Information on the data generating process in the simulations:

We use different numbers of observed and hidden variables (up to 9 total
variables, 2 to 6 observed and 1 to 3 hidden), and we separately consider edge
probabilities of $q=0.25$ and $q=0.5$ (this means that each edge is included
with probability q, independent of all other edges).

The window length tau was kept constant at 3 and the significance level for the
independence tests was set to 0.01. We used samples of different sizes, namely
100, 1000 and 10000.

For the continuous-valued case we use a linear VAR model of order one with
Gaussian error terms to generate the data, X = A X + e. The coefficients 
(non-zero entries of the connection matrix A) are drawn uniformly at random
between 0.2 and 1.5 with random sign (we avoid coefficients close to zero which
are particularly hard to detect). If the randomly chosen coefficients lead to
an unstable linear system (absolute value of one or more eigenvalues of A
greater than or equal to one) we re-select the coefficients. The values of the
variables X(t) are generated as X(t) = A X(t-1) + e(t), where e(t) =
(e_1(t), ... , e_M(t)) are Gaussian temporally uncorrelated and independent
error terms with zero mean and unit variance.

For the discrete case we use binary variables and data are generated using
conditional probability tables. The probabilities in these tables are assigned
uniformly at random between 0.1 and 0.9 (avoiding probabilities close to zero
or one which might yield almost deterministic cases). The value of each
variable i at time t is then assigned according to the probability
P(X_i(t) | X_parents(i)(t-1)).

For both the continuous- and the discrete-valued models we generate data from
the process over both observed and hidden variables, and then omit the samples
of the variables we define as hidden. Note that we don't make a difference
between hidden and observed variables during the generating process, which
means that hidden variables can be parents or children of observed variables as
well as connecting to each other. 
