diff --git a/reference/VAR.html b/reference/VAR.html
index d2c9e73d..e868b70d 100644
--- a/reference/VAR.html
+++ b/reference/VAR.html
@@ -61,7 +61,7 @@
diff --git a/reference/VARIMA.html b/reference/VARIMA.html
index 37cf8f54..7189115f 100644
--- a/reference/VARIMA.html
+++ b/reference/VARIMA.html
@@ -60,7 +60,7 @@
@@ -69,7 +69,7 @@
Estimate a VARIMA model
-
VARIMA(formula, identification = NULL, ...)
+ VARIMA(formula, identification = c("kronecker_indices", "none"), ...)
# S3 method for class 'VARIMA'
forecast(
@@ -112,7 +112,7 @@ Arguments
identification
-The identification technique used to estimate the model. Possible options include NULL (automatic selection), "kronecker_indices" (Kronecker index identification), and "scalar_components" (scalar component identification). More details can be found in the "Identification" section below.
+The identification technique used to estimate the model.
...
@@ -172,7 +172,6 @@ pdq
pdq(p = 0:5, d = 0:2, q = 0:5)
p | The order of the non-seasonal auto-regressive (AR) terms. If multiple values are provided, the one which minimises ic will be chosen. |
d | The order of integration for non-seasonal differencing. If multiple values are provided, one of the values will be selected via repeated KPSS tests. |
q | The order of the non-seasonal moving average (MA) terms. If multiple values are provided, the one which minimises ic will be chosen. |
-
xreg
Exogenous regressors can be included in an VARIMA model without explicitly using the xreg()
special. Common exogenous regressor specials as specified in common_xregs
can also be used. These regressors are handled using stats::model.frame()
, and so interactions and other functionality behaves similarly to stats::lm()
.
@@ -182,53 +181,6 @@
xreg
... | Bare expressions for the exogenous regressors (such as log(x) ) |
-
-
-
Identification
-
-
-
-
-
Kronecker indices ("kronecker_indices"
, the default)
-
Determines the structural complexity and degrees of freedom in a VARIMA model
-by analysing the singularities in the polynomial matrices.
-
Kronecker indices represent the structural properties of the VARIMA system,
-focusing on the relationship between system inputs and outputs. These indices
-define the minimal realisation of the model, helping to determine the order
-and complexity of each equation in the system. They are particularly suited
-for capturing dynamic dependencies in multivariate systems with cointegrated
-processes. This is particularly useful for understanding system-wide
-dependencies and cointegrating relationships, however it is computationally
-intensive for models with many variables.
-
-
-
Scalar components ("scalar_components"
)
-
Simplifies VARIMA models by identifying univariate "scalar components" that
-combine linear combinations of variables into simpler sub-models. This uses
-canonical correlation analysis (CCA) to find linear combinations of variables
-with minimal lag orders. These combinations are then modeled as simpler
-ARIMA processes reducing the complexity and dimensionality of the full
-VARIMA model. This is particularly useful for identifying models with many
-variables, however it assumes good separability of the components.
-
-
-
No identification ("none"
)
-
Directly estimates the model as specified by p
, d
, and q
. This allows
-all coefficients up to lag p
and q
(for the AR and MA components) to be
-freely estimated. This can be problematic as the estimation of parameters
-without identification is not unique.
-
Identification is necessary for VARIMA models to ensure that the model is
-parsimonious, unique, and interpretable. Without proper identification, the
-model can become overly complex, redundant, or ambiguous, making estimation
-and interpretation challenging.
-
-
-
For a more detailed comparison of identification methods, refer to
-Athanasopoulos et al (2012).
-
-
-
References
-
Athanasopoulos, George, D. S. Poskitt, and Farshid Vahid. "Two Canonical VARMA Forms: Scalar Component Models Vis-à-Vis the Echelon Form." Econometric Reviews 31, no. 1 (January 2012): 60–83. https://doi.org/10.1080/07474938.2011.607088.
