#region imports
from AlgorithmImports import *
from arch.unitroot.cointegration import engle_granger
from pykalman import KalmanFilter
#endregion

class PCADemo(QCAlgorithm):
    
    def initialize(self):

        #1. Required: Five years of backtest history
        self.set_start_date(2019, 1, 1)
    
        #2. Required: Alpha Streams Models:
        self.set_brokerage_model(BrokerageName.INTERACTIVE_BROKERS_BROKERAGE)
    
        #3. Required: Significant AUM Capacity
        self.set_cash(1000000)
    
        #4. Required: Benchmark to SPY
        self.set_benchmark("SPY")
    
        self.assets = ["XLK", "XLU"]
        
        # Add Equity ------------------------------------------------ 
        for i in range(len(self.assets)):
            self.add_equity(self.assets[i], Resolution.MINUTE).symbol
            
        # Instantiate our model
        self.recalibrate()
        
        # Set a variable to indicate the trading bias of the portfolio
        self.state = 0
        
        # Set Scheduled Event Method For Kalman Filter updating.
        self.schedule.on(self.date_rules.week_start(), 
            self.time_rules.at(0, 0), 
            self.recalibrate)
        
        # Set Scheduled Event Method For Kalman Filter updating.
        self.schedule.on(self.date_rules.every_day(), 
            self.time_rules.before_market_close("XLK"), 
            self.every_day_before_market_close)
            
            
    def recalibrate(self):
        qb = self
        history = qb.history(self.assets, 252*2, Resolution.DAILY)
        if history.empty: return
        
        # Select the close column and then call the unstack method
        data = history['close'].unstack(level=0)
        
        # Convert into log-price series to eliminate compounding effect
        log_price = np.log(data)
        
        ### Get Cointegration Vectors
        # Get the cointegration vector
        coint_result = engle_granger(log_price.iloc[:, 0], log_price.iloc[:, 1], trend="c", lags=0)
        coint_vector = coint_result.cointegrating_vector[:2]
        
        # Get the spread
        spread = log_price @ coint_vector
        
        ### Kalman Filter
        # Initialize a Kalman Filter. Using the first 20 data points to optimize its initial state. We assume the market has no regime change so that the transitional matrix and observation matrix is [1].
        self.kalman_filter = KalmanFilter(transition_matrices = [1],
                          observation_matrices = [1],
                          initial_state_mean = spread.iloc[:20].mean(),
                          observation_covariance = spread.iloc[:20].var(),
                          em_vars=['transition_covariance', 'initial_state_covariance'])
        self.kalman_filter = self.kalman_filter.em(spread.iloc[:20], n_iter=5)
        (filtered_state_means, filtered_state_covariances) = self.kalman_filter.filter(spread.iloc[:20])
        
        # Obtain the current Mean and Covariance Matrix expectations.
        self.current_mean = filtered_state_means[-1, :]
        self.current_cov = filtered_state_covariances[-1, :]
        
        # Initialize a mean series for spread normalization using the Kalman Filter's results.
        mean_series = np.array([None]*(spread.shape[0]-20))
        
        # Roll over the Kalman Filter to obtain the mean series.
        for i in range(20, spread.shape[0]):
            (self.current_mean, self.current_cov) = self.kalman_filter.filter_update(filtered_state_mean = self.current_mean,
                                                                   filtered_state_covariance = self.current_cov,
                                                                   observation = spread.iloc[i])
            mean_series[i-20] = float(self.current_mean)
        
        # Obtain the normalized spread series.
        normalized_spread = (spread.iloc[20:] - mean_series)
        
        ### Determine Trading Threshold
        # Initialize 50 set levels for testing.
        set_levels = self.get_parameter("set_levels", 50)
        
        s0 = np.linspace(0, max(normalized_spread), set_levels)
        
        # Calculate the profit levels using the 50 set levels.
        f_bar = np.array([None]*set_levels)
        for i in range(set_levels):
            f_bar[i] = len(normalized_spread.values[normalized_spread.values > s0[i]]) / normalized_spread.shape[0]
            
        # Set trading frequency matrix.
        D = np.zeros((set_levels-1, set_levels))
        for i in range(D.shape[0]):
            D[i, i] = 1
            D[i, i+1] = -1
            
        # Set level of lambda.
        l = 1.0
        
        # Obtain the normalized profit level.
        f_star = np.linalg.inv(np.eye(set_levels) + l * D.T@D) @ f_bar.reshape(-1, 1)
        s_star = [f_star[i]*s0[i] for i in range(set_levels)]
        self.threshold = s0[s_star.index(max(s_star))]
        
        # Set the trading weight. We would like the portfolio absolute total weight is 1 when trading.
        self.trading_weight = coint_vector / np.sum(abs(coint_vector))
        
            
    def every_day_before_market_close(self):
        qb = self
        
        # Get the real-time log close price for all assets and store in a Series
        series = pd.Series()
        for symbol in qb.securities.Keys:
            series[symbol] = np.log(qb.securities[symbol].close)
            
        # Get the spread
        spread = np.sum(series * self.trading_weight)
        
        # Update the Kalman Filter with the Series
        (self.current_mean, self.current_cov) = self.kalman_filter.filter_update(filtered_state_mean = self.current_mean,
                                                                           filtered_state_covariance = self.current_cov,
                                                                           observation = spread)
            
        # Obtain the normalized spread.
        normalized_spread = spread - self.current_mean
    
        # ==============================
        
        # Mean-reversion
        if normalized_spread < -self.threshold:
            orders = []
            for i in range(len(self.assets)):
                orders.append(PortfolioTarget(self.assets[i], self.trading_weight[i]))
                self.set_holdings(orders)
                
            self.state = 1
                
        elif normalized_spread > self.threshold:
            orders = []
            for i in range(len(self.assets)):
                orders.append(PortfolioTarget(self.assets[i], -1 * self.trading_weight[i]))
                self.set_holdings(orders)
                
            self.state = -1
                
        # Out of position if spread recovered
        elif self.state == 1 and normalized_spread > -self.threshold or self.state == -1 and normalized_spread < self.threshold:
            self.liquidate()
            
            self.state = 0