How To Compute Moving Average Convergence Divergence (MACD) using F#?

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open System

// Function to calculate EMA of a list of values
let calculateEMA (values: float list) (n: int) =
    let alpha = 2.0 / (float (n + 1))
    
    let rec calcEMA (values: float list) (prevEMA: float) =
        match values with
        | [] -> prevEMA
        | x::xs -> 
            let newEMA = alpha * x + (1.0 - alpha) * prevEMA
            calcEMA xs newEMA
            
    calcEMA values (List.average values)

// Function to calculate MACD values
let calculateMACD (prices: float list) (shortPeriod: int) (longPeriod: int) (signalPeriod: int) =
    let shortEMA = calculateEMA prices shortPeriod
    let longEMA = calculateEMA prices longPeriod
    
    let macdLine = shortEMA - longEMA
    
    let signalLineValues = List.scan (fun prevValue price ->
        let shortEMA = calculateEMA [price] shortPeriod
        let longEMA = calculateEMA [price] longPeriod
        let macdLine = shortEMA - longEMA
        let signalEMA = calculateEMA [macdLine] signalPeriod
        signalEMA
    ) 0.0 prices
    
    let signalLine = List.tail signalLineValues
    
    macdLine, signalLine

// Example usage
let prices = [100.0; 105.0; 110.0; 115.0; 120.0; 125.0]
let shortPeriod = 10
let longPeriod = 20
let signalPeriod = 9

let macdLine, signalLine = calculateMACD prices shortPeriod longPeriod signalPeriod

printfn "MACD Line values: %A" macdLine
printfn "Signal Line values: %A" signalLine