe someone who is excessively boastful and self-important. There are several synonyms that can be used to describe this type of behavior, including bombast, bluster, bravado, swagger, and haughtiness. Bombast refers to exaggerated or inflated language that is used to impress others, while bluster and bravado refer to exaggerated or false displays of confidence. Swagger suggests an overbearing or swaggering manner, while haughtiness implies a sense of superiority or condescension. All of these words can be used to convey the idea of someone who is excessively proud and confident, often to the point of being obnoxious or irritating.