Time series analysis examines observations ordered over time, preserving temporal order to identify trends, seasonality, cycles, noise, and dependence on earlier values. Its practical purpose is forecasting future observations from historical data. section 7.0 section 7.1
Common forecasting approaches include:
- ARIMA combines autoregression, differencing, and moving averages to model temporal dependencies, trends, autocorrelation, and nonstationarity. section 7.1
- Exponential smoothing weights recent observations more heavily, with simple, double, and Holt–Winters methods addressing progressively richer trend and seasonal structure. section 7.0 section 7.1
- Model selection depends on the data’s characteristics: ARIMA suits complex temporal dependence, while exponential smoothing highlights underlying trends and seasonal patterns. section 7.1
Forecasting closing stock prices
A practical workflow imports and plots closing prices, fits ARIMA and exponential-smoothing models to the same series, compares their forecasts, and interprets results cautiously. Stock prices provide a difficult test because abrupt changes, rapidly incorporated information, nonlinear dynamics, and unpredictable public opinion can limit forecast accuracy. section 7.0 section 7.2
