pyperfectforesight.make_initial_guess

pyperfectforesight.make_initial_guess(T, ss_initial, ss_terminal, method='linear', decay=0.9)

Generate an initial guess path for the perfect foresight solver.

Replicates the spirit of Dynare’s perfect_foresight_setup path initialisation and adds an exponential option that better matches the saddle-path dynamics typical of DSGE models.

Parameters:

• T (int) – Number of periods (rows of the returned array).

• ss_initial (array-like, shape (n,)) – Starting values — typically the initial steady state or the period-0 values you expect the path to begin near.

• ss_terminal (array-like, shape (n,)) – Terminal values — typically the terminal steady state ss.

• method ({'linear', 'exponential', 'constant'}, default 'linear') –

  How to interpolate between ss_initial and ss_terminal:

  • 'linear' — evenly spaced from ss_initial (t=0) to ss_terminal (t=T-1). Matches Dynare’s default perfect_foresight_setup behaviour when both initval and endval are supplied.

  • 'exponential' — geometric convergence x(t) = ss_terminal + (ss_initial - ss_terminal) * decay**t. The path closes most of the gap in early periods and flattens near ss_terminal, mimicking saddle-path dynamics. The gap never reaches exactly zero; use decay to control the speed.

  • 'constant' — ss_terminal repeated for all periods. Equivalent to np.tile(ss_terminal, (T, 1)).

• decay (float, default 0.9) – Decay rate for method='exponential'. Must be in (0, 1). Smaller values converge faster (e.g. 0.5 closes half the gap each period); values near 1 converge slowly and approach linear. Ignored for other methods.

Returns:

X0 – Initial guess array, ready to pass as X0 to solve_perfect_foresight or solve_perfect_foresight_expectation_errors.

Return type:

ndarray, shape (T, n)

Examples

Linear interpolation (Dynare default):

>>> X0 = make_initial_guess(T, ss_initial=ss, ss_terminal=ss_new)

Exponential interpolation with faster convergence:

>>> X0 = make_initial_guess(T, ss_initial=ss, ss_terminal=ss_new,
...                         method='exponential', decay=0.85)