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Impulse Response Functions (IRFs)

Impulse Response Functions (IRFs) measure the dynamic response of endogenous variables over time following a one-standard-deviation innovation to an exogenous shock.

Computing IRFs

Once a model is solved via perturbation, call solution.irfs():

from dyno import DynoModel

model = DynoModel("examples/neo.dyno")
solution = model.solve()

# Compute IRFs over 40 periods
irfs = solution.irfs(type="log-deviation", T=40)

The returned irfs object is a dictionary mapping each shock name to a pandas.DataFrame:

for shock_name, df_irf in irfs.items():
    print(f"=== Shock: {shock_name} ===")
    print(df_irf.head())

IRF Types

Dyno supports three scaling transformations via the type parameter:

type Mathematical Definition Interpretation Typical Use Case
"log-deviation" (default) \(\frac{y_t - \bar{y}}{\bar{y}}\) Percentage deviation from steady state (\(100 \times \Delta\%\)) Growth rates, macro aggregates
"deviation" \(y_t - \bar{y}\) Level difference from steady state Rates, ratios (inflation, interest rates)
"level" \(y_t = \bar{y} + \hat{y}_t\) Actual level values in original units Forecasting, levels analysis

Examples

irfs_pct = solution.irfs(type="log-deviation", T=40)

irfs_diff = solution.irfs(type="deviation", T=40)

irfs_levels = solution.irfs(type="level", T=40)

Interactive Visualization with Altair

solution.plot() returns an interactive Altair chart, faceted by variable:

chart = solution.plot(type="log-deviation")

# Display in a Jupyter notebook (or chart.show() / chart.save("irfs.html") elsewhere)
chart

# Customize with the regular Altair API
chart.properties(title="Impulse Response Analysis")

Pass engine="plotext" to get a text chart for the terminal instead.

Exporting Figures

Export as interactive HTML:

chart.save("irf_plots.html")

Or export publication-ready vector images (requires vl-convert-python):

chart.save("irf_plots.svg")
chart.save("irf_plots.png", scale_factor=3)

Plotting with Matplotlib & Pandas

You can plot specific variables directly using Pandas and Matplotlib:

import matplotlib.pyplot as plt

df = irfs["e_z"]

fig, axes = plt.subplots(2, 2, figsize=(10, 8))
variables = ["y", "c", "i", "k"]

for ax, var in zip(axes.flatten(), variables):
    ax.plot(df.index, df[var], lw=2, color="navy")
    ax.axhline(0, color="gray", linestyle="--", lw=0.8)
    ax.set_title(f"Response of {var}")
    ax.set_xlabel("Periods")
    ax.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()