Introduction

PWR: Piecewise Regression (PWR) for time series (or structured longitudinal data) modeling and optimal segmentation by using dynamic programming.

It was written in R Markdown, using the knitr package for production.

See help(package="samurais") for further details and references provided by citation("samurais").

Load data

data("univtoydataset")
x <- univtoydataset$x
y <- univtoydataset$y

Set up PWR model parameters

K <- 5 # Number of segments
p <- 3 # Polynomial degree

Estimation

pwr <- fitPWRFisher(X = x, Y = y, K, p)

Summary

pwr$summary()
## --------------------
## Fitted PWR model
## --------------------
## 
## PWR model with K = 5 components:
## 
## Clustering table (Number of observations in each regimes):
## 
##   1   2   3   4   5 
## 100 120 200 100 150 
## 
## Regression coefficients:
## 
##       Beta(k = 1) Beta(k = 2) Beta(k = 3) Beta(k = 4) Beta(k = 5)
## 1    6.106872e-02   -5.450955   -2.776275    122.7045     4.02081
## X^1 -7.486945e+00  158.922010   43.915969   -482.8929    13.21759
## X^2  2.942201e+02 -651.540876  -94.269414    609.6493   -33.78742
## X^3 -1.828308e+03  866.675017   67.247141   -249.8667    20.41238
## 
## Variances:
## 
##  Sigma2(k = 1) Sigma2(k = 2) Sigma2(k = 3) Sigma2(k = 4) Sigma2(k = 5)
##       1.220624      1.110193      1.079366     0.9779733      1.028329

Plots

Regressors

pwr$plot(what = "regressors")

Segmentation

pwr$plot(what = "segmentation")

A-quick-tour-of-PWR