Prosenttisarjaa

Prosenttisarja is a term used in statistics and data analysis to describe a time series whose observations are expressed as percentages or proportions. Such series measure a quantity relative to a fixed total at each time point, or track shares among categories over time. A prosenttisarja is typically presented either as a single percentage series (univariate) or as a set of category shares that sum to 100 percent at each time point (multivariate or compositional).

Construction and interpretation

A proportion p_t can be computed as p_t = 100 × X_t / N_t, where X_t is the observed count or value of interest at time t and N_t is the corresponding total. In multivariate cases, several categories i have values X_it with p_it summing to 100 for each t. Prosenttisarjat are useful for comparing relative changes over time, normalizing variables with different scales, and monitoring performance or coverage relative to a fixed baseline.

Statistical considerations

Because percentages are bounded between 0 and 100 (or 0 and 1 when expressed as proportions), standard linear models can be inappropriate near the bounds. Transformations such as the logit (log(p/(100−p))) or the arcsine square root can stabilize variance. For multisector shares, compositional data analysis methods and log-ratio transforms help avoid spurious correlations due to the constant-sum constraint. Zeros or ones (0% or 100%) require special handling, and changing denominators can complicate interpretation and modeling.

Applications

Common examples include unemployment rates, vaccination coverage, market or electoral shares, turnout rates, and other indicators expressed as parts of a whole. Prosenttisarjat appear across economics, demography, epidemiology, and market research, where tracking relative changes over time is essential.

See also: time series, rate, proportion, compositional data analysis, logit transformation.