In [20]:

    

using Distributions
using PyPlot


    

In [1]:

    

import Base: +
+(x::Integer, y::ASCIIString) = x + parse(Int, y)


    

    
Out[1]:





+ (generic function with 172 methods)

In [13]:

    

super(Array)
super(DenseArray{Int, 3})
super(AbstractArray{Int, 3})
super(AbstractVector{Int64})


    

    
Out[13]:





Any

In [14]:

    

function sum_array(x)
    sum = 0.0
    for i in 1:length(x)
        sum += x[i]
    end
    return sum
end


    

    
Out[14]:





sum_array (generic function with 1 method)

In [17]:

    

x = linspace(0, 1, 1e6)
y = Any[i/1e6 for i in 0:1e6]

@time sum_array(x)
@time sum_array(y)


    

    




  0.007001 seconds (5 allocations: 176 bytes)
  0.153992 seconds (1.00 M allocations: 15.259 MB, 73.14% gc time)






    
Out[17]:





500000.50000000006

In [30]:

    

type AR1
    a::Real
    b::Real
    sigma::Real
    phi::Distribution
end

function simulate(m::AR1, initial::Real=0.0, repeat::Int=100)
    x_list = Array{Float64}(repeat)
    eps_list = rand(m.phi, repeat)
    x = initial
    
    for i in 1:repeat
        x_list[i] = m.a * x + m.b + m.sigma * eps_list[i]
        x = x_list[i]
    end
    
    return x_list
end


    

    
Out[30]:





simulate (generic function with 3 methods)

In [31]:

    

srand(620)
m = AR1(0.8, 0, 1, Normal(0, 1))
xs = simulate(m, 0, 500)

for x in xs[1:20]
    println(x)
end


    

    




-0.538747415114494
-2.9200983440736206
-3.1806298688602768
-2.049244090628807
-3.652167563577761
-4.929235226749336
-3.049487744595497
-2.999479471291362
-2.0989108105129666
-2.3482040748798787
-1.835165237532889
-1.3196409623902379
-0.1566662297912722
-0.7271499184699923
-1.5569134509991573
-1.5591628346730282
-0.6373032944153231
-0.5493531663308254
0.0833119549551038
0.3151575935026018

In [32]:

    

plot(xs)


    

    













    
Out[32]:





1-element Array{Any,1}:
 PyObject <matplotlib.lines.Line2D object at 0x31fc5b7f0>