Extraction and Forecasting of Trends in Cases of Signal Rank Overestimation

Singular spectrum analysis allows automation for the extraction of trends of arbitrary shapes. Here, we study how the estimation of signal ranks influences the accuracy of trend extraction and forecasting. It is numerically shown that the trend estimates and their forecasting are slightly changed if the signal rank is overestimated. If the trend is not of finite rank, the trend estimates are still stable, while forecasting may be unstable. The method of automation of the trend extraction includes an important step for improving the separability of time series components to avoid their mixture. However, the better the separability improvement, the larger the forecasting variability, since the noise components become separated and can be similar to trend ones.