Analysis of results
Hristos Tyralis, Georgia Papacharalampous
Wednesday, September 06, 2017
- 1 Introduction
- 2 Comparison
- 3 Analysis and figures
- 3.1 ARMA(1,0), AR = 0.6
- 3.2 ARMA(1,0), AR = -0.6
- 3.3 ARMA(2,0), AR = c(0.6, 0.2)
- 3.4 ARMA(2,0), AR = c(-0.6, 0.2)
- 3.5 ARMA(0,1), MA = 0.6
- 3.6 ARMA(0,1), MA = -0.6
- 3.7 ARMA(0,2), MA = c(0.6, 0.2)
- 3.8 ARMA(0,2), MA = c(-0.6, -0.2)
- 3.9 ARMA(1,1), AR = 0.6, MA = 0.6
- 3.10 ARMA(1,1), AR = -0.6, MA = -0.6
- 3.11 ARMA(2,2), AR = c(0.6, 0.2), MA = c(0.6, 0.2)
- 3.12 ARFIMA(0,0.4,0)
- 3.13 ARFIMA(1,0.4,0), AR = 0.6
- 3.14 ARFIMA(0,0.4,1), MA = 0.6
- 3.15 ARFIMA(1,0.4,1), AR = 0.6, MA = 0.6
- 3.16 ARFIMA(2,0.4,2), AR = c(0.6,0.2), MA = c(0.6,0.2)
1 Introduction
1.1 Session information
We will use the following packages for the processing.
library("devtools")
library("ggplot2")
library("reshape2")Some information about the current session follows.
session_info()## Session info -------------------------------------------------------------## setting value
## version R version 3.4.1 (2017-06-30)
## system x86_64, mingw32
## ui RTerm
## language (EN)
## collate English_United Kingdom.1252
## tz Europe/Istanbul
## date 2017-09-06## Packages -----------------------------------------------------------------## package * version date source
