Time Series Analysis

Time series is a sequence of observations of a variable taken at consecutive and regular intervals over time (daily, weekly, monthly, yearly, etc.). In such data, the assumption of independence between observations is generally not valid because observations may be correlated over time. Time series analysis is a set of statistical methods designed to reveal this dependence, model structures that change over time, and make forecasts about the future.

Time series are analyzed not only from a statistical perspective but also in economic, sociological, meteorological, and engineering contexts by their very nature. Time series analysis enables both explanatory (descriptive) and predictive analyses.

Time series data typically consist of four fundamental components:

• Trend (T): The long-term overall direction of the time series. It can be increasing, decreasing, or constant. An upward trend is frequently observed in economic indicators.
• Seasonality (S): Regular fluctuations that repeat at specific times of the year (for example, increased tourism revenues during summer months).
• Cyclical Fluctuations (C): Long-term and irregular fluctuations such as business cycles.
• Random (Irregular, R or I) Component: Deviations caused by unexpected events that cannot be explained by the other components (natural disasters, political crises, etc.).

Stationarity is a fundamental assumption in time series analysis. A series is considered stationary (weakly stationary) if its mean, variance, and autocorrelation do not change over time. Non-stationary series exhibit trends or seasonality and often render most models inapplicable. Differencing is commonly applied to achieve stationarity.

• In univariate analysis, attention is focused on a single series only.
• In multivariate analysis, the relationships between multiple series are examined. For example, the joint behavior of two economic variables such as exchange rates and interest rates can be analyzed.

Time series analysis has an interdisciplinary range of applications:

• Economics: GDP, inflation, interest rate forecasting
• Finance: Stock prices, exchange rates, portfolio analysis
• Energy: Electricity consumption, demand forecasting
• Climate and Meteorology: Temperature and precipitation patterns
• Medicine and Epidemiology: Temporal analysis of case numbers
• Business and Marketing: Sales, inventory, and customer behavior analysis
• Transportation: Traffic congestion, public transit data