diff --git a/src/fit/utilities.jl b/src/fit/utilities.jl
index 9d315a1..ea9e194 100644
--- a/src/fit/utilities.jl
+++ b/src/fit/utilities.jl
@@ -342,9 +342,17 @@ function loglikelihood(model::DynamicFactorModel)
     (n, T) = size(model)[1:end-1]
     (_, _, v, F, _) = filter(model)
 
+    # active factors
+    active = [!all(iszero, λ) for λ ∈ eachcol(loadings(model))]
+
     # annihilator matrix
-    (A_low, Z_basis) = collapse(model)
-    M = I - Z_basis * ((A_low * Z_basis) \ A_low)
+    if any(active)
+        (A_low, Z_basis) = collapse(model)
+        M = I - Z_basis * ((A_low * Z_basis) \ A_low)
+    else
+        A_low = I
+        M = Zeros(eltype(data(model)), n, n)
+    end
 
     # covariance and precision matrices
     H = cov(model)
diff --git a/src/utilities.jl b/src/utilities.jl
index 1024c8b..533e055 100644
--- a/src/utilities.jl
+++ b/src/utilities.jl
@@ -135,8 +135,15 @@ function state_space(model::DynamicFactorModel)
     R = size(process(model))
     Ty = eltype(data(model))
 
+    # active factors
+    active = [!all(iszero, λ) for λ ∈ eachcol(loadings(model))]
+
     # collapsing matrix
-    (A_low, _) = collapse(model)
+    if any(active)
+        (A_low, _) = collapse(model)
+    else
+        A_low = I
+    end
 
     # collapsing
     y_low = [A_low * yt for yt ∈ eachcol(data(model))]