diff --git a/src/ARIMA.jl b/src/ARIMA.jl
index 7adb2e7..f1b9565 100644
--- a/src/ARIMA.jl
+++ b/src/ARIMA.jl
@@ -2,8 +2,8 @@
 # vectors of AR and MA coefficients and a number of differences.
 # This implementation is based on Section 8.3 in Brockwell and Davis 2002,
 # "Introduction to Time Series and Forecasting," 2nd ed.
-function arima_statespace{T, I<:Integer}(ar::Vector{T}, d::I, ma::Vector{T}, 
-		sigma::T)
+function arima_statespace(ar::Vector{T}, d::I, ma::Vector{T}, 
+		sigma::T) where {T, I<:Integer}
 	p = length(ar)
 	q = length(ma)
 	r = max(p, q + 1)
@@ -30,7 +30,7 @@ function arima_statespace{T, I<:Integer}(ar::Vector{T}, d::I, ma::Vector{T},
 	StateSpaceModel(F, V, G, W, x0, P0)
 end
 
-function arima{T, I<:Integer}(y::Vector{T}, p::I, d::I, q::I)
+function arima(y::Vector{T}, p::I, d::I, q::I) where {T, I<:Integer}
 	build(par::Vector{T}) = arima_statespace(par[1:p], par[p+1], par[p+2:end])
 	par0 = zeros(p + d + q)
 	fit(y, build, par0)
diff --git a/src/GARCH.jl b/src/GARCH.jl
index 3615ed4..44c8281 100644
--- a/src/GARCH.jl
+++ b/src/GARCH.jl
@@ -2,7 +2,7 @@
 # Copyright 2013 Andrey Kolev
 # Distributed under MIT license (see LICENSE.md)
 
-type GarchFit
+mutable struct GarchFit
   data::Vector
   params::Vector
   llh::Float64
diff --git a/src/kalman_filter.jl b/src/kalman_filter.jl
index d4bc924..85f5def 100644
--- a/src/kalman_filter.jl
+++ b/src/kalman_filter.jl
@@ -1,4 +1,4 @@
-type KalmanFiltered{T}
+mutable struct KalmanFiltered{T}
     filtered::Array{T}
     predicted::Array{T}
     error_cov::Array{T}
@@ -9,7 +9,7 @@ type KalmanFiltered{T}
     loglik::T
 end
 
-function Base.show{T}(io::IO, filt::KalmanFiltered{T})
+function Base.show(io::IO, filt::KalmanFiltered{T}) where T
     n = size(filt.y, 1)
     dx, dy = filt.model.nx, filt.model.ny
     println("KalmanFiltered{$T}")
@@ -17,7 +17,7 @@ function Base.show{T}(io::IO, filt::KalmanFiltered{T})
     println("Negative log-likelihood: $(filt.loglik)")
 end
 
-function kalman_filter{T}(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=zeros(size(y,1), model.nu))
+function kalman_filter(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=zeros(size(y,1), model.nu)) where T
 
     @assert size(u,1) == size(y,1)
     @assert size(y,2) == model.ny
@@ -72,7 +72,7 @@ function kalman_filter{T}(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=ze
     return KalmanFiltered(x_filt', x_pred', P_filt, P_pred, model, y', u', log_likelihood)
 end
 
-function loglikelihood{T}(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=zeros(size(y,1), model.nu))
+function loglikelihood(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=zeros(size(y,1), model.nu)) where T
 
 
     y, u = y', u'
diff --git a/src/kalman_smooth.jl b/src/kalman_smooth.jl
index aa76725..d8664ab 100644
--- a/src/kalman_smooth.jl
+++ b/src/kalman_smooth.jl
@@ -1,4 +1,4 @@
-type KalmanSmoothed{T}
+mutable struct KalmanSmoothed{T}
 	predicted::Array{T}
 	filtered::Array{T}
 	smoothed::Array{T}
@@ -9,7 +9,7 @@ type KalmanSmoothed{T}
 	loglik::T
 end
 
