Added examples to docs

Author: NikitaKishore

src/arma.jl

@@ -139,6 +139,27 @@ and the inverse Fourier transform.
 - `arma::ARMA`: Instance of `ARMA` type
 - `;num_autocov::Integer(16)` : The number of autocovariances to calculate
 
+##### Returns
+
+- `acov::Vector{Float64}`: `acov[j]` is the autocovariance between two elements with a lag j.
+
+##### Examples
+
+```julia
+using Plots
+
+# AR(2) process
+ar = ARMA([0.8 , 0.5], Vector{Float64}(),1)
+ar_acov = autocovariance(ar)
+plot(1:length(ar_acov),ar_acov,color=:blue, lw=2, marker=:circle, markersize=3, label = "autocovariance")
+
+# ARMA(2,2) process
+lp = ARMA([0.8, 0.5], [0.7, 0.3], 0.5)
+lp_acov = autocovariance(lp, num_autocov = 50)
+plot(1:length(lp_acov),lp_acov,color=:blue, lw=2, marker=:circle, markersize=3, label = "autocovariance")
+
+```
+
 """
 function autocovariance(arma::ARMA; num_autocov::Integer=16)
     # Compute the autocovariance function associated with ARMA process arma
@@ -163,6 +184,21 @@ Get the impulse response corresponding to our model.
 - `psi::Vector{Float64}`: `psi[j]` is the response at lag j of the impulse
   response. We take `psi[1]` as unity.
 
+##### Examples
+
+```julia
+using Plots
+
+lp1 = ARMA([0.5],[0.5],1)
+response1 = impulse_response(lp1)
+plot(1:length(response1),response1,color=:blue, lw=2, marker=:circle, markersize=3)
+
+lp2 = ARMA([0.8, 0.5], [0.7, 0.3], 0.5)
+response2 = impulse_response(lp2)
+plot(1:length(response2),response2,color=:blue, lw=2, marker=:circle, markersize=3)
+
+```
+
 """
 function impulse_response(arma::ARMA; impulse_length=30)
     # Compute the impulse response function associated with ARMA process arma

src/markov/mc_tools.jl

@@ -27,6 +27,19 @@ state transitions.
 
 - `p::AbstractMatrix` : The transition matrix. Must be square, all elements must be nonnegative, and all rows must sum to unity.
 - `state_values::AbstractVector` : Vector containing the values associated with the states.
+
+##### Examples
+
+```julia
+# Without labelling states
+p1 = [1 0 0; 0 1 0; 0 0 1]
+mc1 = MarkovChain(p1)
+
+#Including labels for states
+p2 = [0.3 0.7; 0.25 0.75]
+states = ["unemployed", "employed"]
+mc2 = MarkovChain(p2, states)
+```
 """
 mutable struct MarkovChain{T, TM<:AbstractMatrix{T}, TV<:AbstractVector}
     p::TM # valid stochastic matrix

src/modeltools/utility.jl

@@ -15,6 +15,16 @@ Additionally, this code assumes that if c < 1e-10 then
 
 u(c) = log(1e-10) + 1e10*(c - 1e-10)
 
+##### Examples
+
+```julia
+u1 = LogUtility()
+u1(10.)
+u1.([1.e-15, 1.e15])
+u2 = LogUtility(10)
+u2.([10., 1.e-15])
+```
+
 """
 struct LogUtility <: AbstractUtility
     ξ::Float64

src/zeros.jl

@@ -114,6 +114,18 @@ sequentially with any bracketing pairs that are found.
 - `x1b::Vector{T}`: `Vector` of lower borders of bracketing intervals
 - `x2b::Vector{T}`: `Vector` of upper borders of bracketing intervals
 
+##### Examples
+
+```julia
+x1a, x2a = divide_bracket(sin, -100., 100.)
+
+function poly(x)
+    return x^2 - 2x + 1
+end
+x1b, x2b = divide_bracket(poly, -1., 1., 100)
+
+```
+
 ##### References
 
 This is `zbrack` from Numerical Recepies Recepies in C++