# AutoSSA: time series analysis and forecast

News
• (16 Jan 2008)
Poster from EC^2 conference on extraction of quasi-periodic components in SSA is available goto...
• (16 Jan 2008)
The PhD thesis (in Russian) of Theodore Alexandrov (2006) and the corresponding slides (in Russian) are available goto...
• (17 Oct 2007)
New web resource about SSA, SSAwiki goto...
• (15 Oct 2007)
• (12 Oct 2007)
Version of AutoSSA in Matlab (with and without GUI) is finally available! goto...
• (13 July 2006)
Working paper with an example of seasonality adjustment and trend extraction for a set of US unemployment time series, goto...
• (13 July 2006)
Slides of the presentation at 26th International Symposium on Forecasting, goto...

## AutoSSA: origins

### Introduction

The Caterpillar-SSA is an approach for time series analysis and forecast.

AutoSSA is a collection of parametric methods which allow to use Caterpillar-SSA approach in batch processing.

### Caterpillar-SSA

The Caterpillar-SSA approach can be used for time series analysis and forecast, both univariate and multivariate time series. In some way it represents Principal Components Analysis for time series. The basic algorithm of this approach starts with constructions of a trajectory matrix. Then SVD of this matrix is considered. The components of SVD correspond to additive components of the original time series. Thereby we obtain the decomposition of the time series into additive components together with information about them which is contained in singular vectors and signular values.

This approach allows to solve following problems raising in the area of time series analysis:

• time series forecasting,
• denoising and smoothing,
• extraction of trend/periodic components of time series,
• decomposition of a time series into sum of a signal (trend/periodical components) and a residual,
• change-point detection.

• it does not require a parametric model of time series or sought-for trend,
• requires only a little information about time series,
• allows to process non-stationary time series,
• extracts modulated sine waves and quasi-periodic components made of them,
• finds structure in short time series.

### Caterpillar-SSA vs. AutoSSA

The basic Caterpillar-SSA algorithm in managed by

• changing a window length on the stage of trajectory matrix construction,
• choosing the group of SVD components; we call the procedure of this choice identification.

The identification of eigen triples can be done interactively, by visual examination of singular values and vectors. It is very flexible way bu? the batch processing is impossible and it requires some knowledge of using Caterpillar-SSA.

AutoSSA represents a collection of parametric methods for solution of trend/periodic components extraction.