// simple port of the python code
// from this excellent article 
// https://www.quantstart.com/articles/Basics-of-Statistical-Mean-Reversion-Testing
open System

let gbmts ()  =
    let random =  MathNet.Numerics.Random.SystemRandomSource.FastDoubles(10000)
    random |> Array.fold (fun st x -> st@[((List.last st)+(x-0.5))] ) [1000.0]  |> Seq.toArray

let mrevts ()  =
    MathNet.Numerics.Random.SystemRandomSource.FastDoubles(10000)
       
let trendts ()  =
    let random =  MathNet.Numerics.Random.SystemRandomSource.FastDoubles(10000)
    random |> Array.fold (fun st x -> st@[((List.last st)+(x+1.0))] ) [1000.0]  |> Seq.toArray

let difvec (vecin:float []) lag =
    let vsub = vecin |> Array.skip lag 
    let dif = vsub |> Array.mapi(fun i x -> x - vecin.[i]  )
    MathNet.Numerics.Statistics.ArrayStatistics.StandardDeviation(dif) |> sqrt

let hurst (vecpriceraw:double array) =
    let vecprice = vecpriceraw |> Array.map(log)
    let range = [|2..100|]
    let lagvec = range |> Array.map (difvec vecprice)
    let logvec = lagvec |> Array.map (log)
    let loglag = range |>  Array.map(float >> log)
    let (_,slope) = MathNet.Numerics.LinearRegression.SimpleRegression.Fit (loglag,logvec)
    slope*2.0
/// test the hurst exponent
/// > gbmts() |> hurst;;
/// val it : float = 0.5092820778
/// > mrevts() |> hurst;;
/// val it : float = -0.0003832790107
/// > trendts() |> hurst;;
/// val it : float = 0.9824236056