See also
diff --git a/reference/VECM.html b/reference/VECM.html
index 6fb8bcb2..7dfd9f46 100644
--- a/reference/VECM.html
+++ b/reference/VECM.html
@@ -62,7 +62,7 @@
diff --git a/reference/breusch_godfrey.html b/reference/breusch_godfrey.html
index ca43f75d..73d39b9d 100644
--- a/reference/breusch_godfrey.html
+++ b/reference/breusch_godfrey.html
@@ -60,7 +60,7 @@
diff --git a/reference/common_xregs.html b/reference/common_xregs.html
index 8b1b73c8..665de3a6 100644
--- a/reference/common_xregs.html
+++ b/reference/common_xregs.html
@@ -61,7 +61,7 @@
diff --git a/reference/components.ETS.html b/reference/components.ETS.html
index b7e8d684..5b8ae654 100644
--- a/reference/components.ETS.html
+++ b/reference/components.ETS.html
@@ -60,7 +60,7 @@
diff --git a/reference/fable-package.html b/reference/fable-package.html
index a9058351..fa29d560 100644
--- a/reference/fable-package.html
+++ b/reference/fable-package.html
@@ -61,7 +61,7 @@
diff --git a/reference/fitted.AR.html b/reference/fitted.AR.html
index 840de0a6..83d42dfe 100644
--- a/reference/fitted.AR.html
+++ b/reference/fitted.AR.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.ARIMA.html b/reference/fitted.ARIMA.html
index a178872c..584c8380 100644
--- a/reference/fitted.ARIMA.html
+++ b/reference/fitted.ARIMA.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.ETS.html b/reference/fitted.ETS.html
index dd8315e9..f7004824 100644
--- a/reference/fitted.ETS.html
+++ b/reference/fitted.ETS.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.NNETAR.html b/reference/fitted.NNETAR.html
index 0dbf0dc1..93069f21 100644
--- a/reference/fitted.NNETAR.html
+++ b/reference/fitted.NNETAR.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.RW.html b/reference/fitted.RW.html
index 7efd099f..2a6ed2be 100644
--- a/reference/fitted.RW.html
+++ b/reference/fitted.RW.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.TSLM.html b/reference/fitted.TSLM.html
index f52fb74b..6dddc121 100644
--- a/reference/fitted.TSLM.html
+++ b/reference/fitted.TSLM.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.VAR.html b/reference/fitted.VAR.html
index 6e74b765..081171f5 100644
--- a/reference/fitted.VAR.html
+++ b/reference/fitted.VAR.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.croston.html b/reference/fitted.croston.html
index 1b980532..c94fe22f 100644
--- a/reference/fitted.croston.html
+++ b/reference/fitted.croston.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.fable_theta.html b/reference/fitted.fable_theta.html
index b7b6e1d3..625d91e6 100644
--- a/reference/fitted.fable_theta.html
+++ b/reference/fitted.fable_theta.html
@@ -60,7 +60,7 @@
diff --git a/reference/fitted.model_mean.html b/reference/fitted.model_mean.html
index 9bb1896d..758e674c 100644
--- a/reference/fitted.model_mean.html
+++ b/reference/fitted.model_mean.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.AR.html b/reference/forecast.AR.html
index f9e21356..fd4186e2 100644
--- a/reference/forecast.AR.html
+++ b/reference/forecast.AR.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.ARIMA.html b/reference/forecast.ARIMA.html
index 020f53ba..b1ba76e9 100644
--- a/reference/forecast.ARIMA.html
+++ b/reference/forecast.ARIMA.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.ETS.html b/reference/forecast.ETS.html
index 8e5cd252..b23cf8ec 100644
--- a/reference/forecast.ETS.html
+++ b/reference/forecast.ETS.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.NNETAR.html b/reference/forecast.NNETAR.html
index d77a7d59..3c0cceac 100644
--- a/reference/forecast.NNETAR.html
+++ b/reference/forecast.NNETAR.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.RW.html b/reference/forecast.RW.html
index 732d9ff7..25056379 100644
--- a/reference/forecast.RW.html
+++ b/reference/forecast.RW.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.TSLM.html b/reference/forecast.TSLM.html
index 7edcce1b..c0396ade 100644
--- a/reference/forecast.TSLM.html