-type KalmanSmoothedMinimal{T}
+mutable struct KalmanSmoothedMinimal{T}
 	y::Array{T}
 	smoothed::Array{T}
 	error_cov::Union{Vector{Matrix{T}}, Vector{SparseMatrixCSC{T, Int}}}
@@ -18,7 +18,7 @@ type KalmanSmoothedMinimal{T}
 	loglik::T
 end
 
-function show{T}(io::IO, smoothed::KalmanSmoothed{T})
+function show(io::IO, smoothed::KalmanSmoothed{T}) where T
     n = size(smoothed.y, 1)
     dx, dy = smoothed.model.nx, smoothed.model.ny
     println("KalmanSmoothed{$T}")
@@ -26,7 +26,7 @@ function show{T}(io::IO, smoothed::KalmanSmoothed{T})
     println("Negative log-likelihood: $(smoothed.loglik)")
 end
 
-function show{T}(io::IO, smoothed::KalmanSmoothedMinimal{T})
+function show(io::IO, smoothed::KalmanSmoothedMinimal{T}) where T
     n = size(smoothed.y, 1)
     dx, dy = smoothed.model.nx, smoothed.model.ny
     println("KalmanSmoothedMinimal{$T}")
@@ -35,7 +35,7 @@ function show{T}(io::IO, smoothed::KalmanSmoothedMinimal{T})
 end
 
 # Durbin-Koopman Smoothing
-function kalman_smooth{T}(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=zeros(size(y,1), model.nu))
+function kalman_smooth(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=zeros(size(y,1), model.nu)) where T
 
     Ksparse = issparse(model.A(1)) && issparse(model.V(1)) && issparse(model.C(1))
 
@@ -154,7 +154,7 @@ function kalman_smooth{T}(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=ze
 
 end #smooth
 
-function lag1_smooth{T}(y::Array{T}, u::Array{T}, m::StateSpaceModel{T})
+function lag1_smooth(y::Array{T}, u::Array{T}, m::StateSpaceModel{T}) where T
 
     A_0, A_I  = zeros(m.A(1)), eye(m.A(1))
     B_0, V_0, C_0 = zeros(m.B(1)), zeros(m.V(1)), zeros(m.C(1))
diff --git a/src/parameter_estimation.jl b/src/parameter_estimation.jl
index ebc7f2c..52c3e18 100644
--- a/src/parameter_estimation.jl
+++ b/src/parameter_estimation.jl
@@ -1,7 +1,7 @@
 # ML parameter estimation with filter result log-likelihood (via Nelder-Mead)
 
-function fit{T}(y::Matrix{T}, build::Function, theta0::Vector{T};
-          u::Array{T}=zeros(size(y,1), build(theta0).nu))
+function fit(y::Matrix{T}, build::Function, theta0::Vector{T};
+       u::Array{T}=zeros(size(y,1), build(theta0).nu)) where T
     objective(theta) = kalman_filter(y, build(theta), u=u).loglik
     kfit = Optim.optimize(objective, theta0)
     return (kfit.minimum, build(kfit.minimum), filter(y, build(kfit.minimum)))
@@ -9,8 +9,8 @@ end #fit
 
 # Expectation-Maximization (EM) parameter estimation
 
-function fit{T}(y::Array{T}, pmodel::ParametrizedSSM, params::SSMParameters;
-          u::Array{T}=zeros(size(y,1), pmodel.nu), eps::Float64=1e-6, niter::Int=typemax(Int))
+function fit(y::Array{T}, pmodel::ParametrizedSSM, params::SSMParameters;
+       u::Array{T}=zeros(size(y,1), pmodel.nu), eps::Float64=1e-6, niter::Int=typemax(Int)) where T
 
     n = size(y, 1)
     @assert n == size(u, 1)
@@ -62,7 +62,7 @@ function fit{T}(y::Array{T}, pmodel::ParametrizedSSM, params::SSMParameters;
     estimate_A, estimate_B, estimate_Q, estimate_C, estimate_D, estimate_R,
         estimate_x1, estimate_S = map(x->x>0, [na, nb, nq, nc, nd, nr, nx1, ns])
 
