Fun though it is to imagine a young Julius Caesar patronizing the Roman equivalent of a thrift store or modelling his hairstyle on the retro example of Tiberius Gracchus, there a few problems with the premise of this question. First, of course, the idea of thinking in terms of decades is really a twentieth-century thing (though prefigured earlier). Equally modern is the phenomenon of a mass culture dictating general trends in fashion. There were certainly trends in Roman clothing and hairstyles, as we'll see, and some of those trends were both widespread and cyclical. But they were largely confined to the elite, and were never as closely identified with a generation or era as, say, bell-bottoms and the afro. Finally, and famously, the idea of a distinctive youth culture is another twentieth-century invention. Although Roman adolescents tended to be associated with certain modern-seeming traits (including a want of good judgement in matters sartorial), they were never regarded as a distinctive social group.

So: young Romans did not use fashion choices to signal personal inclinations or group membership in the same way modern youths do. But they did understand fashion as an important marker of personal identity.

Clothing in ancient Rome, as in any premodern society, was relatively expensive (all that weaving and spinning took time, and the best dyes weren't cheap). So most Romans had, by modern standards, a small wardrobe. Because non-elite people didn't buy clothes very often, new styles spread relatively slowly, and to be limited to the minority who could afford to treat clothing as an accessory. But fashions did change, sometimes quite noticeably. In the imperial era, they tended to be dictated, or at least strongly influenced, by the reigning emperor and empress, whose widely-disseminated portraits were imitated by the ambitious throughout the Empire.

Since I only have time to survey a few of these changes, we may as well start with the famous toga. The toga was always massive, semicircular in cut, and woolen in material. But the way it was draped and folded changed over time; compare, for example, the massive sculpted folds of the imperial toga with the slimmed-down version preferred in late antiquity. Women's clothing, though less well-attested artistically, seems to have been susceptible to rapid changes of fashion and cut; scandalized Roman authors sometimes fulminate against unprecedentedly risque silken gowns and the like.

Hairstyles also changed over time. Although Roman men in the classical period almost always wore their hair short, women's styles changed quite rapidly, ranging from the modest bun of the Augustan era to the vast towers of curls affected by the Flavian grande dame. Beard styles changed almost as quickly. Most Roman men shaved clean from the mid-Republican period to the reign of Hadrian, when the emperor's beard made whiskers fashionable. For the rest of the second and third centuries, beards were de rigueur, with styles ranging from the longish "philosopher's beard" of Marcus Aurelius to the stubble of the third-century military emperors.

There were, in short, always stylistic choices available to those Romans who could afford to think about style. But to judge from our evidence - which is, admittedly, mostly artistic, and thus apt to show people in terms of conservative artistic conventions - most fashion-forward Romans keenly adhered to the reigning styles of the day. Some styles were cyclical - beards, for example, oscillated in length and cut - but they do not seem to have done so from any conscious or nostalgic attempt to recall a past time, save insofar as they were inspired by emperors who modeled their look on a famous predecessor.

There were, however, a few oddballs who wished to be identified as representatives of an older, Republican Rome, and dressed accordingly. The most famous of these was of course Cato the Younger, who identified with the past to the extent of wearing an old-fashioned loincloth under his toga (most men of his generation just wore linen under-tunics). Cato's affectations were also influenced by his Stoic creed, and by the Roman association of certain fashion choices (beards, simple clothing) with a philosophical lifestyle.

To return at last to the question, different eras in Roman history were certainly associated with different fashions in hairstyle and clothing. But there is little evidence for individuals consciously evoking past eras by adopting these conventions. The personal qualities that Roman fashion was intended to advertise - class, status, philosophical affiliation, etc. - were most effectively communicated through adherence to (or ostentatious rejection of) the reigning style.