Time Series Analysis
Time series analysis models data indexed in time. It is central to forecasting, econometrics, and quantitative finance.
Key Points
- Stationarity, autocorrelation, and seasonality are key concepts.
- ARMA and ARIMA models capture linear temporal dependencies.
- GARCH models time-varying volatility.
Formulas
AR(1)
$$X_t = c + \phi X_{t-1} + \varepsilon_t$$
MA(1)
$$X_t = \mu + \varepsilon_t + \theta \varepsilon_{t-1}$$
GARCH(1,1)
$$\sigma_t^2 = \omega + \alpha X_{t-1}^2 + \beta \sigma_{t-1}^2$$
Code Example
from statsmodels.tsa.arima.model import ARIMA
model = ARIMA(series, order=(1, 0, 1))
res = model.fit()
print(res.summary())