Overall Statistics
Total Trades
754
Average Win
0.49%
Average Loss
-0.38%
Compounding Annual Return
55.431%
Drawdown
20.100%
Expectancy
0.307
Net Profit
46.673%
Sharpe Ratio
1.272
Probabilistic Sharpe Ratio
61.856%
Loss Rate
43%
Win Rate
57%
Profit-Loss Ratio
1.30
Alpha
0.39
Beta
0.098
Annual Standard Deviation
0.323
Annual Variance
0.104
Information Ratio
0.564
Tracking Error
0.34
Treynor Ratio
4.204
Total Fees
$3598.16
import numpy as np
import pandas as pd
from hmmlearn.hmm import GaussianHMM

def CreateHMM(algorithm, symbol):
    history = algorithm.History([symbol], 900, Resolution.Daily)
    returns = np.array(history.loc[symbol].close.pct_change().dropna())
    # Reshape returns
    returns = np.array(returns).reshape((len(returns),1))
    # Initialize Gaussian Hidden Markov Model
    return GaussianHMM(n_components=2, covariance_type="full", n_iter=1000).fit(returns)
    
def PredictState(algorithm, model, symbol):
    # Predict current state
    if algorithm.CurrentSlice.ContainsKey(symbol):
        price = np.array(algorithm.CurrentSlice[symbol].Close).reshape((1,1))
    else:
        price = np.array(algorithm.Securities[symbol].Price).reshape((1,1))
    return model.predict(price)[0]
    
def RefitModel(algorithm, symbol, model):
    history = algorithm.History([symbol], 900, Resolution.Daily)
    returns = np.array(history.loc[symbol].close.pct_change().dropna())
    # Reshape returns
    returns = np.array(returns).reshape((len(returns),1))
    return model.fit(returns)
import numpy as np
import pandas as pd
from statsmodels.tsa.stattools import adfuller

def TestStationartiy(returns):
    
    # Return pandas Series with True/False for each symbol
    return pd.Series([adfuller(values)[1] < 0.05 for columns, values in returns.iteritems()], index = returns.columns)
    
def GetZScores(returns):
    # Return pandas DataFrame containing z-scores
    return returns.subtract(returns.mean()).div(returns.std())
from HMM import *
import numpy as np
from StationarityAndZScores import *
from QuantConnect.Data.UniverseSelection import *

class ModulatedDynamicCircuit(QCAlgorithm):

    def Initialize(self):
        self.SetStartDate(2019, 1, 1)  # Set Start Date
        self.SetCash(100000)  # Set Strategy Cash
        
        self.SetBrokerageModel(AlphaStreamsBrokerageModel())
        
        self.SetExecution(ImmediateExecutionModel())

        self.SetPortfolioConstruction(EqualWeightingPortfolioConstructionModel())

        self.SetUniverseSelection(LiquidETFUniverse())

        self.models = {}
        
        self.AddEquity('GLD')
        self.Schedule.On(self.DateRules.EveryDay('GLD'), self.TimeRules.AfterMarketOpen('GLD', 5), self.GenerateInsights)
        self.Schedule.On(self.DateRules.MonthStart('GLD'), self.TimeRules.At(19,0), self.RefitModels)


    def RefitModels(self):
        for symbol, model in self.models.items():
            RefitModel(self, symbol, model)

    
    def GenerateInsights(self):
        insights = []
        
        qb = self
        
        symbols = [x.Symbol for x in qb.ActiveSecurities.Values]
        # Copy and paste from research notebook
        # -----------------------------------------------------------------------------
        # Fetch history
        history = qb.History(symbols, 500, Resolution.Hour)
        # Convert to returns
        returns = history.unstack(level = 1).close.transpose().pct_change().dropna()
        # Test for stationarity
        stationarity = TestStationartiy(returns)
        # Get z-scores
        z_scores = GetZScores(returns)
        # -----------------------------------------------------------------------------

        insights = []

        # Iterate over symbols
        for symbol, value in stationarity.iteritems():
            # Only emit Insights for those whose returns exhibit stationary behavior
            if value:
                # Get Hidden Markov model
                model = self.CheckForHMM(symbol)
                # Predict current state
                state_prediction = PredictState(self, model, symbol)
                # Get most recent z_score
                z_score = z_scores[symbol].tail(1).values[0]
                # Determine if we want to invest or not
                if (z_score < -1) and (state_prediction == 0):
                    insights.append(Insight.Price(symbol, timedelta(1), InsightDirection.Up))
                elif z_score > 1:
                    if self.Portfolio[symbol].Invested:
                        insights.append(Insight.Price(symbol, timedelta(1), InsightDirection.Flat))
                elif self.Portfolio[symbol].Invested and (state_prediction == 1):
                    insights.append(Insight.Price(symbol, timedelta(1), InsightDirection.Flat))

        self.EmitInsights(insights)

    
    def CheckForHMM(self, symbol):
        if self.models.get(symbol, None) is None:
            self.models[symbol] = CreateHMM(self, symbol)
        return self.models.get(symbol, None)

    
    def OnSecuritiesChanged(self, changes):
        symbols = [x.Symbol for x in changes.AddedSecurities]
        # Build model for each symbol
        for symbol in symbols:
            self.models[symbol] = CreateHMM(self, symbol)