Linear regression for non-overlapping segments of a wave

<code>#pragma rtGlobals=1       // Use modern global access method.

Function PriceTrend(Startlevel)
    Variable Startlevel     // Price of share at time = 0
   
    Variable Simulation = CreatePrices(Startlevel)  // Fuction to simulate random walk of share
                                                    // prices  
    Variable Returncalc =  CalcReturn(input)        // Function to calculate  natural logs of return
                                                // per period  
    Variable Demeanedcalc = Demeaned(periodreturn)      // Function to calculate demeaned returns  
    Variable FFactor = Fluctuationmagnitude(squareddiff)    // Function to calculate local trend
                                                            // and fluctuation magnitude
End


Function CreatePrices(Startlevel)   // Function to simulate random walk of share prices
    Variable Startlevel //Share price at time = 0 in euros 
   
    Make/O/N=961  input // Create wave for share prices
   
    Input[0] = Startlevel   // Share price at time = 0 
    Input[1,960] =Input(p-1) + gnoise(0.15) // Share prices in subsequent period, where price is
                                            // price in preceding period plus period return drawn
                                            // from a Gaussian (noise) distribution
End


Function CalcReturn(input)  // Function to calculate natural logs of return per period
    Wave Input  // Read share prices  generated by preceding function
    String OutputName = NameOfWave(input)+"_logarithm"      // Store the name of wave plus
                                                                // "logartihm" into the new wave
                                                                // OuputName

    Duplicate/O input $OutputName   // Duplicate the wave with generated share prices as the
                                    // wave named input_logarithm
   
    Wave output = $OutputName       // Reference input_logarithm so that you can use it    
    output = Ln(input)  // Calculate logarithmic values of wave
   
    Make/O/N=960 Periodreturn
   
    Periodreturn[0]= 0  // Assume return in first period to be zero
    Periodreturn[1,959] = output(p) - output(p-1)   // In next period logartihmic return equals logarithmic
                                            //  share price of this period minus logarithmic
                                            // share price in previous period
End





Function Demeaned(periodreturn) // Function to calculate demeaned returns
    Wave periodreturn   // Read return values generated by previous function
   
    WaveStats/Q periodreturn    // Determine statistis of return wave
    Variable avg = V_avg    // Determine average return
   
    Make/O/N=960 Cumulative // Create wave that will include each period's return above or
                                //  below the average for all periods
    Cumulative[0] = Periodreturn[0]-V_avg   // Determine return below or above the average for
                                        // the first period
    Cumulative[1,959] = Cumulative(p-1) + Periodreturn(p) - V_avg   // Determine return below or
                                                                // above the average for all
                                                                // subsequent periods
End


Function Fluctuationmagnitude(cumulative)   // Function to calculate local trend and fluctuation magnitude  
    Wave cumulative // Read cumulative demeaned returns from previous function
   
    Make/O/N=960 Number     // Create a new wave to show the period numbers
   
    Variable i = 0  // Initialise i
   
    do  

    Number[i] = i +1    // Add the number 1 to the level in the preceding period, so that the first
                        // period carries the number 1  
   
    i += 1
   
    while(i+1<959)
   
    CurveFit line cumulative[0,959] /x=NUMBER /D // Generate a linear regression function in which
                                                    // the y values (demeaned cumulative
                                                    // returns are regressed against the x values)
                                                    // (the period numbers)
                                                   
                                                   
    Wave Fitted = fit_Cumulative    // Read fitted regression line into Wave named 'Fitted'
   
    Wave Squareddiff    // Create wave squared differences
   
    Squareddiff = (Cumulative - Fitted)^2   // Calculate squared differences between
                                                        //  cumulative demeaned returns and fitted
                                                        // regression line
   
    WaveStats Squareddiff   // Dtermine statistics of wave squared differences
   
    Variable Sumofsquareddiff   // Create parameter sum of squared differences
   
    Sumofsquareddiff = V_Sum //Determine sum
   
    Variable Fluctuationmagn    // Create wave Fluctuation magnitude
   
    Fluctuationmagn = Sqrt(V_Sum/960)   // Calculate fluctuation magnitude
End<pre><code class="language-igor"><code>