improve docs and readme (#35)

* improve docs and readme

* change theta to f

* improve text

Author: raphaelsaavedra

.gitignore

@@ -1,2 +1,4 @@
 Manifest.toml
-docs/build/
+docs/build/
+.DS_Store
+docs/.DS_Store

README.md

@@ -13,10 +13,11 @@
 ScoreDrivenModels.jl is a Julia package for modeling, forecasting and simulating time series with score-driven models, also known as dynamic conditional score models (DCS) or generalized autoregressive score models (GAS). Implementations are based on the paper [Generalized Autoregressive Models with Applications](http://dx.doi.org/10.1002/jae.1279) by D. Creal, S. J. Koopman and A. Lucas.
 
 # Features
-* SARIMA structure
+* Autoregressive structure
 * Maximum likelihood estimation
 * Monte Carlo simulation
-* Several available distributions:
+* General link/unlink interface
+* Available distributions:
   * Normal
   * Lognormal
   * Poisson
@@ -25,4 +26,5 @@ ScoreDrivenModels.jl is a Julia package for modeling, forecasting and simulating
 
 # Roadmap
 * Weibull distribution
-* Unobserved components structure
+* Student's t distribution
+* Dynamic components structure

docs/src/manual.md

@@ -2,6 +2,8 @@
 
 ## Links
 
+Links are reparametrizations utilized in the estimation. For example, if we want to estimate a parameter ``f`` which is by definition strictly positive, then an obvious way to estimate ``f`` via numerical optimization is to model ``\tilde{f} = \ln{f}``. We refer to this procedure as **linking**. After obtaining the optimal value of ``\tilde{f}``, we can then **unlink** it to obtain ``f`` by computing ``f = e^{\tilde{f}}``.
+
 ### Types of links
 
 The abstract type `Link` subsumes any type of link that can be expressed.

src/ScoreDrivenModels.jl

@@ -25,7 +25,7 @@ include("distributions/common_interface.jl")
 include("distributions/normal.jl")
 include("distributions/poisson.jl")
 include("distributions/beta.jl")
-include("distributions/log_normal.jl")
+include("distributions/lognormal.jl")
 include("distributions/gamma.jl")
 include("distributions/weibull.jl")
 

src/distributions/log_normal.jl renamed to src/distributions/lognormal.jl

@@ -10,7 +10,7 @@ function link end
 """
     unlink(args...)
 
-The unlink function is the inverse map of [`link`](@ref link). It brings ``\\tilde f`` in ``\\mathbb{R}`` to the subspace ``\\mathcal{F} \\subset \\mathbb{R}``.
+The unlink function is the inverse map of [`link`](@ref link). It brings ``\\tilde{f}`` in ``\\mathbb{R}`` to the subspace ``\\mathcal{F} \\subset \\mathbb{R}``.
 """
 function unlink end
 
@@ -24,7 +24,7 @@ function jacobian_link end
 """
     IdentityLink <: Link
 
-Define the map ``\\ \\tilde f = f`` where ``\\ \\tilde f \\in \\mathbb{R}`` and ``\\ \\tilde f \\in \\mathbb{R}``
+Define the map ``\\tilde{f} = f`` where ``\\tilde{f} \\in \\mathbb{R}`` and ``\\tilde{f} \\in \\mathbb{R}``
 """
 struct IdentityLink <: Link end
 
@@ -35,7 +35,7 @@ jacobian_link(::Type{IdentityLink}, param_tilde::T) where T = one(T)
 """
     LogLink <: Link
 
-Define the map ``\\ \\tilde f = \\ln(f - a)`` where ``\\ f \\in [a, \\infty), a \\in \\mathbb{R}`` and ``\\ \\tilde f \\in \\mathbb{R}``
+Define the map ``\\tilde{f} = \\ln(f - a)`` where ``f \\in [a, \\infty), a \\in \\mathbb{R}`` and ``\\tilde{f} \\in \\mathbb{R}``
 """
 struct LogLink <: Link end