Aikasarjade

Aikasarjad are sequences of observations indexed in time, typically collected at regular intervals such as days, months, or quarters. Each observation y t corresponds to a point in time t, and the primary goal of aikasarja analysis is to describe patterns, identify underlying components, and forecast future values. Aikasarjade typical features include trend (long-term rise or fall), seasonality (regular short-term fluctuations within a fixed period), cyclic behavior, and an irregular component (random variation).

Common modeling approaches include the ARIMA family (autoregressive integrated moving average), which handles autocorrelation and non-stationarity through differencing and moving averages. Seasonal ARIMA (SARIMA) extends this to capture periodic seasonal patterns. Exponential smoothing methods, such as Holt-Winters, forecast by smoothing level, trend, and seasonality. State-space models provide a flexible framework for time-varying structures, and newer tools like Prophet offer automated handling of trend and seasonality with robust forecasting. Machine learning methods and Gaussian processes are also employed for complex patterns.

Analysis of aikasarjad often involves decomposing the series into components, testing for stationarity, and examining autocorrelation and partial autocorrelation functions. Forecast evaluation uses measures such as MAE, RMSE, and MAPE, with time-series cross-validation to assess predictive performance.

Applications span finance, economics, meteorology, energy, and public health. Data quality issues, like missing values, outliers, and structural breaks, must be addressed to avoid biased forecasts. Software tools include R (forecast, tsibble), Python (statsmodels, Prophet), and other statistical packages.