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SimpleDataRegression.Rmd
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---
title: "Simple Data Regression"
output: html_notebook
---
Created by Aubry
Date : 22/10/19
Load data
```{r}
library(data.table)
library(dplyr)
library(formattable)
library(tidyr)
library(rlist)
load_all <- read.csv("./data/processed/inline/inline_all_zone_and_sum.csv")
load_all <- load_all[,2:24]
library(lubridate)
load_all$Date <- ymd_hm(paste(load_all$datetime, load_all$time))
clean_all <- data.frame(load_all$Date,load_all[,3:23])
colnames(clean_all)[colnames(clean_all) == "load_all.Date"] <- "Date"
#for each missing row, we find previous year values
missing_idx <- which(is.na(clean_all),arr.ind = TRUE)[,1]
doublons <- which(duplicated(missing_idx))
missing_idx <- missing_idx[-doublons]
#seasonal naive method
for(i in missing_idx){
clean_all[i,2:22] = clean_all[i-24*365,2:22]
}
missing_idx <- which(is.na(clean_all),arr.ind = TRUE)[,1]
```
Discribe data
```{r}
dim(clean_all)
summary(clean_all)
head(clean_all)
```
Remarques :
1. Data are taken from 2004-01-01 to 2008-07-07
2. Total of 1650 rows
3. 63 of which are NA -> missing values
```{r}
library(forecast)
hl <- 7*24
#dropping the last week as it is NA
data.X1 <- ts(clean_all$X1[1:(length(clean_all$X1)-hl)])
data.X2 <- ts(clean_all$X2[1:(length(clean_all$X2)-hl)])
#data.mean <- meanf(ts(data.X1$X1, frequency = 24*365),h=hl)
#data.naive <- rwf(ts(data.X1$X1, frequency = 24*365),h=hl)
#data.snaive <- snaive(ts(data.X1$X1, frequency = 24*365),h=hl)
#data.X1$X1[1:(length(data.X1$X1)-hl)]
fit.rwf <- rwf(data.X1[1:(length(data.X1)-hl)],h=hl)
fit.drift <- rwf(data.X1[1:(length(data.X1)-hl)],h=hl, drift = TRUE)
fit.meanf <- meanf(data.X1[1:(length(data.X1)-hl)],h=hl)
fit.snaive <- snaive(ts(data.X1[1:(length(data.X1)-hl)],freq = 24),h=hl)
fit.rwf.acc <- accuracy(fit.rwf, data.X1[(length(data.X1)-hl+1):length(data.X1)])
fit.drift.acc <- accuracy(fit.drift, data.X1[(length(data.X1)-hl+1):length(data.X1)])
fit.meanf.acc <- accuracy(fit.meanf, data.X1[(length(data.X1)-hl+1):length(data.X1)])
fit.snaive.acc <- accuracy(fit.snaive, data.X1[(length(data.X1)-hl+1):length(data.X1)])
`````
Dealing with accuracies
```{r}
print(fit.rwf.acc)
print(fit.drift.acc)
print(fit.meanf.acc)
print(fit.snaive.acc)
fit.meanf.acc <- cbind(fit.meanf.acc, c(NA, NA))
colnames(fit.meanf.acc)[7] <- "ACF1"
print(fit.meanf.acc)
data.acc <- rbind(fit.rwf.acc, fit.drift.acc, fit.meanf.acc, fit.snaive.acc)
data.acc <- cbind(data.acc, c("rwf", "rwf", "drift", "drift", "meanf", "meanf", "snaive", "snaive"))
colnames(data.acc)[8] <- "Forecast"
data.df <- data.frame(data.acc)
print(data.df)
model <- c(rep("rwf" , 7), rep("drift", 7), rep("meanf" , 7) , rep("snaive" , 7) )
metrics <- rep(c("ME" , "RMSE" ,"MAE", "MPE", "MAPE", "MASE", "ACF1") , 4)
value <- c(fit.rwf.acc[2,], fit.drift.acc[2,], fit.meanf.acc[2,], fit.snaive.acc[2,])
names(value) <- NULL
