small demo file running hurst calcs for creating plots added to examp…

…les/ directory

examples/hurst.jl

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+#using Revise
+using Indicators, Distributions
+using Plots
+pyplot()
+
+# define inputs
+seed = 0
+N = 1_000
+
+# produce toy data
+seed > 0 ? srand(seed) : nothing
+r = rand(Normal(0, 1/252), N)
+R = cumprod(1.0+r)
+t = 2:N
+t = [2^i for i in 1:floor(Int, log2(size(r,1)))]
+beta, x, y = Indicators.hurst_exponent(r, t=t)
+h = beta[end]
+
+# generate visualizations
+p1 = plot(R, xlabel="Time", ylabel="Return", color=:red, label="Cumulative Returns")
+p2 = histogram(r, xlabel="Return", ylabel="Frequency", color=:orange, label="Returns Distribution")
+if length(beta) == 1
+    p3 = plot(x, y, xlabel="Sample Size", ylabel="Rescaled Range", color=:blue, label="Rescaled Range by Period Length")
+    reg_x = [0; x[end]]
+    reg_y = [0; beta[1]*x[end]]
+else
+    p3 = plot(x[:,2], y, xlabel="Sample Size", ylabel="Rescaled Range", color=:blue, label="Rescaled Range by Period Length")
+    reg_x = [0; x[end]]
+    reg_y = [beta[1], beta[2]*x[end]+beta[1]]
+end
+plot!(p3, reg_x, reg_y, color=:green, label="Hurst Exponent Estimation")
+
+# aggregate the plots together
+plot(p1, p2, p3, layout=(3,1))