Comparing Methods for Forecasting Time Series with Multiple Observations per Period using Singular Spectrum Analysis

In practice, a univariate time series typically represents the value of a quantitative variable in successive order over a period of time. However, in certain fields like hydrology, multiple observations may be available for each time point. Commonly, functions such as the average, maximum, and minimum are used to summarize these observations into a univariate time series, potentially losing valuable information. This paper proposes an alternative approach by constructing a time series of distributions from the observations. We explore two methods: (1) a non-parametric approach using boxplots to create a time series of boxplots, and (2) a parametric approach using a parametric distribution, where the parameters of the distribution form the time series. These methods allow for the application of multivariate time series analysis techniques to better capture the underlying information. To demonstrate the practical application of these approaches, we employ singular spectrum analysis to model real climate change data from Europe.