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The properties of the Milky Way's nuclear stellar disc give crucialinformation on the epoch of bar formation. Mira variables are promising brightcandidates to study the nuclear stellar disc, and through their period-agerelation dissect its star formation history. We report on a sample of $1782$Mira variable candidates across the central $3\times3\,\mathrm{deg}^2$ of theGalaxy using the multi-epoch infrared VISTA Variables in Via Lactea (VVV)survey. We describe the algorithms employed to select candidate variable starsand then model their light curves using periodogram and Gaussian processmethods. By combining with WISE, 2MASS and other archival photometry, we modelthe multi-band light curves to refine the periods and inspect the amplitudevariation between different photometric bands. The infrared brightness of theMira variables means many are too bright and missed by VVV. However, our samplefollows a well-defined selection function as expected from artificial startests. The multi-band photometry is modelled using stellar models withcircumstellar dust that characterise the mass loss rates. We demonstrate how$\gtrsim90$ per cent of our sample is consistent with O-rich chemistry.Comparison to period-luminosity relations demonstrates that the bulk of theshort period stars are situated at the Galactic Centre distance. Many of thelonger period variables are very dusty, falling significantly under the O-richMagellanic Cloud and solar neighbourhood period-luminosity relations andexhibit high mass-loss rates of$\sim2.5\times10^{-5}M_\odot\,\mathrm{yr}^{-1}$. The period distributionappears consistent with the nuclear stellar disc forming$\gtrsim8\,\mathrm{Gyr}$ ago although it is not possible to disentangle therelative contributions of the nuclear stellar disc and the contaminating bulge.

Mira variables in the Milky Way's nuclear stellar disc: discovery and classification