In halleybrantley/detrendr: Quantile Trend Filtering

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "70%"
)

detrendr

The goal of detrendr is to estimate smooth quantile trends in evenly spaced series. Missing values are allowed. The methods implemented in this package are described here: https://arxiv.org/abs/1904.10582.

Installation

You can install the development version of detrendr from Github with:

``` {r load} library(devtools) install_github("halleybrantley/detrendr")

The \r{detrendr} functions are much faster when used with the Gurobi solver. Directions for obtaining a license and installing the gurobi package are available here: https://cran.r-project.org/web/packages/prioritizr/vignettes/gurobi_installation.html

## Examples

Estimate the 5th and 20th quantile trends using a fixed value of the smoothing parameter $\lambda$. 

```r
library(detrendr)
n <- 100
x <- seq(1, n, 1)
y <- sin(x*2*pi/n) + rnorm(n, 0, .4)
lambda <- 10
k <- 3
tau <- c(0.05, .2)
trend <- get_trend(y, tau, lambda, k)
plot(y~x, type="l", col="grey")
lines(trend[,1]~x, col="red")
lines(trend[,2]~x, col="blue")

Use eBIC criterion to choose smoothing parameter:

trend_fit <- get_trend_BIC(y, tau, k, plot_lambda = TRUE)
trend <- trend_fit$trend
plot(y~x, type="l", col="grey")
lines(trend[,1]~x, col="red")
lines(trend[,2]~x, col="blue")

Use ADMM algorithm for long time series:

library(ggplot2)
library(splines)
set.seed(987651)
overlap <- 50 
window_size <- 100 
n <- window_size*3 - overlap*2
df.data <- generate_peaks(n)
df.data$x <- seq(1, n, 1)
tau <- c(0.05, 0.1)

lambda <- length(df.data$y)
max_iter <- 25
trend1 <- get_trend(df.data$y, tau, lambda, k=3)

trend2 <- get_trend_windows(df.data$y, tau, lambda, k=3,
                            window_size, 
                            use_gurobi = TRUE, # Change to FALSE if you do
                            # not have gurobi installed
                            overlap, 
                            max_iter=max_iter, update = 1, 
                            rho = 1, eps_abs = 0.01, 
                            scale=FALSE)


df_no <- rbind(data.frame(x=df.data$x , method = "Single Fit", trend1), 
               data.frame(x=df.data$x , method = "Windows", trend2))


ggplot(df.data, aes(x=x, y=y)) +
  geom_line(col="grey") +
  geom_line(data = df_no, aes(y=X1, col = "0.05", linetype = method))+
  geom_line(data = df_no, aes(y=X2, col = "0.10", linetype = method))+
  scale_color_brewer(palette = "Set1")+
  labs(col="Quantile", linetype = "", x = "") + 
  theme_bw()