Description Usage Arguments Details Value Author(s) References See Also Examples

Time series preprocessing for subsequent regression modeling. Based on a (seasonal) time series, a data frame with the response, seasonal terms, a trend term, (seasonal) autoregressive terms, and covariates is computed. This can subsequently be employed in regression models.

1 2 3 |

`data` |
A time series of class |

`order` |
numeric. Order of the harmonic term, defaulting to |

`lag` |
numeric. Orders of the autoregressive term, by default omitted. |

`slag` |
numeric. Orders of the seasonal autoregressive term, by default omitted. |

`na.action` |
function for handling |

`stl` |
character. Prior to all other preprocessing, STL (season-trend decomposition
via LOESS smoothing) can be employed for trend-adjustment and/or season-adjustment.
The |

To facilitate (linear) regression models of time series data, `bfastpp`

facilitates
preprocessing and setting up regressor terms. It returns a `data.frame`

containing the
first column of the `data`

as the `response`

while further columns (if any) are
used as covariates `xreg`

. Additionally, a linear trend, seasonal dummies, harmonic
seasonal terms, and (seasonal) autoregressive terms are provided.

Optionally, each column of `data`

can be seasonally adjusted and/or trend-adjusted via
STL (season-trend decomposition via LOESS smoothing) prior to preprocessing. The idea would
be to capture season and/or trend nonparametrically prior to regression modelling.

`bfastpp`

returns a `"data.frame"`

with the following variables (some of which may be matrices).

`time` |
numeric vector of time stamps, |

`response` |
response vector (first column of |

`trend` |
linear time trend (running from 1 to number of observations), |

`season` |
factor indicating season period, |

`harmon` |
harmonic seasonal terms (of specified |

`lag` |
autoregressive terms (or orders |

`slag` |
seasonal autoregressive terms (or orders |

`xreg` |
covariate regressor (all columns of |

Achim Zeileis

Verbesselt J, Zeileis A, Herold M (2011). Near Real-Time Disturbance Detection in Terrestrial Ecosystems Using Satellite Image Time Series: Drought Detection in Somalia. Working Paper 2011-18. Working Papers in Economics and Statistics, Research Platform Empirical and Experimental Economics, Universitaet Innsbruck. http://EconPapers.RePEc.org/RePEc:inn:wpaper:2011-18. Submitted to Remote Sensing and Environment.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## set up time series
library(zoo)
ndvi <- as.ts(zoo(cbind(a = som$NDVI.a, b = som$NDVI.b), som$Time))
ndvi <- window(ndvi, start = c(2006, 1), end = c(2009, 23))
## parametric season-trend model
d1 <- bfastpp(ndvi, order = 2)
d1lm <- lm(response ~ trend + harmon, data = d1)
summary(d1lm)
## autoregressive model (after nonparametric season-trend adjustment)
d2 <- bfastpp(ndvi, stl = "both", lag = 1:2)
d2lm <- lm(response ~ lag, data = d2)
summary(d2lm)
``` |

```
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Call:
lm(formula = response ~ trend + harmon, data = d1)
Residuals:
Min 1Q Median 3Q Max
-0.228691 -0.041100 -0.004046 0.055139 0.169111
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.145e-01 1.610e-02 25.748 < 2e-16 ***
trend -7.742e-05 3.024e-04 -0.256 0.798563
harmoncos1 7.279e-03 1.109e-02 0.657 0.513237
harmoncos2 3.868e-02 1.109e-02 3.488 0.000768 ***
harmonsin1 -3.747e-02 1.130e-02 -3.316 0.001337 **
harmonsin2 -1.041e-01 1.114e-02 -9.351 9.51e-15 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.07517 on 86 degrees of freedom
Multiple R-squared: 0.5648, Adjusted R-squared: 0.5395
F-statistic: 22.32 on 5 and 86 DF, p-value: 2.8e-14
Call:
lm(formula = response ~ lag, data = d2)
Residuals:
Min 1Q Median 3Q Max
-0.153435 -0.030022 -0.001384 0.021004 0.214001
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0003608 0.0060051 0.060 0.9522
lag1 0.2697747 0.1045785 2.580 0.0116 *
lag2 0.2204984 0.1045727 2.109 0.0379 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.05696 on 87 degrees of freedom
Multiple R-squared: 0.1626, Adjusted R-squared: 0.1433
F-statistic: 8.446 on 2 and 87 DF, p-value: 0.0004445
```

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