Merge pull request #673 from bashtage/bug-figarch-forecast

BUG: Correct multistep forecasting for FIGARCH

Author: bashtage

arch/tests/univariate/test_forecast.py

@@ -49,11 +49,27 @@
     EGARCH(),
 ]
 
+ANALYTICAL_VOLATILITIES = [
+    ConstantVariance(),
+    GARCH(),
+    FIGARCH(),
+    EWMAVariance(lam=0.94),
+    MIDASHyperbolic(),
+    HARCH(lags=[1, 5, 22]),
+    RiskMetrics2006(),
+]
+
+
 MODEL_SPECS = list(product(MEAN_MODELS, VOLATILITIES))
+ANALYTICAL_MODEL_SPECS = list(product(MEAN_MODELS, ANALYTICAL_VOLATILITIES))
 
 IDS = [
     f"{str(mean).split('(')[0]}-{str(vol).split('(')[0]}" for mean, vol in MODEL_SPECS
 ]
+ANALYTICAL_IDS = [
+    f"{str(mean).split('(')[0]}-{str(vol).split('(')[0]}"
+    for mean, vol in ANALYTICAL_MODEL_SPECS
+]
 
 
 @pytest.fixture(params=MODEL_SPECS, ids=IDS)
@@ -63,6 +79,13 @@ def model_spec(request):
     return mean
 
 
+@pytest.fixture(params=ANALYTICAL_MODEL_SPECS, ids=ANALYTICAL_IDS)
+def analytical_model_spec(request):
+    mean, vol = request.param
+    mean.volatility = vol
+    return mean
+
+
 class TestForecasting:
     @classmethod
     def setup_class(cls):
@@ -1053,3 +1076,31 @@ def test_rescale_ar():
     fcasts = res.forecast(horizon=100).variance
     fcasts_no_rs = res_no_rs.forecast(horizon=100).variance
     assert_allclose(fcasts.iloc[0, -10:], fcasts_no_rs.iloc[0, -10:], rtol=1e-5)
+
+
+def test_figarch_multistep():
+    # GH 670
+    mod = ConstantMean(SP500, volatility=FIGARCH())
+    res = mod.fit(disp="off")
+    fcasts = res.forecast(horizon=10)
+    rv = fcasts.residual_variance
+    assert np.all(np.isfinite(rv))
+    assert rv.shape == (1, 10)
+    fcasts_ri = res.forecast(horizon=10, reindex=True)
+    rv_ri = fcasts_ri.residual_variance
+    assert_frame_equal(rv, rv_ri.iloc[-1:])
+    assert rv_ri.shape == (SP500.shape[0], 10)
+
+
+def test_multistep(analytical_model_spec):
+    # GH 670
+    # Ensure all work as expected
+    res = analytical_model_spec.fit(disp="off")
+    fcasts = res.forecast(horizon=10)
+    rv = fcasts.residual_variance
+    assert np.all(np.isfinite(rv))
+    assert rv.shape == (1, 10)
+    fcasts_ri = res.forecast(horizon=10, reindex=True)
+    rv_ri = fcasts_ri.residual_variance
+    assert_frame_equal(rv, rv_ri.iloc[-1:])
+    assert rv_ri.shape == (SP500.shape[0], 10)

arch/univariate/volatility.py

@@ -3235,6 +3235,7 @@ def _analytic_forecast(
         temp_forecasts = np.empty(truncation + horizon)
         resids2 = resids**2
         for i in range(start, t):
+            fcast_loc = i - start
             available = i + 1 - max(0, i - truncation + 1)
             temp_forecasts[truncation - available : truncation] = resids2[
                 max(0, i - truncation + 1) : i + 1
@@ -3246,9 +3247,8 @@ def _analytic_forecast(
                 temp_forecasts[truncation + h] = omega_tilde + lam_rev.dot(
                     lagged_forecasts
                 )
-            forecasts[i, :] = temp_forecasts[truncation:]
+            forecasts[fcast_loc, :] = temp_forecasts[truncation:]
 
-        forecasts[:start] = np.nan
         return VarianceForecast(forecasts)
 
     def _simulation_forecast(