+++ b/reference/forecast.TSLM.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.VAR.html b/reference/forecast.VAR.html
index 8ba2c546..7bd9bbb8 100644
--- a/reference/forecast.VAR.html
+++ b/reference/forecast.VAR.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.croston.html b/reference/forecast.croston.html
index a56bd7c2..d41a042c 100644
--- a/reference/forecast.croston.html
+++ b/reference/forecast.croston.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.fable_theta.html b/reference/forecast.fable_theta.html
index da9cb08a..9f02ea28 100644
--- a/reference/forecast.fable_theta.html
+++ b/reference/forecast.fable_theta.html
@@ -60,7 +60,7 @@
diff --git a/reference/forecast.model_mean.html b/reference/forecast.model_mean.html
index daf1a658..eea35cde 100644
--- a/reference/forecast.model_mean.html
+++ b/reference/forecast.model_mean.html
@@ -60,7 +60,7 @@
diff --git a/reference/generate.AR.html b/reference/generate.AR.html
index 02959c55..b823bbfc 100644
--- a/reference/generate.AR.html
+++ b/reference/generate.AR.html
@@ -63,7 +63,7 @@
diff --git a/reference/generate.ARIMA.html b/reference/generate.ARIMA.html
index aa4db388..3c9e6dc4 100644
--- a/reference/generate.ARIMA.html
+++ b/reference/generate.ARIMA.html
@@ -63,7 +63,7 @@
diff --git a/reference/generate.ETS.html b/reference/generate.ETS.html
index 1ce8ea42..b07824ae 100644
--- a/reference/generate.ETS.html
+++ b/reference/generate.ETS.html
@@ -63,7 +63,7 @@
diff --git a/reference/generate.NNETAR.html b/reference/generate.NNETAR.html
index 955f72bc..37d2848d 100644
--- a/reference/generate.NNETAR.html
+++ b/reference/generate.NNETAR.html
@@ -63,7 +63,7 @@
diff --git a/reference/generate.RW.html b/reference/generate.RW.html
index f891c2a8..1e6b4089 100644
--- a/reference/generate.RW.html
+++ b/reference/generate.RW.html
@@ -63,7 +63,7 @@
diff --git a/reference/generate.TSLM.html b/reference/generate.TSLM.html
index 4bbf48f1..8bf3b0a1 100644
--- a/reference/generate.TSLM.html
+++ b/reference/generate.TSLM.html
@@ -63,7 +63,7 @@
diff --git a/reference/generate.VAR.html b/reference/generate.VAR.html
index 004cf71e..cec8fd6d 100644
--- a/reference/generate.VAR.html
+++ b/reference/generate.VAR.html
@@ -63,7 +63,7 @@
diff --git a/reference/generate.VECM.html b/reference/generate.VECM.html
index f6491aa6..9b230521 100644
--- a/reference/generate.VECM.html
+++ b/reference/generate.VECM.html
@@ -63,7 +63,7 @@
diff --git a/reference/generate.model_mean.html b/reference/generate.model_mean.html
index 3ef0e5bf..8edc59b0 100644
--- a/reference/generate.model_mean.html
+++ b/reference/generate.model_mean.html
@@ -63,7 +63,7 @@
diff --git a/reference/glance.AR.html b/reference/glance.AR.html
index 9a94bb7b..656dd135 100644
--- a/reference/glance.AR.html
+++ b/reference/glance.AR.html
@@ -60,7 +60,7 @@
diff --git a/reference/glance.ARIMA.html b/reference/glance.ARIMA.html
index 79044775..eb870aec 100644
--- a/reference/glance.ARIMA.html
+++ b/reference/glance.ARIMA.html
@@ -60,7 +60,7 @@
diff --git a/reference/glance.ETS.html b/reference/glance.ETS.html
index b45c4b93..59f7a0ea 100644
--- a/reference/glance.ETS.html
+++ b/reference/glance.ETS.html
@@ -60,7 +60,7 @@
diff --git a/reference/glance.NNETAR.html b/reference/glance.NNETAR.html
index 9b4ea689..0b8f0975 100644
--- a/reference/glance.NNETAR.html
+++ b/reference/glance.NNETAR.html
@@ -61,7 +61,7 @@
diff --git a/reference/glance.RW.html b/reference/glance.RW.html
index b63d2770..944da13b 100644
--- a/reference/glance.RW.html
+++ b/reference/glance.RW.html
@@ -61,7 +61,7 @@
diff --git a/reference/glance.TSLM.html b/reference/glance.TSLM.html
index 55cc07a5..91743a67 100644
--- a/reference/glance.TSLM.html
+++ b/reference/glance.TSLM.html
@@ -60,7 +60,7 @@
diff --git a/reference/glance.VAR.html b/reference/glance.VAR.html
index b258559d..833d50d1 100644
--- a/reference/glance.VAR.html
+++ b/reference/glance.VAR.html
@@ -60,7 +60,7 @@
diff --git a/reference/glance.VECM.html b/reference/glance.VECM.html
index 2e7158fa..d7af9271 100644
--- a/reference/glance.VECM.html