data.acc <- data.frame(model,metrics,value)
# Grouped
ggplot(data.acc, aes(fill=model, y=value, x=metrics)) +
geom_bar(position="dodge", stat="identity")
```
```{r}
fit.rwf$my_mean <- ts(fit.rwf$mean, start = 39265 , end = 39432 , frequency = 1)
fit.drift$my_mean <- ts(fit.drift$mean, start = 39265 , end = 39432 , frequency = 1)
fit.meanf$my_mean <- ts(fit.meanf$mean, start = 39265 , end = 39432 , frequency = 1)
fit.snaive$my_mean <- ts(fit.snaive$mean, start = 39265 , end = 39432 , frequency = 1)
autoplot(window(data.X1, start= 39096,end = 39432)) +
autolayer(fit.meanf$my_mean, series="Mean", PI=FALSE) +
autolayer(fit.drift$my_mean, series="Drift", PI=FALSE) +
autolayer(fit.rwf$my_mean, series="Naïve", PI=FALSE) +
autolayer(fit.snaive$my_mean, series="Seasonal", PI=FALSE)+
labs(x = "Time (h)", y="Load")
```
Cross-Validation
Impossible to run for all data
```{r}
cv.rwf <- tsCV(data.X1[(length(data.X1)-30*hl):(length(data.X1))], rwf, drift =TRUE, h=7*24)
# Compute the MSE values and remove missing values
cv.rwf.mse <- colMeans(cv.rwf^2, na.rm = T)
cv.meanf <- tsCV(data.X1[(length(data.X1)-30*hl):(length(data.X1))], forecast::meanf, h=7*24)
# Compute the MSE values and remove missing values
cv.meanf.mse <- colMeans(cv.meanf^2, na.rm = T)
cv.snaive <- tsCV(data.X1[(length(data.X1)-30*hl):(length(data.X1))], snaive, drift =TRUE, h=7*24)
# Compute the MSE values and remove missing values
cv.snaive.mse <- colMeans(cv.snaive^2, na.rm = T)
# Plot the MSE values against the forecast horizon
cv.rwf.df <- data.frame(h = 1:(hl), MSE= cv.rwf.mse)
cv.meanf.df <- data.frame(h = 1:(hl), MSE = cv.meanf.mse)
cv.snaive.df <- data.frame(h = 1:(hl), MSE = cv.snaive.mse)
print(cv.meanf.df)
#(24*7):1680
autoplot(ts((rowMeans(cv.rwf^2))[(24*7):1680], frequency = 1, start = 24*7), series = "rwf")+
autolayer(ts((rowMeans(cv.meanf^2))[(24*7):1680], frequency = 1, start = 24*7), series ="meanf")+
autolayer(ts((rowMeans(cv.snaive^2))[(24*7):1680], frequency = 1, start = 24*7), series = "snaive")+
labs(x="T of the last sample of training data", y="MSE")
ggplot()+
geom_line(data = cv.rwf.df, aes(x = h, y = MSE, color ="rwf"))+
geom_line(data = cv.meanf.df, aes(x = h, y = MSE, color = "meanf"))+
geom_line(data = cv.snaive.df, aes(x = h, y = MSE, color="snaive"))
```
# Simple Mean Prediction
```{r}
mean_forecast <- meanf(load_all$X1, 7*24)
accuracy(mean_forecast)
```
# Naive prédiction, previous value
```{r}
naive_forecast <- naive(load_all$X1, 7*24)
accuracy(naive_forecast)
```
# Correlation between zones
$$norm\_corr(x,y)=\dfrac{\sum_{n=0}^{n-1} x[n]*y[n]}{\sqrt{\sum_{n=0}^{n-1} x[n]^2 * \sum_{n=0}^{n-1} y[n]^2}}$$
```{r}
correlationTable = function(graphs) {
cross = matrix(nrow = length(graphs)-3, ncol = length(graphs)-3)
for(graph1Id in 3:length(graphs)-1){
graph1 = graphs[[graph1Id]]
print(graph1Id)
for(graph2Id in 3:length(graphs)-1) {
graph2 = graphs[[graph2Id]]
if(graph1Id == graph2Id){
break;
} else {
