In Techtonique/ahead: Time Series Forecasting with uncertainty quantification

ahead is a package for univariate and multivariate time series forecasting, with uncertainty quantification (R and Python).

The model used in this demo is the one presented in this paper, and has actually been significantly improved since 2018, as you'll see here.

Currently for this model (as of 2023-08-28), for uncertainty quantification, I have:

• Gaussian distribution
• Independent bootstrap simulation
• Multivariate circular block bootstrap simulation
• Multivariate moving block bootstrap simulation
• Copula simulation
• More options to come in the future.

Please remember that in real life, this model's hyperparameters will have to be tuned.

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Contents:

• 0 - Install ahead
• 1 - Prediction intervals based on Gaussian distribution (meh, but quick)
• 2 - Prediction intervals based on independent bootstrap
• 3 - Prediction intervals based on block bootstrap
• 4 - Prediction intervals based on moving block bootstrap
• 5 - Prediction intervals based on R-Vine copula simulation

0 - Install ahead

Here's how to install the R version of the package:

• 1st method: from R-universe

  In R console:

  ``` r options(repos = c( techtonique = 'https://techtonique.r-universe.dev', CRAN = 'https://cloud.r-project.org'))

  install.packages("ahead") ```

• 2nd method: from Github

  In R console:

  r devtools::install_github("Techtonique/ahead")

  Or

  r remotes::install_github("Techtonique/ahead")

And here are the packages that will be used in this vignette:

library(ahead)
library(fpp)

library(ahead)
library(fpp)

1 - Prediction intervals based on Gaussian distribution (meh, but quick)

1 - 1 With default parameters

h <- 10L # forecasting horizon

(res1 <- ahead::ridge2f(fpp::insurance, h = h))

print(summary(res1$residuals))

print(apply(res1$residuals, 2, function (x) Box.test(x)$p.value)) # stationarity is overrated?:)

print(apply(res1$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res1, "Quotes")
plot(res1, "TV.advert")

1 - 2 With external regressors

xreg <- as.numeric(time(fpp::insurance))
(res2 <- ahead::ridge2f(fpp::insurance, xreg = xreg, h = h))

print(summary(res2$residuals))

print(apply(res2$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res2$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res2, "Quotes")
plot(res2, "TV.advert")

1 - 3 With external regressors and K-Means clustering

centers <- 2L
(res3 <- ahead::ridge2f(fpp::insurance, xreg = xreg, centers = centers, h = h))

print(summary(res3$residuals))

print(apply(res3$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res3$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res3, "Quotes")
plot(res3, "TV.advert")

1 - 4 With K-Means clustering

centers <- 2L
(res10 <- ahead::ridge2f(fpp::insurance, centers = centers, h = h))

print(summary(res10$residuals))

print(apply(res10$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res10$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res10, "Quotes")
plot(res10, "TV.advert")

2 - Prediction intervals based on independent bootstrap

2 - 1 With default parameters

B <- 10L # number of bootstrap replications -- increase this
(res4 <- ahead::ridge2f(fpp::insurance, 
                        type_pi = "bootstrap", B = B, h = h))

print(summary(res4$residuals))

print(apply(res4$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res4$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res4, "Quotes")
plot(res4, "TV.advert")

2 - 2 With external regressors

(res5 <- ahead::ridge2f(fpp::insurance, xreg = xreg, 
                        type_pi = "bootstrap", B = B, h = h))

print(summary(res5$residuals))

print(apply(res5$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res5$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res5, "Quotes")
plot(res5, "TV.advert")

2 - 3 With external regressors and K-Means clustering

(res6 <- ahead::ridge2f(fpp::insurance, xreg = xreg, 
                        centers = centers, 
                        type_pi = "bootstrap", B = B, h = h))

print(summary(res6$residuals))

print(apply(res6$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res6$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res6, "Quotes")
plot(res6, "TV.advert")

2 - 4 With K-Means clustering

centers <- 2L
(res11 <- ahead::ridge2f(fpp::insurance, 
                         centers = centers, 
                         type_pi = "bootstrap", B = B, h = h))

print(summary(res11$residuals))

print(apply(res11$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res11$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res11, "Quotes")
plot(res11, "TV.advert")

3 - Prediction intervals based on block bootstrap

3 - 1 With default parameters

block_length <- 5L
(res7 <- ahead::ridge2f(fpp::insurance, 
                        type_pi = "blockbootstrap", 
                        block_length = block_length,
                        B = B, h = h))

print(summary(res7$residuals))

