Time series Analysis

What is a Time Series? A time series is any sequence of measurements taken at regular, equally spaced intervals—seconds, minutes, hours, days, months, quarters, or years. Common examples include weather (daily temperature or rainfall), financial markets (daily stock prices or returns), industry indicators (monthly production or sales), electricity demand, traffic counts, and hospital admissions. In time-series analysis we study how these values evolve: their level, trend, seasonal or calendar patterns (e.g., weekdays vs. weekends, holiday effects), cycles, and anomalies. Typical goals are to describe behavior clearly, forecast future values, and quantify the impact of events or policies.

Because observations are ordered in time, nearby points tend to be correlated (autocorrelation). This violates the independent-and-identically-distributed assumption behind many standard statistical methods, so naïve cross-sectional tools often mislead. Time-series work must explicitly handle dependence, trend, and seasonality—for example by differencing, seasonal adjustment, and models that use lagged values and errors (e.g., ARIMA/SARIMA, ARIMAX/SARIMAX with external drivers, VAR for multiple series, state-space/ETS, or GARCH when volatility changes over time). Analysts also watch for structural breaks (e.g., policy shifts, COVID), outliers, and missing periods, and they evaluate models with time-aware validation (rolling or blocked splits) rather than random shuffles.