namespace QuantConnect 
{   
    /*
    *   QuantConnect University: Full Basic Template:
    *
    *   The underlying QCAlgorithm class is full of helper methods which enable you to use QuantConnect.
    *   We have explained some of these here, but the full algorithm can be found at:
    *   https://github.com/QuantConnect/QCAlgorithm/blob/master/QuantConnect.Algorithm/QCAlgorithm.cs
    */
    public class BasicTemplateAlgorithm : QCAlgorithm
    {
    	private AnnualizedExponentialSlope adjustedSlope;
    	
        //Initialize the data and resolution you require for your strategy:
        public override void Initialize() 
        {
			
            //Start and End Date range for the backtest:
            SetStartDate(1998, 1, 1);
            SetEndDate(2015, 1, 1);
            
            //Cash allocation
            SetCash(25000);
            
            //Add as many securities as you like. All the data will be passed into the event handler:
            AddSecurity(SecurityType.Equity, "SPY", Resolution.Daily);
            
            adjustedSlope = new AnnualizedExponentialSlope(90);
            RegisterIndicator("SPY", adjustedSlope, Resolution.Daily, Field.Close);
            PlotIndicator("AdjSlope", true, adjustedSlope);
        }

        //Data Event Handler: New data arrives here. "TradeBars" type is a dictionary of strings so you can access it by symbol.
        public void OnData(TradeBars data) 
        {
        	if (!adjustedSlope.IsReady) return;
        	
        	var quantity = Portfolio["SPY"].Quantity;
        	if (quantity <= 0 && adjustedSlope > 20)
        	{
        		SetHoldings("SPY", .75);
        	}
        	if (quantity >= 0 && adjustedSlope < -2.5m)
        	{
        		if (adjustedSlope < -10)
        		{
        			SetHoldings("SPY", -.5);
        		}
        		else
        		{
        			SetHoldings("SPY", 0);
        		}
        	}
        }
    }
}

using MathNet.Numerics;

namespace QuantConnect
{
	public class AnnualizedExponentialSlope : WindowIndicator<IndicatorDataPoint>
    {
        public AnnualizedExponentialSlope(int period)
            : base("AdjustedSlope" + period, period)
        {
        }

        public AnnualizedExponentialSlope(string name, int period)
            : base(name, period)
        {
        }

        protected override decimal ComputeNextValue(IReadOnlyWindow<IndicatorDataPoint> window, IndicatorDataPoint input)
        {
            if (window.Count < 3) return 0m;

            var xVals = new double[window.Count];
            var yVals = new double[window.Count];

            // load input data for regression
            for (int i = 0; i < window.Count; i++)
            {
                xVals[i] = i;
                // we want the log of our y values
                yVals[i] = Math.Log((double)window[window.Count - i - 1].Value);
            }

            //http://numerics.mathdotnet.com/Regression.html

            // solves y=a + b*x via linear regression
            var fit = Fit.Line(xVals, yVals);
            var intercept = fit.Item1;
            var slope = fit.Item2;

            // compute rsquared
            var rsquared = GoodnessOfFit.RSquared(xVals.Select(x => intercept + slope*x), yVals);

            // anything this small can be viewed as flat
            if (double.IsNaN(slope) || Math.Abs(slope) < 1e-25) return 0m;

            // trading days per year for us equities
            const int dayCount = 252;

            // annualize dy/dt
            var annualSlope = ((Math.Pow(Math.Exp(slope), dayCount)) - 1) * 100;

            // scale with rsquared
            annualSlope = annualSlope * rsquared;

            return (decimal) annualSlope;
        }
    }
}