Autoregressive moving average modeling for finger tapping with an external stimulus

We report the Autoregressive Moving Average (ARMA) structures of interresponse interval and interstimulus interval in rhythmic finger tapping and how tapping schemes arise from these structures. The interstimulus interval is chosen to be a metronome cue slightly perturbed from its periodic mode by a zero-mean sine-wave modulated sequence. These metronome sequences were chosen to follow an exact Autoregressive model of the third order and are generated using metronome interval durations of 400, 500, and 600 msec. At each frequency, four different perturbation rates were presented to seven subjects: 1, 2, 5, and 7% of the base interval. Synchronization error, i.e., tap-to-beat phase deviations, induced by these ARMA models are stable and thus were bounded. This framework is useful in characterizing the relationship between motor control variables, interresponse interval, synchronization error, and interstimulus interval. Also, several known models can be easily derived and analyzed in this setting.