using InstantiateFromURL
github_project("QuantEcon/quantecon-notebooks-julia", version = "0.2.0")

using LinearAlgebra, Statistics, Compat

using QuantEcon, Plots, Random
Random.seed!(42) # For reproducible results.

n = 40              # Data size
ϕ = 0.5             # AR parameter
θ = [0, -0.8]       # MA parameter
σ = 1.0
lp = ARMA(ϕ, θ, σ)
X = simulation(lp, ts_length = n)

x, y = periodogram(X)
x_sd, y_sd = spectral_density(lp, two_pi=false, res=120)

plot(x, y,linecolor="blue", linewidth=2, linealpha=0.5, lab="periodogram")
plot!(x_sd, y_sd, linecolor="red", linewidth=2, linealpha=0.8, lab="spectral density")

function hanning_window(M)
    w = [0.5 - 0.5 * cos(2 * pi * n / (M - 1)) for n = 0:(M-1)]
    return w
end

window = hanning_window(25) / sum(hanning_window(25))
x = range(-12, 12, length = 25)
plot(x, window, color="darkblue", title="Hanning window", ylabel="Weights",
    xlabel="Position in sequence of weights", legend=false, grid=false)

n = 400
ϕ = 0.5
θ = [0, -0.8]
σ = 1.0
lp = ARMA(ϕ, θ, 1.0)
X = simulation(lp, ts_length = n)

xs = []
x_sds = []
x_sms = []
ys = []
y_sds = []
y_sms = []
titles = []

for (i, wl) in enumerate([15, 55, 175])  # window lengths
    x, y = periodogram(X)
    push!(xs, x)
    push!(ys, y)

    x_sd, y_sd = spectral_density(lp, two_pi=false, res=120)
    push!(x_sds, x_sd)
    push!(y_sds, y_sd)

    x, y_smoothed = periodogram(X, "hamming", wl)
    push!(x_sms, x)
    push!(y_sms, y_smoothed)

    t = "window length = $wl"
    push!(titles, t)
end

plot(xs, ys, layout=(3,1), color=:blue, alpha=0.5,
    linewidth=2, label=["periodogram" "" ""])
plot!(x_sds, y_sds, layout=(3,1), color=:red, alpha=0.8,
    linewidth=2, label=["spectral density" "" ""])
plot!(x_sms, y_sms, layout=(3,1), color=:black,
    linewidth=2, label=["smoothed periodogram" "" ""])
plot!(title=reshape(titles,1,length(titles)))

lp2 = ARMA(-0.9, 0.0, 1.0)
wl = 65
p = plot(layout=(3,1))

for i in 1:3
    X = simulation(lp2,ts_length=150)
    plot!(p[i],xlims = (0,pi))

    x_sd, y_sd = spectral_density(lp2,two_pi=false, res=180)
    plot!(p[i],x_sd, y_sd, linecolor=:red, linestyle=:solid,
        yscale=:log10, linewidth=2, linealpha=0.75,
        label="spectral density",legend=:topleft)

    x, y_smoothed = periodogram(X, "hamming", wl)
    plot!(p[i],x, y_smoothed, linecolor=:black, linestyle=:solid,
        yscale=:log10, linewidth=2, linealpha=0.75,
        label="standard smoothed periodogram",legend=:topleft)

    x, y_ar = ar_periodogram(X, "hamming", wl)
    plot!(p[i],x, y_ar, linecolor=:blue, linestyle=:solid,
        yscale=:log10, linewidth=2, linealpha=0.75,
        label="AR smoothed periodogram",legend=:topleft)
end
p