## backports 1.1.0 2017-05-22 CRAN (R 3.4.0)
## base * 3.4.1 2017-06-30 local
## colorspace 1.3-2 2016-12-14 CRAN (R 3.4.0)
## compiler 3.4.1 2017-06-30 local
## datasets * 3.4.1 2017-06-30 local
## devtools * 1.13.3 2017-08-02 CRAN (R 3.4.1)
## digest 0.6.12 2017-01-27 CRAN (R 3.4.0)
## evaluate 0.10.1 2017-06-24 CRAN (R 3.4.0)
## ggplot2 * 2.2.1 2016-12-30 CRAN (R 3.4.0)
## graphics * 3.4.1 2017-06-30 local
## grDevices * 3.4.1 2017-06-30 local
## grid 3.4.1 2017-06-30 local
## gtable 0.2.0 2016-02-26 CRAN (R 3.4.0)
## htmltools 0.3.6 2017-04-28 CRAN (R 3.4.0)
## knitr 1.17 2017-08-10 CRAN (R 3.4.1)
## lazyeval 0.2.0 2016-06-12 CRAN (R 3.4.0)
## magrittr 1.5 2014-11-22 CRAN (R 3.4.0)
## memoise 1.1.0 2017-04-21 CRAN (R 3.4.0)
## methods * 3.4.1 2017-06-30 local
## munsell 0.4.3 2016-02-13 CRAN (R 3.4.0)
## plyr 1.8.4 2016-06-08 CRAN (R 3.4.0)
## Rcpp 0.12.12 2017-07-15 CRAN (R 3.4.1)
## reshape2 * 1.4.2 2016-10-22 CRAN (R 3.4.0)
## rlang 0.1.2 2017-08-09 CRAN (R 3.4.1)
## rmarkdown 1.6 2017-06-15 CRAN (R 3.4.0)
## rprojroot 1.2 2017-01-16 CRAN (R 3.4.0)
## scales 0.5.0 2017-08-24 CRAN (R 3.4.1)
## stats * 3.4.1 2017-06-30 local
## stringi 1.1.5 2017-04-07 CRAN (R 3.4.0)
## stringr 1.2.0 2017-02-18 CRAN (R 3.4.0)
## tibble 1.3.4 2017-08-22 CRAN (R 3.4.1)
## tools 3.4.1 2017-06-30 local
## utils * 3.4.1 2017-06-30 local
## withr 2.0.0 2017-07-28 CRAN (R 3.4.1)
## yaml 2.1.14 2016-11-12 CRAN (R 3.4.0)We set a seed, to reproduce the analysis.
set.seed(12345)1.2 Data and functions loading
source("figure_functions.R")
source("test_functions.R")
load("ar1_06.Rdata")
load("ar1__06.Rdata")
load("ar2_06_02.Rdata")
load("ar2__06_02.RData")
load("ma1_06.Rdata")
load("ma1__06.Rdata")
load("ma2_06_02.RData")
load("ma2__06__02.RData")
load("arma11_06_06.Rdata")
load("arma11__06__06.RData")
load("arma22_06_02_06_02.RData")
load("arfima_0_040_0.Rdata")
load("arfima10_06_040_0.RData")
load("arfima01_0_040_06.RData")
load("arfima11_06_040_06.RData")
load("arfima22_06_02_040_06_02.RData")predlist <- list(pred_df_ar1_06,
pred_df_ar1__06,
pred_df_ar2_06_02,
pred_df_ar2__06_02,
pred_df_ma1_06,
pred_df_ma1__06,
pred_df_ma2_06_02,
pred_df_ma2__06__02,
pred_df_arma11_06_06,
pred_df_arma11__06__06,
pred_df_arma22_06_02_06_02,
pred_df_arfima00_0_040_0,
pred_df_arfima10_06_040_0,
pred_df_arfima01_0_040_06,
pred_df_arfima11_06_040_06,
pred_df_arfima22_06_02_040_06_02)
names(predlist) <- c("pred_df_ar1_06",
"pred_df_ar1__06",
"pred_df_ar2_06_02",
"pred_df_ar2__06_02",
"pred_df_ma1_06",
"pred_df_ma1__06",
"pred_df_ma2_06_02",
"pred_df_ma2__06__02",
"pred_df_arma11_06_06",
"pred_df_arma11__06__06",
"pred_df_arma22_06_02_06_02",
"pred_df_arfima00_0_040_0",
"pred_df_arfima10_06_040_0",
"pred_df_arfima01_0_040_06",
"pred_df_arfima11_06_040_06",
"pred_df_arfima22_06_02_040_06_02")modellist <- list(model_df_ar1_06,
model_df_ar1__06,
model_df_ar2_06_02,
model_df_ar2__06_02,
model_df_ma1_06,
model_df_ma1__06,
model_df_ma2_06_02,
model_df_ma2__06__02,
model_df_arma11_06_06,
model_df_arma11__06__06,
model_df_arma22_06_02_06_02,
model_df_arfima00_0_040_0,
model_df_arfima10_06_040_0,
model_df_arfima01_0_040_06,
model_df_arfima11_06_040_06,
model_df_arfima22_06_02_040_06_02)
names(modellist) <- c("model_df_ar1_06",
"model_df_ar1__06",
"model_df_ar2_06_02",
"model_df_ar2__06_02",
"model_df_ma1_06",
"model_df_ma1__06",
"model_df_ma2_06_02",
