Alternative trend fomula

[timboldt]

When one's weight change is a fairly steady slope (as typically happens during dieting), an EMA lags because it assumes a constant level with noise.

It would be nice to have a choice of an alternative method (selectable in Settings). One example is Holt’s Linear Trend Method (Double Exponential Smoothing), which tracks the actual weight better.

Rough sketch:

/// <summary>
    /// Computes weight trends using Holt's Linear Trend (Double Exponential Smoothing)
    /// to reduce lag during consistent weight loss (e.g., Wegovy).
    /// </summary>
    private static List<ComputedMeasurement> ComputeWeightTrends(List<SourceMeasurement> sourceMeasurements)
    {
        // Alpha: Smoothing factor for the Level (Weight). 0.1 is standard for weight.
        const decimal ALPHA = 0.1m;
        // Beta: Smoothing factor for the Trend (Slope). 0.1 allows quick adaptation to rate changes.
        const decimal BETA = 0.1m;

        decimal level = 0;
        decimal trend = 0;
        var measurements = new List<ComputedMeasurement>();

        for (int i = 0; i < sourceMeasurements.Count; i++)
        {
            var sourceMeasurement = sourceMeasurements[i];
            var weight = sourceMeasurement.Weight;

            if (i == 0)
            {
                // Initialization
                level = weight;
                
                // If we have at least two points, initialize the trend (slope) 
                // based on the first real change. Otherwise assume flat (0).
                if (sourceMeasurements.Count > 1)
                {
                    trend = sourceMeasurements[1].Weight - sourceMeasurements[0].Weight;
                }
                else
                {
                    trend = 0;
                }
            }
            else
            {
                decimal prevLevel = level;
                decimal prevTrend = trend;

                // 1. Update Level (The smoothed weight value)
                // We combine the new reading with the *expected* value (prevLevel + prevTrend)
                level = ALPHA * weight + (1 - ALPHA) * (prevLevel + prevTrend);

                // 2. Update Trend (The rate of change/slope)
                // We combine the recent change (level - prevLevel) with the previous trend
                trend = BETA * (level - prevLevel) + (1 - BETA) * prevTrend;
            }

            measurements.Add(new ComputedMeasurement
            {
                Date = sourceMeasurement.Date.ToString("yyyy-MM-dd", CultureInfo.InvariantCulture),
                ActualWeight = Math.Round(sourceMeasurement.Weight, 3),
                // 'level' is now the best estimate of the current true weight
                TrendWeight = Math.Round(level, 3), 
                WeightIsInterpolated = sourceMeasurement.WeightIsInterpolated,
                FatIsInterpolated = false
            });
        }

        return measurements;
    }

[timboldt]

I used some data I had to compare the TrendWeight formula against Holt's. As you can see, it follows the trend more accurately when there is a clear slope: