# trenddecomp

## Syntax

## Description

finds trends in a vector of data using singular spectrum analysis (SSA), which assumes an
additive decomposition of the data such that `LT`

= trenddecomp(`A`

)`A = LT+ST+R`

. In this
decomposition, `LT`

is the long-term trend in the data,
`ST`

is the seasonal, or oscillatory, trend (or trends), and
`R`

is the remainder. `LT`

is a vector with the same
length as `A`

.

SSA is a useful algorithm when the periods of the seasonal trends are unknown. The SSA algorithm assumes that the input data is uniformly spaced.

also uses the SSA algorithm to find trends in `LT`

= trenddecomp(`A`

,"ssa",`lag`

)`A`

and additionally
specifies a lag value, which determines the size of the matrix on which the singular value
decomposition is computed, as described in [1]. Larger values of
`lag`

typically result in more separation of the trends.

The value of `lag`

must be a scalar in the interval
[3,*N*/2] where *N* is the length of
`A`

. If the period of the seasonal trend is known, then specify
`lag`

as a multiple of the period.

finds the trends in `LT`

= trenddecomp(`A`

,"stl",`period`

)`A`

through seasonal trend decomposition using Loess
(STL), which is an additive decomposition based on a locally weighted regression, as
described in [2]. STL requires a period for the
seasonal trend. When the data has only one seasonal trend, specify
`period`

as a scalar value. For multiple seasonal trends, specify
`period`

as a vector whose elements are the periods for each seasonal
trend.

The STL algorithm assumes that the input data is uniformly spaced.

finds trends in a table or timetable of data using SSA. `D`

= trenddecomp(`T`

)`trenddecomp`

operates on each table variable separately. `D`

is a table or timetable
whose variables contain the long-term trend, seasonal trends, and remainder for each
variable. `trenddecomp`

returns multiple seasonal trends as one variable
in `D`

, whose columns contain each seasonal trend.

## Examples

## Input Arguments

## Output Arguments

## Tips

An additive decomposition model is appropriate for data where the seasonal variation is relatively constant throughout the time series. If the seasonal variation is proportional to the level of the time series, to use an additive decomposition model, use a log transformation on the data before the decomposition.

## References

[1] Golyandina, Nina, and Anatoly
Zhigljavsky. *Singular Spectrum Analysis for Time Series*.
SpringerBriefs in Statistics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.
https://doi.org/10.1007/978-3-642-34913-3.

[2] Cleveland, R.B., W.S. Cleveland,
J.E. McRae, and I. Terpenning. “STL: A Seasonal-Trend Decomposition Procedure Based on Loess.”
*Journal of Official Statistics* 6 (1990):
3–73.

## Version History

**Introduced in R2021b**