"model_df_ma2__06__02",
"model_df_arma11_06_06",
"model_df_arma11__06__06",
"model_df_arma22_06_02_06_02",
"model_df_arfima00_0_040_0",
"model_df_arfima10_06_040_0",
"model_df_arfima01_0_040_06",
"model_df_arfima11_06_040_06",
"model_df_arfima22_06_02_040_06_02")tslist <- list(sim_ts_ar1_06,
sim_ts_ar1__06,
sim_ts_ar2_06_02,
sim_ts_ar2__06_02,
sim_ts_ma1_06,
sim_ts_ma1__06,
sim_ts_ma2_06_02,
sim_ts_ma2__06__02,
sim_ts_arma11_06_06,
sim_ts_arma11__06__06,
sim_ts_arma22_06_02_06_02,
sim_ts_arfima00_0_040_0,
sim_ts_arfima10_06_040_0,
sim_ts_arfima01_0_040_06,
sim_ts_arfima11_06_040_06,
sim_ts_arfima22_06_02_040_06_02)
names(tslist) <- c("sim_ts_ar1_06",
"sim_ts_ar1__06",
"sim_ts_ar2_06_02",
"sim_ts_ar2__06_02",
"sim_ts_ma1_06",
"sim_ts_ma1__06",
"sim_ts_ma2_06_02",
"sim_ts_ma2__06__02",
"sim_ts_arma11_06_06",
"sim_ts_arma11__06__06",
"sim_ts_arma22_06_02_06_02",
"sim_ts_arfima00_0_040_0",
"sim_ts_arfima10_06_040_0",
"sim_ts_arfima01_0_040_06",
"sim_ts_arfima11_06_040_06",
"sim_ts_arfima22_06_02_040_06_02")errors_df_ar1_06 <- errors_compute(predlist$pred_df_ar1_06)
errors_df_ar1__06 <- errors_compute(predlist$pred_df_ar1__06)
errors_df_ar2_06_02 <- errors_compute(predlist$pred_df_ar2_06_02)
errors_df_ar2__06_02 <- errors_compute(predlist$pred_df_ar2__06_02)
errors_df_ma1_06 <- errors_compute(predlist$pred_df_ma1_06)
errors_df_ma1__06 <- errors_compute(predlist$pred_df_ma1__06)
errors_df_ma2_06_02 <- errors_compute(predlist$pred_df_ma2_06_02)
errors_df_ma2__06__02 <- errors_compute(predlist$pred_df_ma2__06__02)
errors_df_arma11_06_06 <- errors_compute(predlist$pred_df_arma11_06_06)
errors_df_arma11__06__06 <- errors_compute(predlist$pred_df_arma11__06__06)
errors_df_arma22_06_02_06_02 <- errors_compute(predlist$pred_df_arma22_06_02_06_02)
errors_df_arfima00_0_040_0 <- errors_compute(predlist$pred_df_arfima00_0_040_0)
errors_df_arfima10_06_040_0 <- errors_compute(predlist$pred_df_arfima10_06_040_0)
errors_df_arfima01_0_040_06 <- errors_compute(predlist$pred_df_arfima01_0_040_06)
errors_df_arfima11_06_040_06 <- errors_compute(predlist$pred_df_arfima11_06_040_06)
errors_df_arfima22_06_02_040_06_02 <- errors_compute(predlist$pred_df_arfima22_06_02_040_06_02)
errlist <- list(errors_df_ar1_06,
errors_df_ar1__06,
errors_df_ar2_06_02,
errors_df_ar2__06_02,
errors_df_ma1_06,
errors_df_ma1__06,
errors_df_ma2_06_02,
errors_df_ma2__06__02,
errors_df_arma11_06_06,
errors_df_arma11__06__06,
errors_df_arma22_06_02_06_02,
errors_df_arfima00_0_040_0,
errors_df_arfima10_06_040_0,
errors_df_arfima01_0_040_06,
errors_df_arfima11_06_040_06,
errors_df_arfima22_06_02_040_06_02)
names(errlist) <- c("errors_df_ar1_06",
"errors_df_ar1__06",
"errors_df_ar2_06_02",
"errors_df_ar2__06_02",
"errors_df_ma1_06",
"errors_df_ma1__06",
"errors_df_ma2_06_02",
"errors_df_ma2__06__02",
"errors_df_arma11_06_06",
"errors_df_arma11__06__06",
"errors_df_arma22_06_02_06_02",
"errors_df_arfima00_0_040_0",
"errors_df_arfima10_06_040_0",
"errors_df_arfima01_0_040_06",
"errors_df_arfima11_06_040_06",
"errors_df_arfima22_06_02_040_06_02")2 Comparison
2.1 Means
2.1.1 Absolute errors
abserr_val <- rbind(errlist$errors_df_ar1_06$Mabserr,
errlist$errors_df_ar1__06$Mabserr,
errlist$errors_df_ar2_06_02$Mabserr,
errlist$errors_df_ar2__06_02$Mabserr,
errlist$errors_df_ma1_06$Mabserr,
errlist$errors_df_ma1__06$Mabserr,
errlist$errors_df_ma2_06_02$Mabserr,
