  Aim: We have collected the most complete multi-wavelength ($6.0 - 6.0 \times
10^{-18} cm$) dataset of very high energy (VHE) $\gamma$-ray emitting (TeV) BL
Lacs, which are the most numerous extragalactic VHE sources. Using significant
correlations between different bands, we aim to identify the best TeV BL Lac
candidates that can be discovered by the current and next generation of imaging
air Cherenkov telescopes.
  Methods: We formed five datasets from lower energy data, i.e. radio,
mid-infrared, optical, X-rays, and GeV $\gamma$-ray, and five VHE $\gamma$-ray
datasets to perform a correlation study between different bands and to
construct the prediction method. The low energy datasets were averaged for
individual sources, while the VHE $\gamma$-ray data were divided into subsets
according to the flux state of the source. We then looked for significant
correlations and determined their best-fit parameters. Using the best-fit
parameters we predicted the level of VHE $\gamma$-ray flux for a sample of 182
BL Lacs, which have not been detected at TeV energies. We identified the most
promising TeV BL Lac candidates based on the predicted VHE $\gamma$-ray flux
for each source.
  Results: We found 14 significant correlations between radio, mid-infrared,
optical, $\gamma$-ray, and VHE $\gamma$-ray bands. The correlation between
optical and VHE $\gamma$-ray luminosity is established for the first time. We
attribute this to the more complete sample and more accurate handling of host
galaxy flux in our work. We found nine BL Lac candidates whose predicted VHE
$\gamma$-ray flux is high enough for detection in less than 25 hours with
current imaging air Cherenkov telescopes.