-    function em_kernel!{T}(params::SSMParameters{T})
+    function em_kernel!(params::SSMParameters{T}) where T
 
         m = pmodel(params)
 
@@ -337,8 +337,8 @@ function fit{T}(y::Array{T}, pmodel::ParametrizedSSM, params::SSMParameters;
 
 end #fit
 
-function fit{T}(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=zeros(size(y,1), model.nu),
-              eps::Float64=1e-6, niter::Int=typemax(Int))
+function fit(y::Array{T}, model::StateSpaceModel{T}; u::Array{T}=zeros(size(y,1), model.nu),
+           eps::Float64=1e-6, niter::Int=typemax(Int)) where T
 
     # B, Z, x1 default to parametrized as fully unconstrained
     A, A_params = parametrize_full(model.A(1))
diff --git a/src/statespacemodel.jl b/src/statespacemodel.jl
index df1d128..6d87954 100644
--- a/src/statespacemodel.jl
+++ b/src/statespacemodel.jl
@@ -1,6 +1,6 @@
 abstract type AbstractStateSpaceModel{T<:Real} end
 
-immutable StateSpaceModel{T} <: AbstractStateSpaceModel{T}
+struct StateSpaceModel{T} <: AbstractStateSpaceModel{T}
 
     # Process transition matrix, control matrix, and noise covariance
     A::Function
@@ -36,20 +36,20 @@ immutable StateSpaceModel{T} <: AbstractStateSpaceModel{T}
 end
 
 # Time-dependent constructor
-StateSpaceModel{T}(A::Function, V::Function, C::Function, W::Function,
-                          x1::Vector{T}, P1::Union{Matrix{T}, SparseMatrixCSC{T}};
-                          B::Function=_->zeros(size(V(1), 1), 1),
-                          D::Function=_->zeros(size(W(1), 1), 1)) =
+StateSpaceModel(A::Function, V::Function, C::Function, W::Function,
+                       x1::Vector{T}, P1::Union{Matrix{T}, SparseMatrixCSC{T}};
+                       B::Function=_->zeros(size(V(1), 1), 1),
+                       D::Function=_->zeros(size(W(1), 1), 1)) where {T} =
 	  StateSpaceModel{T}(A, B, V, C, D, W, x1, P1)
 
 # Time-independent constructor
-StateSpaceModel{T}(A::Matrix{T}, V::Matrix{T}, C::Matrix{T}, W::Matrix{T},
-                          x1::Vector{T}, P1::Union{Matrix{T}, SparseMatrixCSC{T}};
-                          B::Matrix{T}=zeros(size(A, 1), 1),
-                          D::Matrix{T}=zeros(size(C, 1), 1)) =
+StateSpaceModel(A::Matrix{T}, V::Matrix{T}, C::Matrix{T}, W::Matrix{T},
+                       x1::Vector{T}, P1::Union{Matrix{T}, SparseMatrixCSC{T}};
+                       B::Matrix{T}=zeros(size(A, 1), 1),
+                       D::Matrix{T}=zeros(size(C, 1), 1)) where {T} =
 	  StateSpaceModel{T}(_->A, _->B, _->V, _->C, _->D, _->W, x1, P1)
 
-function show{T}(io::IO, mod::StateSpaceModel{T})
+function show(io::IO, mod::StateSpaceModel{T}) where T
     dx, dy = mod.nx, mod.ny
     println("StateSpaceModel{$T}, $dx-D process x $dy-D observations")
     println("Process evolution matrix A:")
@@ -68,7 +68,7 @@ end
 
 # Time-independent parametrized matrix type
 # TODO: A more general ParametrizedArray (allowing vectors) could be preferable
-immutable ParametrizedMatrix{T}
+struct ParametrizedMatrix{T}
 
     f::AbstractVector{T}
     D::Union{Matrix{T}, SparseMatrixCSC{T}}
@@ -84,13 +84,13 @@ immutable ParametrizedMatrix{T}
 
 end #ParametrizedMatrix
 
-ParametrizedMatrix{T}(f::Vector{T}, D::Matrix{T}, dims::Tuple{Int, Int}) = ParametrizedMatrix{T}(f, D, dims)
+ParametrizedMatrix(f::Vector{T}, D::Matrix{T}, dims::Tuple{Int, Int}) where {T} = ParametrizedMatrix{T}(f, D, dims)
 
