# ctbi

Please cite the following companion paper if you’re using the ctbi package: Ritter, F.: Technical note: A procedure to clean, decompose, and aggregate time series, Hydrol. Earth Syst. Sci., 27, 349–361, https://doi.org/10.5194/hess-27-349-2023, 2023.

The goal of ctbi is to clean, decompose, impute and aggregate univariate time series. Ctbi stands for Cyclic/Trend decomposition using Bin Interpolation : the time series is divided into a sequence of non-overlapping bins. The long-term trend is a linear interpolation of the mean values between successive bins and the cyclic component is the mean stack of detrended data within all bins. Outliers present in the residuals are flagged using an enhanced Boxplot rule (called Logbox) that is adapted to non-Gaussian data and keeps the type I error at $$\frac{0.1}{\sqrt{n}}$$ % (percentage of erroneously flagged outliers). Logbox replaces the original 1.5 constant with $$A \times \log(n)+B+C/n$$. The variable n is the sample size, $$C = 36$$ corrects for biases emerging in small samples, and A and B are automatically calculated on a predictor of the maximum tail weight. The strength of the cyclic pattern within each bin is quantified by a new metric, the Stacked Cycles Index (SCI), with SCI ~ 0 associated with no cyclicity and SCI = 1 a perfectly cyclic signal.

## Example

library(ctbi)
example1 <- data.frame(year = 1700:1988,sunspot = as.numeric(sunspot.year))
example1[sample(1:289,30),'sunspot'] <- NA # contaminate data with missing values
example1[c(5,30,50),'sunspot'] <- c(-50,300,400) # contaminate data with outliers
example1 <- example1[-(70:100),]
bin.period <- 11 # aggregation performed every 11 years (the year is numeric here)
bin.side <- 1989 # to capture the last year, 1988, in a complete bin
bin.FUN <- 'mean'
bin.max.f.NA <- 0.2 # maximum of 20% of missing data per bin
ylim <- c(0,Inf) # negative values are impossible

list.main <- ctbi(example1,bin.period=bin.period,
bin.side=bin.side,bin.FUN=bin.FUN,
ylim=ylim,bin.max.f.NA=bin.max.f.NA)
data0.example1 <- list.main$data0 # cleaned raw dataset data1.example1 <- list.main$data1 # aggregated dataset.
mean.cycle.example1 <- list.main$mean.cycle # this data set shows a moderate seasonality summary.bin.example1 <- list.main$summary.bin # confirmed with SCI = 0.50
summary.outlier.example1 <- list.main\$summary.outlier