print(apply(res7$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res7$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res7, "Quotes")
plot(res7, "TV.advert")

3 - 2 With external regressors

(res8 <- ahead::ridge2f(fpp::insurance, xreg = xreg, 
                        type_pi = "blockbootstrap", 
                        block_length = block_length,
                        B = B, h = h))

print(summary(res8$residuals))

print(apply(res8$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res8$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res8, "Quotes")
plot(res8, "TV.advert")

3 - 3 With external regressors and K-Means clustering

(res9 <- ahead::ridge2f(fpp::insurance, 
                        xreg = xreg, centers = centers, 
                        type_pi = "blockbootstrap", 
                        block_length = block_length,
                        B = B, h = h))

print(summary(res9$residuals))

print(apply(res9$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res9$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res9, "Quotes")
plot(res9, "TV.advert")

3 - 4 With K-Means clustering

(res12 <- ahead::ridge2f(fpp::insurance, 
                         centers = centers, 
                         type_pi = "blockbootstrap", 
                         block_length = block_length,
                         B = B, h = h))

print(summary(res12$residuals))

print(apply(res12$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res12$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res12, "Quotes")
plot(res12, "TV.advert")

3 - 5 Using the median instead of the mean in bootstrap aggregation

(res13 <- ahead::ridge2f(fpp::insurance, 
                         centers = centers, 
                         type_pi = "blockbootstrap", 
                         type_aggregation = "median",
                         block_length = block_length,
                         B = B, h = h))

print(apply(res13$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

print(summary(res13$residuals))

print(apply(res13$residuals, 2, function (x) Box.test(x)$p.value))

plot(res13, "Quotes")
plot(res13, "TV.advert")

4 - Prediction intervals based on moving block bootstrap

4 - 1 With default parameters

block_length <- 5L
(res16 <- ahead::ridge2f(fpp::insurance, 
                        type_pi = "movingblockbootstrap", 
                        block_length = block_length,
                        B = B, h = h))

print(summary(res16$residuals))

print(apply(res16$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res16$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res16, "Quotes", type = "sims")
plot(res16, "TV.advert")

4 - 2 With external regressors

(res8 <- ahead::ridge2f(fpp::insurance, xreg = xreg, 
                        type_pi = "movingblockbootstrap", 
                        block_length = block_length,
                        B = B, h = h))

print(summary(res8$residuals))

print(apply(res8$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res8$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res8, "Quotes")
plot(res8, "TV.advert", type = "dist")

4 - 3 With external regressors and K-Means clustering

(res15 <- ahead::ridge2f(fpp::insurance, 
                        xreg = xreg, centers = centers, 
                        type_pi = "movingblockbootstrap", 
                        block_length = block_length,
                        B = B, h = h))

print(summary(res15$residuals))

print(apply(res15$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res15$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res15, "Quotes", type = "dist")
plot(res15, "TV.advert")

4 - 4 With K-Means clustering

(res12 <- ahead::ridge2f(fpp::insurance, 
                         centers = centers, 
                         type_pi = "movingblockbootstrap", 
                         block_length = block_length,
                         B = B, h = h))

print(summary(res12$residuals))

print(apply(res12$residuals, 2, function (x) Box.test(x)$p.value))

print(apply(res12$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

plot(res12, "Quotes")
plot(res12, "TV.advert", type = "sims")

4 - 5 Using the median instead of the mean in bootstrap aggregation

(res14 <- ahead::ridge2f(fpp::insurance, 
                         centers = centers, 
                         type_pi = "movingblockbootstrap", 
                         type_aggregation = "median",
                         block_length = block_length,
                         B = B, h = h))

print(apply(res14$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?

print(summary(res14$residuals))

print(apply(res14$residuals, 2, function (x) Box.test(x)$p.value))

plot(res14, "Quotes", type = "dist")
plot(res14, "TV.advert")

5 - Prediction intervals based on R-Vine copula simulation

(obj <- ahead::ridge2f(fpp::insurance, 
                         type_pi = "rvinecopula", 
                         B = B, h = h))


plot(obj, "Quotes", type = "dist")
plot(obj, "TV.advert", type = "sims")

Techtonique/ahead documentation built on Nov. 24, 2024, 10:33 a.m.