Abstract In recent years Singular Spectrum Analysis (SSA), a relatively novel but powerful
technique in time series analysis, has been developed and applied to many practical …

This article presents a review of some modern approaches to trend extraction for one-
dimensional time series, which is one of the major tasks of time series analysis. The trend of …

The subject of this book is the estimation of random vectors given observations of a related
random process assuming that there is a linear relation between them. Since the class of …

This tutorial explores the class of non-parametric time series basis decomposition methods
particularly suited for nonstationary time series known as Empirical Mode Decomposition …

Summary The Hodrick–Prescott (HP) filter is widely used in the field of economics to
estimate trends and cycles from time series data. For certain applications—such as deriving …

This paper provides analyses of daily retail data, extracting annual and weekly seasonal
patterns along with moving holiday effects, using an unobserved components framework. It …

Gegenbauer processes and their generalizations represent a general way of modeling long
memory and seasonal long memory; they include ARFIMA, seasonal ARFIMA, and GARMA …

In collaboration with the current developers of the SEATS seasonal adjustment program, an
experimental version of X-12-ARIMA that produces model–based seasonal adjustments …

The most fundamental seasonal adjustment deficiency is detectable seasonality after
adjustment. Residual seasonality has reduced amplitudes and other properties which make …

The HP filter is the most popular filter for extracting the unobserved trend and cycle
components from a time series. Many researchers consider the smoothing parameter λ …