correlation = ccf(graph1, graph2, lag.max = 0, na.action = na.pass, plot = FALSE)
cross[graph1Id-2, graph2Id-2] = correlation$acf[1]
}
}
}
cross
}
graphs = load_all
corr = correlationTable(graphs)
#print(corr)
# Obtenir le triangle inférieur
get_lower_tri<-function(cormat){
cormat[upper.tri(cormat)] <- NA
return(cormat)
}
lower_tri <- get_lower_tri(corr)
# Fondre la matrice de corrélation
library(reshape2)
melted_cormat <- melt(lower_tri, na.rm = TRUE)
print(melted_cormat)
# Heatmap
library(ggplot2)
ggplot(data = melted_cormat, aes(Var2, Var1, fill = value))+
geom_tile(color = "white")+
scale_fill_gradient2(low = "blue", high = "red", mid = "white",
midpoint = 0, limit = c(-1,1), space = "Lab",
name="Pearson\nCorrelation") +
theme_minimal()+
labs(y= "Zone 1", x = "Zone 2")+
theme(axis.text.x = element_text(angle = 45, vjust = 1,
size = 12, hjust = 1))+
coord_fixed()
```
See the revered correlated ts
```{r}
ts.X9 <-ts(load_all$X9[(length(load_all$X9)-24*7*30):(length(load_all$X9)-24*7*27)])
ts.X10 <-ts(load_all$X10[(length(load_all$X10)-24*7*30):(length(load_all$X10)-24*7*27)])
ts.X6 <-ts(load_all$X6[(length(load_all$X6)-24*7*30):(length(load_all$X6)-24*7*27)])
ts.X12 <-ts(load_all$X12[(length(load_all$X12)-24*7*30):(length(load_all$X12)-24*7*27)])
autoplot(ts.X9)+autolayer(ts.X10)+autolayer(ts.X6)+autolayer(ts.X12)+labs(y="load", x="time (h)")
```
```{r}
ccf(load_all$X6, load_all$X12, na.action = na.pass)+
scale_x_continuous(breaks = seq(-40, 40, by=5))
```
```{r}
VAR <- c (65.00252964, 67.95751522, 71.31060956, 74.51020723, 77.20331451,
79.55855226, 81.24217121, 82.48658745, 83.06384171, 82.48150083,
81.42869664, 80.36389915, 78.22829342, 75.3403245 , 72.16611972,
69.45152037, 67.57997846, 66.20915574, 65.04496667, 63.81352579,
63.07243765, 62.62683939, 62.30716981, 62.27874736, 63.64637688,
66.47395524, 69.78197102, 72.84574535, 75.52967286, 77.92393012,
79.73219736, 81.13714485, 81.73222267, 81.07694254, 79.96133859,
78.98470239, 77.00557616, 74.25213394, 71.20425812, 68.52124695,
66.65054883, 65.36397845, 64.33879605, 63.26135991, 62.61282595,
62.35853711, 62.32890085, 62.57946906, 64.17323295, 66.83558658,
69.8638937 , 72.83127669, 75.49221516, 77.84153758, 79.64242278,
80.94783556, 81.32661173, 80.67712697, 79.66774428, 78.53646844,
76.64229363, 73.97167769, 71.00856685, 68.39031613, 66.48310166,
65.21079629, 64.13731739, 63.06217743, 62.39288674, 62.19910625,
62.22662456, 62.66920973, 64.20971055, 66.76234453, 69.69651577,
72.50319864, 75.09152057, 77.36475486, 79.1546215 , 80.43679029,
80.91727402, 80.43450411, 79.53375494, 78.43529294, 76.55982341,
73.95148552, 71.04777053, 68.43086506, 66.47933219, 65.1231291 ,
63.99129442, 62.92573338, 62.26290088, 62.02859421, 62.05089325,
62.49679733, 63.97028146, 66.43060444, 69.26856971, 72.00621919,
74.53746265, 76.77448072, 78.56711556, 79.87255822, 80.37025972,
79.9417823 , 79.05877855, 77.91528086, 76.05106678, 73.4740589 ,
