import numpy as np import pandas as pd from sklearn.metrics import mean_absolute_error from sklearn.metrics import mean_squared_error from statsmodels.graphics.tsaplots import plot_pacf from math import sqrt import matplotlib.pyplot as plt import matplotlib.dates as mdates import seaborn as sns plt.style.use('seaborn-darkgrid') import statsmodels.api as sm import statsmodels.formula.api as smf import statsmodels.stats as sms from statsmodels.tsa.stattools import adfuller from statsmodels.tsa.stattools import acf, pacf from statsmodels.tsa.arima.model import ARIMA def model_performance(observed, predicted): """This function will print the Mean Absolute Error, Mean Squared Error, Root Mean Squared Error and Mean Absolute Percentage Error. This function will also display the residula plot and the ACF. """ # Mean Absolute Error mae = mean_absolute_error(observed, predicted) print('The Mean Absolute Error is %.2f' % mae) # Mean Squared Error mse = mean_squared_error(observed, predicted) print('The Mean Squared Error is %.2f' % mse) # Root Mean Squared Error rmse = sqrt(mean_squared_error(observed, predicted)) print('The Root Mean Squared Error is %.2f' % rmse) # Mean Absolute Percentage Error mape = 100 * ((observed-predicted)/observed).abs().mean() print('The Mean Absolute Percentage Error is %.2f' % mape) # Residuals residuals = observed - predicted labels = observed.index fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(10, 11)) # Plot residual observed.plot(ax=ax1, color='purple') predicted.plot(ax=ax1, color='green') ax1.set_ylabel('Price') ax1.set_title('Predicted vs. observed') # Plot residual ax2.fill_between(residuals.index, residuals.values, color='red') ax2.set_ylabel('Error') ax2.set_xlabel('Date') ax2.set_title('Residuals') ax2.set_xticklabels(labels, rotation=45, ha='right') ax2.xaxis.set_major_formatter(mdates.DateFormatter("%d-%m-%Y")) ax2.xaxis.set_minor_formatter(mdates.DateFormatter("%d-%m-%Y")) _=plt.xticks(rotation=45) # Autocorrelation plot of residuals sm.graphics.tsa.plot_pacf(residuals, ax=ax3, color='blue') ax3.set_xlabel('Lags') ax3.set_ylabel('Partial autocorrelation') ax3.set_title('Partial autocorrelation of residuals') plt.tight_layout() plt.show() def analyze_strategy(strategy_returns): sharpe_ratio = strategy_returns.mean() / strategy_returns.std() * np.sqrt(252) # Cumulative Returns cumulative_returns = (strategy_returns + 1).cumprod() # ---------- Drawdown calculations ------------------- # Calculate the running maximum running_max = np.maximum.accumulate(cumulative_returns.dropna()) # Ensure the value never drops below 1 running_max[running_max < 1] = 1 # Calculate the percentage drawdown drawdown = 100*((cumulative_returns)/running_max - 1) # Calculate the maximum drawdown max_dd = drawdown.min() # Print the statistics print('The Sharpe Ratio is %.2f' % sharpe_ratio) print('The cumulative return is %.2f' % ( ((cumulative_returns[-1])-1)*100) + "%") print("The maximum drawdown is %.2f" % max_dd + "%") # Plot labels = strategy_returns.index fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 7)) # Plot strategy returns ax1.plot(cumulative_returns, color='b') ax1.set_title('Cumulative returns', fontsize=14) ax1.set_ylabel('Cumulative returns', fontsize=12) ax1.set_xlabel('Date', fontsize=12) ax1.set_xticklabels(labels, rotation=45, ha='right') ax1.xaxis.set_major_formatter(mdates.DateFormatter("%d-%m-%Y")) ax1.xaxis.set_minor_formatter(mdates.DateFormatter("%d-%m-%Y")) # Plot max DD ax2.plot(drawdown, color='red') # Fill in-between the drawdown ax2.fill_between(drawdown.index, drawdown.values, color='red') ax2.set_title('Strategy drawdown', fontsize=14) ax2.set_ylabel('Drawdown (%)', fontsize=12) ax2.set_xlabel('Date', fontsize=12) ax2.set_xticklabels(labels, rotation=45, ha='right') ax2.xaxis.set_major_formatter(mdates.DateFormatter("%d-%m-%Y")) ax2.xaxis.set_minor_formatter(mdates.DateFormatter("%d-%m-%Y")) plt.tight_layout() plt.show() def check_stationarity(y, wl1=21, wl2=252, lags=40, figsize=(18, 12)): """ Checks the stationarity of a pandas Series (default is daily prices or returns), using plots, correlograms and the ADF test """ ## Calculating rolling statistics rolling_wl1_mean = y.rolling(window=wl1).mean() rolling_wl2_mean = y.rolling(window=wl2).mean() rolling_wl1_vol = y.rolling(window=wl1).std() rolling_wl2_vol = y.rolling(window=wl2).std() ## Plotting the price, rolling statistics and correlograms fig = plt.figure(figsize=(18, 14)) sns.set(font_scale=1) layout = (2, 2) y_ax = plt.subplot2grid(layout, (0, 0)) vol_ax = plt.subplot2grid(layout, (0, 1)) acf_ax = plt.subplot2grid(layout, (1, 0)) pacf_ax = plt.subplot2grid(layout, (1, 1)) y.plot(ax=y_ax) rolling_wl1_mean.plot(ax=y_ax) rolling_wl2_mean.plot(ax=y_ax) rolling_wl1_vol.plot(ax=vol_ax) rolling_wl2_vol.plot(ax=vol_ax) y_ax.set_title('Rolling means over time') y_ax.legend(['observed', f'{wl1}-period MA of observed', f'{wl2}-period MA of observed'], loc='best') #y_ax.set_ylabel("Gold prices(in INR)/oz.") vol_ax.set_title('Rolling volatility over time') vol_ax.legend([f'{wl1}-period MA of volatility', f'{wl2}-period MA of volatility'], loc='best') sm.graphics.tsa.plot_acf(y, lags=lags, ax=acf_ax, alpha=0.05) sm.graphics.tsa.plot_pacf(y, lags=lags, ax=pacf_ax, alpha=0.05) ## Running the Augmented Dickey-Fuller test print('--------------------------------------------------------------') print('--------- The augmented Dickey-Fuller test results -----------') print('--------------------------------------------------------------') adftest = adfuller(y, autolag='AIC') results = pd.Series(adftest[0:4], index=['Test Statistic','p-value','# of Lags','# of Observations']) for key,value in adftest[4].items(): results[f'Critical Value ({key})'] = '{0:.3f}'.format(value) print(results) print('--------------------------------------------------------------')