errlist$errors_df_ma2__06__02$Mabserr,
errlist$errors_df_arma11_06_06$Mabserr,
errlist$errors_df_arma11__06__06$Mabserr,
errlist$errors_df_arma22_06_02_06_02$Mabserr,
errlist$errors_df_arfima00_0_040_0$Mabserr,
errlist$errors_df_arfima10_06_040_0$Mabserr,
errlist$errors_df_arfima01_0_040_06$Mabserr,
errlist$errors_df_arfima11_06_040_06$Mabserr,
errlist$errors_df_arfima22_06_02_040_06_02$Mabserr)
abserr_ranked <- t(apply(abserr_val, 1, rank))
abserr_ranked <- melt(abserr_ranked)
names(abserr_ranked) <- c("Experiment", "Method", "Ranking")
abserr_val <- melt(abserr_val)
names(abserr_val) <- c("Experiment", "Method", "value")
2.1.2 Squared errors
sqrerr_val <- rbind(errlist$errors_df_ar1_06$Msqrerr,
errlist$errors_df_ar1__06$Msqrerr,
errlist$errors_df_ar2_06_02$Msqrerr,
errlist$errors_df_ar2__06_02$Msqrerr,
errlist$errors_df_ma1_06$Msqrerr,
errlist$errors_df_ma1__06$Msqrerr,
errlist$errors_df_ma2_06_02$Msqrerr,
errlist$errors_df_ma2__06__02$Msqrerr,
errlist$errors_df_arma11_06_06$Msqrerr,
errlist$errors_df_arma11__06__06$Msqrerr,
errlist$errors_df_arma22_06_02_06_02$Msqrerr,
errlist$errors_df_arfima00_0_040_0$Msqrerr,
errlist$errors_df_arfima10_06_040_0$Msqrerr,
errlist$errors_df_arfima01_0_040_06$Msqrerr,
errlist$errors_df_arfima11_06_040_06$Msqrerr,
errlist$errors_df_arfima22_06_02_040_06_02$Msqrerr)
sqrerr_ranked <- t(apply(sqrerr_val, 1, rank))
sqrerr_ranked <- melt(sqrerr_ranked)
names(sqrerr_ranked) <- c("Experiment", "Method", "Ranking")
sqrerr_val <- melt(sqrerr_val)
names(sqrerr_val) <- c("Experiment", "Method", "value")
2.2 Medians
2.2.1 Absolute errors
abserr_val <- rbind(as.matrix(errlist$errors_df_ar1_06$medabserr),
as.matrix(errlist$errors_df_ar1__06$medabserr),
as.matrix(errlist$errors_df_ar2_06_02$medabserr),
as.matrix(errlist$errors_df_ar2__06_02$medabserr),
as.matrix(errlist$errors_df_ma1_06$medabserr),
as.matrix(errlist$errors_df_ma1__06$medabserr),
as.matrix(errlist$errors_df_ma2_06_02$medabserr),
as.matrix(errlist$errors_df_ma2__06__02$medabserr),
as.matrix(errlist$errors_df_arma11_06_06$medabserr),
as.matrix(errlist$errors_df_arma11__06__06$medabserr),
as.matrix(errlist$errors_df_arma22_06_02_06_02$medabserr),
as.matrix(errlist$errors_df_arfima00_0_040_0$medabserr),
as.matrix(errlist$errors_df_arfima10_06_040_0$medabserr),
as.matrix(errlist$errors_df_arfima01_0_040_06$medabserr),
as.matrix(errlist$errors_df_arfima11_06_040_06$medabserr),
as.matrix(errlist$errors_df_arfima22_06_02_040_06_02$medabserr))
abserr_ranked <- t(apply(abserr_val, 1, rank))
abserr_ranked <- melt(abserr_ranked)
names(abserr_ranked) <- c("Experiment", "Method", "Ranking")
abserr_val <- melt(abserr_val)
names(abserr_val) <- c("Experiment", "Method", "value")
2.2.2 Squared errors
sqrerr_val <- rbind(as.matrix(errlist$errors_df_ar1_06$medsqrerr),
as.matrix(errlist$errors_df_ar1__06$medsqrerr),
as.matrix(errlist$errors_df_ar2_06_02$medsqrerr),
as.matrix(errlist$errors_df_ma1_06$medsqrerr),
as.matrix(errlist$errors_df_ma1__06$medsqrerr),
as.matrix(errlist$errors_df_arma11_06_06$medsqrerr),
as.matrix(errlist$errors_df_arfima00_0_040_0$medsqrerr),
as.matrix(errlist$errors_df_arfima10_06_040_0$medsqrerr),
as.matrix(errlist$errors_df_arfima01_0_040_06$medsqrerr),
as.matrix(errlist$errors_df_arfima11_06_040_06$medsqrerr),
as.matrix(errlist$errors_df_arfima22_06_02_040_06_02$medsqrerr),
as.matrix(errlist$errors_df_ma2_06_02$medsqrerr),