70.60332397, 67.98723996, 65.99669837, 64.60066433, 63.45953632,
62.4356897 , 61.79258543, 61.57512347, 61.63974566, 62.136611 ,
63.60276297, 65.97709388, 68.70578521, 71.37977557, 73.88103305,
76.10188326, 77.90437332, 79.19646705, 79.66695093, 79.25661881,
78.3944784 , 77.21378682, 75.3717469 , 72.85393776, 70.04864424,
67.4718375 , 65.48698648, 64.08568782, 62.95009859, 61.96102422,
61.34630355, 61.16962045, 61.29256523, 61.88188496, 63.35407143,
65.65824603, 68.31074237, 70.92645037, 73.38911211, 75.58132562,
77.3711595 , 78.6280978 , 79.08775786, 78.70876301, 77.85758932,
76.6624669 , 74.83549029, 72.3751646 , 69.64148062, 67.11316677,
65.14398926, 63.7321356 , 62.59469903, 61.63218012, 61.04408016,
60.88220257, 61.04619771, 61.67833766)
val <- c(68.09090909, 70.27272727, 72.81818182, 75.81818182, 77.45454545,
79.81818182, 82.27272727, 83.63636364, 84.81818182, 85. ,
84.72727273, 83.18181818, 81.45454545, 78.18181818, 73.54545455,
71.09090909, 68.54545455, 68.09090909, 66.63636364, 64.45454545,
63.45454545, 62.09090909, 61.63636364, 60.27272727, 62.72727273,
67.81818182, 71.90909091, 75.72727273, 77.45454545, 79.81818182,
81.54545455, 82.72727273, 83.09090909, 83.54545455, 84.45454545,
83.72727273, 82.54545455, 78.63636364, 72.54545455, 70. ,
67.09090909, 65.18181818, 64.27272727, 63.09090909, 62.45454545,
61.63636364, 60.45454545, 60.63636364, 62.72727273, 69.36363636,
74.27272727, 78.72727273, 81.81818182, 83.90909091, 85.45454545,
86.54545455, 87.36363636, 88. , 87.90909091, 87.18181818,
85.54545455, 81.81818182, 76.72727273, 73.54545455, 71.81818182,
70.72727273, 70.72727273, 69.36363636, 69.09090909, 68.27272727,
67.45454545, 67.81818182, 69.90909091, 73.63636364, 78.63636364,
82.72727273, 85.63636364, 88.45454545, 90.54545455, 92.18181818,
93.27272727, 93.72727273, 93.90909091, 93. , 89.72727273,
85.90909091, 82.45454545, 79.09090909, 77.63636364, 76.45454545,
76.09090909, 75.18181818, 74.90909091, 73.27272727, 72.09090909,
72.09090909, 72.72727273, 76.81818182, 80.36363636, 84.18181818,
86.45454545, 88.90909091, 90.45454545, 89.18181818, 90.27272727,
87.27272727, 86.27272727, 84.36363636, 83. , 80.72727273,
78.18181818, 76.09090909, 74.90909091, 73.81818182, 72.81818182,
73.09090909, 73.09090909, 72.27272727, 71.09090909, 70.72727273,
72.81818182, 76.36363636, 80.36363636, 83.72727273, 86.90909091,
88.63636364, 90.36363636, 91.36363636, 92.81818182, 93.27272727,
91.36363636, 89.63636364, 87.54545455, 85.27272727, 81. ,
79.54545455, 78.54545455, 77.72727273, 77.45454545, 75.81818182,
75.36363636, 74.63636364, 74. , 73.81818182, 74.54545455,
77.18181818, 79.90909091, 83. , 84.45454545, 86.09090909,
86.81818182, 86.27272727, 87.45454545, 88.18181818, 87.63636364,
86.72727273, 84.45454545, 82. , 77.18181818, 75.63636364,
73.45454545, 72.54545455, 72.09090909, 71.09090909, 70.81818182,
70.27272727, 70.09090909, 69.81818182)
accuracy(ts(VAR, frequency = 1), ts(val, frequency=1))
```