-function ParametrizedMatrix{T}(f::SparseVector{T}, D::SparseMatrixCSC{T}, dims::Tuple{Int, Int})
+function ParametrizedMatrix(f::SparseVector{T}, D::SparseMatrixCSC{T}, dims::Tuple{Int, Int}) where T
     ParametrizedMatrix{T}(f, D, dims)
 end #ParametrizedMatrix
 
-function show{T}(io::IO, cpm::ParametrizedMatrix{T})
+function show(io::IO, cpm::ParametrizedMatrix{T}) where T
 
     function combinestrelems(a, b)
         if (a != "") & (b != "")
@@ -137,10 +137,10 @@ function (pm::ParametrizedMatrix{T})(params::Vector{T}) where {T}
         reshape(pm.f + pm.D * sparse(params), pm.dims)
 end #call
 
-parametrize_full{T}(X::Matrix{T}) =
+parametrize_full(X::Matrix{T}) where {T} =
         ParametrizedMatrix{T}(zeros(length(X)), eye(length(X)), size(X))
 
-function parametrize_diag{T}(x::Vector{T}; sparse=false)
+function parametrize_diag(x::Vector{T}; sparse=false) where T
     n = length(x)
     f = sparse ? spzeros(n^2, 1) : zeros(n^2)
     D = sparse ? spzeros(n^2, n) : zeros(n^2, n)
@@ -148,14 +148,14 @@ function parametrize_diag{T}(x::Vector{T}; sparse=false)
     return ParametrizedMatrix{T}(f, D, (n,n))
 end #parametrize_diag
 
-parametrize_none{T}(X::Matrix{T}) =
+parametrize_none(X::Matrix{T}) where {T} =
         ParametrizedMatrix{T}(vec(X), zeros(length(X), 0), size(X))
 
-parametrize_none{T}(X::SparseMatrixCSC{T}) =
+parametrize_none(X::SparseMatrixCSC{T}) where {T} =
         ParametrizedMatrix{T}(vec(X), spzeros(length(X), 0), size(X))
 
 # Time-independent parametrized state space model
-immutable ParametrizedSSM{T} <: AbstractStateSpaceModel{T}
+struct ParametrizedSSM{T} <: AbstractStateSpaceModel{T}
 
     # Transition equation and noise covariance
 
@@ -207,21 +207,21 @@ immutable ParametrizedSSM{T} <: AbstractStateSpaceModel{T}
 
 end #ParametrizedSSM
 
-ParametrizedSSM{T}(A2::ParametrizedMatrix{T}, Q::ParametrizedMatrix{T},
-                          C2::ParametrizedMatrix{T}, R::ParametrizedMatrix{T},
-                          x1::ParametrizedMatrix{T}, S::ParametrizedMatrix{T};
-                          A1::Function=_->speye(size(A2,1)), A3::Function=_->speye(size(A2,2)),
-                          B1::Function=_->speye(size(x1,1)),
-                          B2::ParametrizedMatrix{T}=parametrize_none(spzeros(size(B1(1),2), 1)),
-                          G::Function=_->speye(size(x1,1)),
-                          C1::Function=_->speye(size(C2, 1)), C3::Function=_->speye(size(C2,2)),
-                          D1::Function=_->speye(size(C1(1),1)),
-                          D2::ParametrizedMatrix{T}=parametrize_none(spzeros(size(C1(1),1), 1)),
-                          H::Function=_->speye(size(C1(1),1)), J::AbstractMatrix=speye(size(x1, 1))) =
+ParametrizedSSM(A2::ParametrizedMatrix{T}, Q::ParametrizedMatrix{T},
+                       C2::ParametrizedMatrix{T}, R::ParametrizedMatrix{T},
+                       x1::ParametrizedMatrix{T}, S::ParametrizedMatrix{T};
+                       A1::Function=_->speye(size(A2,1)), A3::Function=_->speye(size(A2,2)),
+                       B1::Function=_->speye(size(x1,1)),
+                       B2::ParametrizedMatrix{T}=parametrize_none(spzeros(size(B1(1),2), 1)),
+                       G::Function=_->speye(size(x1,1)),
+                       C1::Function=_->speye(size(C2, 1)), C3::Function=_->speye(size(C2,2)),
+                       D1::Function=_->speye(size(C1(1),1)),
+                       D2::ParametrizedMatrix{T}=parametrize_none(spzeros(size(C1(1),1), 1)),
+                       H::Function=_->speye(size(C1(1),1)), J::AbstractMatrix=speye(size(x1, 1))) where {T} =
           ParametrizedSSM{T}(A1, A2, A3, B1, B2, G, Q, C1, C2, C3, D1, D2, H, R, x1, J, S)
 