+++ b/reference/glance.VECM.html
@@ -60,7 +60,7 @@
diff --git a/reference/glance.fable_theta.html b/reference/glance.fable_theta.html
index 666496b7..d4219c65 100644
--- a/reference/glance.fable_theta.html
+++ b/reference/glance.fable_theta.html
@@ -60,7 +60,7 @@
diff --git a/reference/glance.model_mean.html b/reference/glance.model_mean.html
index 90814ded..f587fd83 100644
--- a/reference/glance.model_mean.html
+++ b/reference/glance.model_mean.html
@@ -60,7 +60,7 @@
diff --git a/reference/interpolate.ARIMA.html b/reference/interpolate.ARIMA.html
index dcc06462..edc313af 100644
--- a/reference/interpolate.ARIMA.html
+++ b/reference/interpolate.ARIMA.html
@@ -60,7 +60,7 @@
diff --git a/reference/interpolate.TSLM.html b/reference/interpolate.TSLM.html
index 58367218..38a6305a 100644
--- a/reference/interpolate.TSLM.html
+++ b/reference/interpolate.TSLM.html
@@ -60,7 +60,7 @@
diff --git a/reference/interpolate.model_mean.html b/reference/interpolate.model_mean.html
index c8f1f131..655efdb6 100644
--- a/reference/interpolate.model_mean.html
+++ b/reference/interpolate.model_mean.html
@@ -60,7 +60,7 @@
diff --git a/reference/reexports.html b/reference/reexports.html
index ad7a4dca..a641baeb 100644
--- a/reference/reexports.html
+++ b/reference/reexports.html
@@ -71,7 +71,7 @@
diff --git a/reference/refit.AR.html b/reference/refit.AR.html
index dcc8b725..af3c6da2 100644
--- a/reference/refit.AR.html
+++ b/reference/refit.AR.html
@@ -60,7 +60,7 @@
diff --git a/reference/refit.ARIMA.html b/reference/refit.ARIMA.html
index 311ffba2..f86713f6 100644
--- a/reference/refit.ARIMA.html
+++ b/reference/refit.ARIMA.html
@@ -60,7 +60,7 @@
diff --git a/reference/refit.ETS.html b/reference/refit.ETS.html
index b021e7a7..9e109500 100644
--- a/reference/refit.ETS.html
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index 2fa56ea8..95b378e9 100644
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@@ -60,7 +60,7 @@
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index 0e2bc727..e42960dc 100644
--- a/reference/refit.RW.html
+++ b/reference/refit.RW.html
@@ -60,7 +60,7 @@
diff --git a/reference/refit.TSLM.html b/reference/refit.TSLM.html
index 7f0772f3..41df5696 100644
--- a/reference/refit.TSLM.html
+++ b/reference/refit.TSLM.html
@@ -60,7 +60,7 @@
diff --git a/reference/refit.model_mean.html b/reference/refit.model_mean.html
index d6293b95..22538825 100644
--- a/reference/refit.model_mean.html
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@@ -60,7 +60,7 @@
diff --git a/reference/residuals.AR.html b/reference/residuals.AR.html
index 4412ceda..26f339b1 100644
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index 48271499..83054a00 100644
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@@ -60,7 +60,7 @@
diff --git a/reference/residuals.ETS.html b/reference/residuals.ETS.html
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diff --git a/reference/residuals.TSLM.html b/reference/residuals.TSLM.html
index 6fca407a..36582b87 100644
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@@ -60,7 +60,7 @@
diff --git a/reference/residuals.VAR.html b/reference/residuals.VAR.html
index 7d9f94d0..e0bbff53 100644
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@@ -60,7 +60,7 @@
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index 12ad323f..0ec40ca7 100644
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@@ -60,7 +60,7 @@
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@@ -60,7 +60,7 @@
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index 3011ed34..70353b6c 100644
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@@ -60,7 +60,7 @@
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index 2b27f037..4618f7de 100644
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@@ -60,7 +60,7 @@
diff --git a/reference/tidy.ETS.html b/reference/tidy.ETS.html
index 041ca168..81f562b2 100644
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@@ -60,7 +60,7 @@
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