Correlation

Binder

Summary: This tutorial demonstrates how to autocorrelate a signal in FSharp.Stats

Table of contents

Autocorrelation

Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.

open FSharp.Stats
open FSharp.Stats.Distributions
open FSharp.Stats.Distributions.Continuous
open FSharp.Stats.Correlation

let lags = [0..100]
let x = [0. .. 100.]

//// Autocorrelation of a gaussian signal
let gaussPDF = Normal.PDF 10. 2.
let yGauss = x |> List.map gaussPDF |> vector

let autoCorrGauss = lags |> List.map (fun lag -> autoCorrelation lag yGauss)

open Plotly.NET

let gaussAC =
    Chart.Point(lags,autoCorrGauss)
    |> Chart.withTraceName "Autocorrelation"
    |> Chart.withTitle "Autocorrelation of a gaussian sine wave"
    |> fun c -> Chart.Stack 1 [Chart.Point(x,yGauss,Name="gaussian");c]
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namespace FSharp

--------------------
namespace Microsoft.FSharp
namespace FSharp.Stats
namespace FSharp.Stats.Distributions
module Continuous

from FSharp.Stats.Distributions
module Correlation

from FSharp.Stats
val lags : int list
val x : float list
val gaussPDF : (float -> float)
type Normal =
  static member CDF : mu:float -> sigma:float -> x:float -> float
  static member Estimate : samples:seq<float> -> Distribution<float,float>
  static member Mean : mu:float -> sigma:float -> float
  static member PDF : mu:float -> sigma:float -> x:float -> float
  static member Sample : mu:float -> sigma:float -> float
  static member StandardDeviation : mu:float -> sigma:float -> float
  static member Support : mu:float -> sigma:float -> float * float
  static member Variance : mu:float -> sigma:float -> float
  static member init : mu:float -> sigma:float -> Distribution<float,float>
static member Normal.PDF : mu:float -> sigma:float -> x:float -> float
val yGauss : Vector<float>
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module List

from FSharp.Stats

--------------------
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
  | ( [] )
  | ( :: ) of Head: 'T * Tail: 'T list
    interface IReadOnlyList<'T>
    interface IReadOnlyCollection<'T>
    interface IEnumerable
    interface IEnumerable<'T>
    member GetReverseIndex : rank:int * offset:int -> int
    member GetSlice : startIndex:int option * endIndex:int option -> 'T list
    member Head : 'T
    member IsEmpty : bool
    member Item : index:int -> 'T with get
    member Length : int
    ...
val map : mapping:('T -> 'U) -> list:'T list -> 'U list
Multiple items
val vector : l:seq<float> -> Vector<float>

--------------------
type vector = Vector<float>
val autoCorrGauss : float list
val lag : int
val autoCorrelation : lag:int -> v1:vector -> float
namespace Plotly
namespace Plotly.NET
val gaussAC : GenericChart.GenericChart
type Chart =
  static member Area : xy:seq<#IConvertible * #IConvertible> * ?Name:string * ?ShowMarkers:bool * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<string> * ?TextPosition:TextPosition * ?TextFont:Font * ?Dash:DrawingStyle * ?Width:'a2 -> GenericChart
  static member Area : x:seq<#IConvertible> * y:seq<#IConvertible> * ?Name:string * ?ShowMarkers:bool * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<string> * ?TextPosition:TextPosition * ?TextFont:Font * ?Dash:DrawingStyle * ?Width:'a2 -> GenericChart
  static member Bar : keysvalues:seq<#IConvertible * #IConvertible> * ?Name:string * ?Showlegend:bool * ?Color:'a2 * ?Opacity:float * ?Labels:seq<string> * ?TextPosition:TextPosition * ?TextFont:Font * ?Marker:Marker -> GenericChart
  static member Bar : keys:seq<#IConvertible> * values:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?Color:'a2 * ?Opacity:float * ?Labels:seq<string> * ?TextPosition:TextPosition * ?TextFont:Font * ?Marker:Marker -> GenericChart
  static member BoxPlot : xy:seq<'a0 * 'a1> * ?Name:string * ?Showlegend:bool * ?Color:string * ?Fillcolor:'a2 * ?Opacity:float * ?Whiskerwidth:'a3 * ?Boxpoints:Boxpoints * ?Boxmean:BoxMean * ?Jitter:'a4 * ?Pointpos:'a5 * ?Orientation:Orientation * ?Marker:Marker * ?Line:Line * ?Alignmentgroup:'a6 * ?Offsetgroup:'a7 * ?Notched:bool * ?NotchWidth:float * ?QuartileMethod:QuartileMethod -> GenericChart
  static member BoxPlot : ?x:'a0 * ?y:'a1 * ?Name:string * ?Showlegend:bool * ?Color:string * ?Fillcolor:'a2 * ?Opacity:float * ?Whiskerwidth:'a3 * ?Boxpoints:Boxpoints * ?Boxmean:BoxMean * ?Jitter:'a4 * ?Pointpos:'a5 * ?Orientation:Orientation * ?Marker:Marker * ?Line:Line * ?Alignmentgroup:'a6 * ?Offsetgroup:'a7 * ?Notched:bool * ?NotchWidth:float * ?QuartileMethod:QuartileMethod -> GenericChart
  static member Bubble : xysizes:seq<#IConvertible * #IConvertible * #IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<string> * ?TextPosition:TextPosition * ?TextFont:Font * ?StackGroup:string * ?Orientation:Orientation * ?GroupNorm:GroupNorm * ?UseWebGL:bool -> GenericChart
  static member Bubble : x:seq<#IConvertible> * y:seq<#IConvertible> * sizes:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<string> * ?TextPosition:TextPosition * ?TextFont:Font * ?StackGroup:string * ?Orientation:Orientation * ?GroupNorm:GroupNorm * ?UseWebGL:bool -> GenericChart
  static member Candlestick : stockTimeSeries:seq<DateTime * StockData> * ?Increasing:Line * ?Decreasing:Line * ?WhiskerWidth:float * ?Line:Line * ?XCalendar:Calendar -> GenericChart
  static member Candlestick : open:seq<#IConvertible> * high:seq<#IConvertible> * low:seq<#IConvertible> * close:seq<#IConvertible> * x:seq<#IConvertible> * ?Increasing:Line * ?Decreasing:Line * ?WhiskerWidth:float * ?Line:Line * ?XCalendar:Calendar -> GenericChart
  ...
static member Chart.Point : xy:seq<#System.IConvertible * #System.IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:StyleParam.Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<string> * ?TextPosition:StyleParam.TextPosition * ?TextFont:Font * ?StackGroup:string * ?Orientation:StyleParam.Orientation * ?GroupNorm:StyleParam.GroupNorm * ?UseWebGL:bool -> GenericChart.GenericChart
static member Chart.Point : x:seq<#System.IConvertible> * y:seq<#System.IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:StyleParam.Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<string> * ?TextPosition:StyleParam.TextPosition * ?TextFont:Font * ?StackGroup:string * ?Orientation:StyleParam.Orientation * ?GroupNorm:StyleParam.GroupNorm * ?UseWebGL:bool -> GenericChart.GenericChart
static member Chart.withTraceName : ?Name:string * ?Showlegend:bool * ?Legendgroup:string * ?Visible:StyleParam.Visible -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withTitle : title:string * ?Titlefont:Font -> (GenericChart.GenericChart -> GenericChart.GenericChart)
val c : GenericChart.GenericChart
module GenericChart

from Plotly.NET
val toChartHTML : gChart:GenericChart.GenericChart -> string