# Break Detection in the Seasonal and Trend Component of a Univariate Time Series

### Description

Iterative break detection in seasonal and trend component of a time series. Seasonal breaks is a function that combines the iterative decomposition of time series into trend, seasonal and remainder components with significant break detection in the decomposed components of the time series.

### Usage

1 2 |

### Arguments

`Yt` |
univariate time series to be analyzed. This should be an object of class "ts" with a frequency greater than one without NA's. |

`h` |
minimal segment size between potentially detected breaks in the trend model given as fraction relative to the sample size (i.e. the minimal number of observations in each segment divided by the total length of the timeseries. |

`season` |
the seasonal model used to fit the seasonal component and detect seasonal breaks (i.e. significant phenological change). There are three options: "dummy", "harmonic", or "none" where "dummy" is the model proposed in the first Remote Sensing of Environment paper and "harmonic" is the model used in the second Remote Sensing of Environment paper (See paper for more details) and where "none" indicates that no seasonal model will be fitted (i.e. St = 0 ). If there is no seasonal cycle (e.g. frequency of the time series is 1) "none" can be selected to avoid fitting a seasonal model. |

`max.iter` |
maximum amount of iterations allowed for estimation of breakpoints in seasonal and trend component. |

`breaks` |
integer specifying the maximal number of breaks to be calculated. By default the maximal number allowed by h is used. |

`hpc` |
A character specifying the high performance computing support. Default is "none", can be set to "foreach". Install the "foreach" package for hpc support. |

`level` |
numeric; threshold value for the sctest.efp test; if a length 2 vector is passed, the first value is used for the trend, the second for the seasonality |

`type` |
character, indicating the type argument to efp |

### Details

To be completed.

### Value

An object of the class "bfast" is a list with the following elements:

`Yt` |
equals the Yt used as input. | ||||||||||||||||||

`output` |
is a list with the following elements (for each iteration):
| ||||||||||||||||||

`nobp` |
is a list with the following elements:
| ||||||||||||||||||

`Magnitude` |
magnitude of the biggest change detected in the trend component | ||||||||||||||||||

`Time` |
timing of the biggest change detected in the trend component |

### Author(s)

Jan Verbesselt

### References

Verbesselt J, Hyndman R, Newnham G, Culvenor D (2010).
Detecting Trend and Seasonal Changes in Satellite Image Time Series.
*Remote Sensing of Environment*, **114**(1), 106–115.
http://dx.doi.org/10.1016/j.rse.2009.08.014

Verbesselt J, Hyndman R, Zeileis A, Culvenor D (2010).
Phenological Change Detection while Accounting for Abrupt and Gradual Trends in Satellite Image Time Series.
*Remote Sensing of Environment*, **114**(12), 2970–2980.
http://dx.doi.org/10.1016/j.rse.2010.08.003

### See Also

`plot.bfast`

for plotting of bfast() results.

`breakpoints`

for more examples and background information about estimation of breakpoints in time series.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 | ```
## Not run:
rm(list = ls())
install.packages("bfast", repos="http://R-Forge.R-project.org", type = "source")
update.packages(checkBuilt=TRUE)
# make sure all your package are up to date
# and built correctly for your current R version
## End(Not run)
## Simulated Data
plot(simts) # stl object containing simulated NDVI time series
datats <- ts(rowSums(simts$time.series))
# sum of all the components (season,abrupt,remainder)
tsp(datats) <- tsp(simts$time.series) # assign correct time series attributes
plot(datats)
## Not run:
if (requireNamespace("forecast", quietly = TRUE)) {
fit <- bfast(datats,h=0.15, season="dummy", max.iter=1)
plot(fit,sim=simts)
fit
# prints out whether breakpoints are detected
# in the seasonal and trend component
} else {
## do something else not involving forecast related functions
## like seasonaldummy() and tsdisply()
}
## End(Not run)
## Real data
## The data should be a regular ts() object without NA's
## See Fig. 8 b in reference
plot(harvest, ylab="NDVI")
# MODIS 16-day cleaned and interpolated NDVI time series
(rdist <- 10/length(harvest))
# ratio of distance between breaks (time steps) and length of the time series
## Not run:
if (requireNamespace("forecast", quietly = TRUE)) {
fit <- bfast(harvest,h=rdist, season="harmonic", max.iter=1,breaks=2)
plot(fit)
## plot anova and slope of the trend identified trend segments
#plot(fit, ANOVA=TRUE)
## plot the trend component and identify the break with
## the largest magnitude of change
plot(fit,type="trend",largest=TRUE)
## plot all the different available plots
plot(fit,type="all")
## output
niter <- length(fit$output) # nr of iterations
out <- fit$output[[niter]]
# output of results of the final fitted seasonal and trend models and
## #nr of breakpoints in both.
## running bfast on yearly data
t <- ts(as.numeric(harvest), frequency = 1, start = 2006)
fit <- bfast(t, h = 0.23, season = "none", max.iter = 1)
plot(fit)
fit
}
## End(Not run)
``` |