Statsmodels للنمذجة الإحصائية
نماذج إحصائية واختبارات فرضية واستكشاف بيانات. ARIMA و GARCH والانحدار لتحليل الأسواق.
الصعوبة: متوسط
الفئة: إحصائي
التثبيت
$ pip install statsmodels
Key Modules for Trading
ARIMA / SARIMAX
Time series forecasting with autoregressive integrated moving average models
Cointegration Tests
Test if two currency pairs move together — essential for pairs trading
Stationarity Tests (ADF)
Test if a price series is mean-reverting or trending
OLS Regression
Linear regression for factor analysis and beta calculations
GARCH Models
Volatility modeling for risk management and option pricing
Granger Causality
Test if one time series can predict another
أمثلة الكود
Installation
Install statsmodels
Python
pip install statsmodels
# Verify
python -c "import statsmodels; print(statsmodels.__version__)"
Stationarity Test (ADF)
Test if price data is stationary — critical for choosing the right strategy
Python
from statsmodels.tsa.stattools import adfuller
import yfinance as yf
df = yf.download("EURUSD=X", period="1y")
close = df['Close'].values.flatten()
# Augmented Dickey-Fuller test
result = adfuller(close)
print(f"ADF Statistic: {result[0]:.4f}")
print(f"p-value: {result[1]:.4f}")
print(f"Used lags: {result[2]}")
if result[1] < 0.05:
print("Result: STATIONARY — mean-reversion strategies may work")
else:
print("Result: NON-STATIONARY — trend-following strategies preferred")
# Test on returns instead (usually stationary)
returns = close[1:] / close[:-1] - 1
result_returns = adfuller(returns)
print(f"\nReturns ADF p-value: {result_returns[1]:.4f}")
print(f"Returns are {'stationary' if result_returns[1] < 0.05 else 'non-stationary'}")
Price Forecasting with ARIMA
Forecast future prices using ARIMA models
Python
from statsmodels.tsa.arima.model import ARIMA
import yfinance as yf
import numpy as np
df = yf.download("EURUSD=X", period="1y")
close = df['Close'].values.flatten()
# Fit ARIMA model on returns (stationary)
returns = np.diff(np.log(close)) # Log returns
model = ARIMA(returns, order=(5, 0, 2)) # (p, d, q)
fitted = model.fit()
# Print model summary
print(fitted.summary().tables[1])
# Forecast next 5 days
forecast = fitted.forecast(steps=5)
print("\nForecasted returns (next 5 days):")
for i, f in enumerate(forecast):
direction = "UP" if f > 0 else "DOWN"
print(f" Day {i+1}: {f:.6f} ({direction})")
Cointegration Test for Pairs Trading
Find pairs of currencies that move together
Python
from statsmodels.tsa.stattools import coint
import yfinance as yf
import numpy as np
# Download two correlated pairs
eurusd = yf.download("EURUSD=X", period="1y")['Close'].values.flatten()
gbpusd = yf.download("GBPUSD=X", period="1y")['Close'].values.flatten()
# Align lengths
min_len = min(len(eurusd), len(gbpusd))
eurusd = eurusd[-min_len:]
gbpusd = gbpusd[-min_len:]
# Test cointegration
score, pvalue, _ = coint(eurusd, gbpusd)
print(f"Cointegration Score: {score:.4f}")
print(f"p-value: {pvalue:.4f}")
if pvalue < 0.05:
print("COINTEGRATED — pairs trading viable!")
# Calculate spread
from statsmodels.regression.linear_model import OLS
from statsmodels.tools import add_constant
X = add_constant(eurusd)
model = OLS(gbpusd, X).fit()
hedge_ratio = model.params[1]
spread = gbpusd - hedge_ratio * eurusd
print(f"Hedge Ratio: {hedge_ratio:.4f}")
print(f"Current Spread: {spread[-1]:.5f}")
print(f"Spread Mean: {spread.mean():.5f}")
print(f"Z-Score: {(spread[-1] - spread.mean()) / spread.std():.2f}")
else:
print("NOT cointegrated — pairs trading not recommended")
Granger Causality Test
Test if one pair can predict another
Python
from statsmodels.tsa.stattools import grangercausalitytests
import yfinance as yf
import pandas as pd
import numpy as np
# Download data
eurusd = yf.download("EURUSD=X", period="1y")['Close']
usdjpy = yf.download("USDJPY=X", period="1y")['Close']
# Align
combined = pd.DataFrame({
'EURUSD': eurusd,
'USDJPY': usdjpy
}).dropna()
# Use returns (stationary)
combined = combined.pct_change().dropna()
print("Testing: Does USDJPY Granger-cause EURUSD?")
print("=" * 50)
result = grangercausalitytests(
combined[['EURUSD', 'USDJPY']],
maxlag=5, verbose=True
)
Factor Regression Analysis
Analyze how different factors affect currency returns
Python
from statsmodels.regression.linear_model import OLS
from statsmodels.tools import add_constant
import yfinance as yf
import pandas as pd
import numpy as np
# Download multiple factors
eurusd = yf.download("EURUSD=X", period="1y")['Close'].pct_change()
dxy = yf.download("DX-Y.NYB", period="1y")['Close'].pct_change()
gold = yf.download("GC=F", period="1y")['Close'].pct_change()
# Combine
factors = pd.DataFrame({
'EURUSD': eurusd,
'DXY': dxy,
'GOLD': gold
}).dropna()
# Run regression: EURUSD = α + β1*DXY + β2*GOLD + ε
X = add_constant(factors[['DXY', 'GOLD']])
model = OLS(factors['EURUSD'], X).fit()
print(model.summary())
print(f"\nR-squared: {model.rsquared:.4f}")
print(f"DXY Beta: {model.params['DXY']:.4f}")
print(f"GOLD Beta: {model.params['GOLD']:.4f}")
أفضل الممارسات
Test Stationarity First
Always run ADF test before applying ARIMA — most price data is non-stationary
Use Returns, Not Prices
Work with log returns or percentage returns which are more likely stationary
ARIMA Limitations
ARIMA forecasts are unreliable beyond a few periods — use for short-term only
Cointegration Changes
Cointegration relationships can break down — retest regularly