as.matrix(errlist$errors_df_ma2__06__02$medsqrerr),
as.matrix(errlist$errors_df_ar2__06_02$medsqrerr),
as.matrix(errlist$errors_df_arma11__06__06$medsqrerr),
as.matrix(errlist$errors_df_arma22_06_02_06_02$medsqrerr))
sqrerr_ranked <- t(apply(sqrerr_val, 1, rank))
sqrerr_ranked <- melt(sqrerr_ranked)
names(sqrerr_ranked) <- c("Experiment", "Method", "Ranking")
sqrerr_val <- melt(sqrerr_val)
names(sqrerr_val) <- c("Experiment", "Method", "value")
2.3 Regression coefficient
lincoef_val <- rbind(as.matrix(errlist$errors_df_ar1_06$lincoef),
as.matrix(errlist$errors_df_ar1__06$lincoef),
as.matrix(errlist$errors_df_ar2_06_02$lincoef),
as.matrix(errlist$errors_df_ar2__06_02$lincoef),
as.matrix(errlist$errors_df_ma1_06$lincoef),
as.matrix(errlist$errors_df_ma1__06$lincoef),
as.matrix(errlist$errors_df_ma2_06_02$lincoef),
as.matrix(errlist$errors_df_ma2__06__02$lincoef),
as.matrix(errlist$errors_df_arma11_06_06$lincoef),
as.matrix(errlist$errors_df_arma11__06__06$lincoef),
as.matrix(errlist$errors_df_arma22_06_02_06_02$lincoef),
as.matrix(errlist$errors_df_arfima00_0_040_0$lincoef),
as.matrix(errlist$errors_df_arfima10_06_040_0$lincoef),
as.matrix(errlist$errors_df_arfima01_0_040_06$lincoef),
as.matrix(errlist$errors_df_arfima11_06_040_06$lincoef),
as.matrix(errlist$errors_df_arfima22_06_02_040_06_02$lincoef))
lincoef_ranked <- t(apply(-lincoef_val, 1, rank))
lincoef_ranked <- melt(lincoef_ranked)
names(lincoef_ranked) <- c("Experiment", "Method", "Ranking")
lincoef_val <- melt(lincoef_val)
names(lincoef_val) <- c("Experiment", "Method", "value")
3 Analysis and figures
3.1 ARMA(1,0), AR = 0.6
3.1.1 Forecasts
3.1.2 Summary of results
3.1.2.1 Boxplots
3.1.2.2 Barplots
3.2 ARMA(1,0), AR = -0.6
3.2.1 Forecasts
3.2.2 Summary of results
3.2.2.1 Boxplots
3.2.2.2 Barplots
3.3 ARMA(2,0), AR = c(0.6, 0.2)
3.3.1 Forecasts
3.3.2 Summary of results
3.3.2.1 Boxplots
3.3.2.2 Barplots
3.4 ARMA(2,0), AR = c(-0.6, 0.2)
3.4.1 Forecasts
3.4.2 Summary of results
3.4.2.1 Boxplots
3.4.2.2 Barplots
3.5 ARMA(0,1), MA = 0.6
3.5.1 Forecasts
3.5.2 Summary of results
3.5.2.1 Boxplots
3.5.2.2 Barplots
3.6 ARMA(0,1), MA = -0.6
3.6.1 Forecasts
3.6.2 Summary of results
3.6.2.1 Boxplots
3.6.2.2 Barplots
3.7 ARMA(0,2), MA = c(0.6, 0.2)
3.7.1 Forecasts
3.7.2 Summary of results
3.7.2.1 Boxplots
3.7.2.2 Barplots
3.8 ARMA(0,2), MA = c(-0.6, -0.2)
3.8.1 Forecasts
3.8.2 Summary of results
3.8.2.1 Boxplots
3.8.2.2 Barplots
3.9 ARMA(1,1), AR = 0.6, MA = 0.6
3.9.1 Forecasts
3.9.2 Summary of results
3.9.2.1 Boxplots
3.9.2.2 Barplots
3.10 ARMA(1,1), AR = -0.6, MA = -0.6
3.10.1 Forecasts
3.10.2 Summary of results
3.10.2.1 Boxplots
3.10.2.2 Barplots
3.11 ARMA(2,2), AR = c(0.6, 0.2), MA = c(0.6, 0.2)
3.11.1 Forecasts
3.11.2 Summary of results
3.11.2.1 Boxplots
3.11.2.2 Barplots
3.12 ARFIMA(0,0.4,0)
3.12.1 Forecasts
3.12.2 Summary of results
3.12.2.1 Boxplots
3.12.2.2 Barplots
3.13 ARFIMA(1,0.4,0), AR = 0.6
3.13.1 Forecasts
3.13.2 Summary of results
3.13.2.1 Boxplots
3.13.2.2 Barplots
3.14 ARFIMA(0,0.4,1), MA = 0.6
3.14.1 Forecasts
3.14.2 Summary of results
3.14.2.1 Boxplots
3.14.2.2 Barplots
3.15 ARFIMA(1,0.4,1), AR = 0.6, MA = 0.6
3.15.1 Forecasts
3.15.2 Summary of results
3.15.2.1 Boxplots
3.15.2.2 Barplots
3.16 ARFIMA(2,0.4,2), AR = c(0.6,0.2), MA = c(0.6,0.2)
3.16.1 Forecasts
3.16.2 Summary of results
3.16.2.1 Boxplots
3.16.2.2 Barplots