 # State space model parameters
-immutable SSMParameters{T}
+struct SSMParameters{T}
 
     # Process transition and noise covariance
     A::Vector{T}
@@ -239,9 +239,9 @@ immutable SSMParameters{T}
 
 end #SSMParameters
 
-SSMParameters{T}(__::T; A::Vector{T}=T[], B::Vector{T}=T[], Q::Vector{T}=T[],
-                  C::Vector{T}=T[], D::Vector{T}=T[], R::Vector{T}=T[],
-                  x1::Vector{T}=T[], S::Vector{T}=T[]) =
+SSMParameters(__::T; A::Vector{T}=T[], B::Vector{T}=T[], Q::Vector{T}=T[],
+               C::Vector{T}=T[], D::Vector{T}=T[], R::Vector{T}=T[],
+               x1::Vector{T}=T[], S::Vector{T}=T[]) where {T} =
               SSMParameters{T}(A, B, Q, C, D, R, x1, S)
 
 function (m::ParametrizedSSM{T})(p::SSMParameters{T}) where {T}
@@ -281,13 +281,13 @@ function confirm_matrix_sizes(F::AbstractMatrix, B::AbstractMatrix, V::AbstractM
 
 end #confirm_matrix_sizes
 
-function confirm_matrix_sizes{T}(A1::AbstractMatrix, A2::ParametrizedMatrix{T}, A3::AbstractMatrix,
-                              B1::AbstractMatrix, B2::ParametrizedMatrix{T},
-                              G::AbstractMatrix, Q::ParametrizedMatrix{T},
-                              C1::AbstractMatrix, C2::ParametrizedMatrix{T}, C3::AbstractMatrix,
-                              D1::AbstractMatrix, D2::ParametrizedMatrix{T},
-                              H::AbstractMatrix, R::ParametrizedMatrix{T},
-                              x1::ParametrizedMatrix{T}, J::AbstractMatrix, S::ParametrizedMatrix{T})
+function confirm_matrix_sizes(A1::AbstractMatrix, A2::ParametrizedMatrix{T}, A3::AbstractMatrix,
+                           B1::AbstractMatrix, B2::ParametrizedMatrix{T},
+                           G::AbstractMatrix, Q::ParametrizedMatrix{T},
+                           C1::AbstractMatrix, C2::ParametrizedMatrix{T}, C3::AbstractMatrix,
+                           D1::AbstractMatrix, D2::ParametrizedMatrix{T},
+                           H::AbstractMatrix, R::ParametrizedMatrix{T},
+                           x1::ParametrizedMatrix{T}, J::AbstractMatrix, S::ParametrizedMatrix{T}) where T
 
     @assert size(B2, 2) == size(D2, 2)
 
@@ -345,7 +345,7 @@ Arguments:
   u : Array (optional)
   n x nu array of exogenous inputs
 "
-function simulate{T}(model::StateSpaceModel{T}, n::Int; u::Array{T}=zeros(n, model.nu))
+function simulate(model::StateSpaceModel{T}, n::Int; u::Array{T}=zeros(n, model.nu)) where T
     @assert size(u, 1) == n
     @assert size(u, 2) == model.nu