  We study the statistical characteristics of a box-fitting algorithm to
analyze stellar photometric time series in the search for periodic transits by
extrasolar planets. The algorithm searches for signals characterized by a
periodic alternation between two discrete levels, with much less time spent at
the lower level. We present numerical as well as analytical results to predict
the possible detection significance at various signal parameters. It is shown
that the crucial parameter is the effective signal-to-noise ratio -- the
expected depth of the transit divided by the standard deviation of the measured
photometric average within the transit. When this parameter exceeds the value
of 6 we can expect a significant detection of the transit. We show that the
box-fitting algorithm performs better than other methods available in the
astronomical literature, especially for low signal-to-noise ratios.
