library$($forecast$)$ # ARIMA

library$($randomForest$)$ # Random Forest

library$($kernlab$)$ # Support Vector Machines

# dataset$<-$ read.csv$($E:$\backslash$New folder$\backslash$EE$623\_$W$3\_$XREG$3$MonthsData$\_$LOADFORECAST.csv$)$

dataset$=$read.csv$($file$.$choose$(),$header$=$TRUE$)$

head$($dataset$)$ #displays first few rows of the dataset

names$($dataset$)$ #displays columns names of the dataset

pastset$<-$ dataset$[1$:$2184,]$

Yts$=$ts$($pastset$Actual,start$=$c$(2015,1),$ frequency$=8760)$ # The ts$()$ function will convert a numeric vector into an R time series object

require$($forecast$)$ # can be used to attach and load add$-$on packages which are alredy installed

fit$<-$ auto.arima$($Yts$)$

fit

print$($dim$($pastset$[1$:$2184,$ c$(3,4)]))$

print$($dim$($pastset$[2185$:$2208,$ c$(3,4)]))$

# Initialize the Multivariate ARIMA model

# The relationship between the predictor$($input$)$ variables and forecasted variable$($Load$)$ is initialized through this model

InitializedModel $=$ arima$($Yts$,$order $=$ c$(4,1,5),$xreg $=$ pastset$[1$:$2184,$c$(3,4)])$

# Assuming InitializedModel is correctly fitted

# Predict the next day load$-$next $24$ samples

# single day has been selected$($July $31,2015)-$forecast & validate the performance of the proposed model

future$\_$xreg $<-$ dataset$[2185$:$2208,$ c$(3,4)$

# Prediction$=$forecast$($InitializedModel$,$h$=24,$xreg$=$dataset$[2185$:$2208,$c$(3,4,5,6,7)])$ #add xreg for multivariate

str$($predictions$)$

# plot$($predictions$pred, type$="1")$

# Basic plot of the predictions

plot$($predictions$pred, type$="1",$main $=$"Forecasted Values",xlab $=$ "Time",ylab $=$ "Predicted Value"$)$

# Adding a ribbon for standard error $($assuming a normal distribution for the error$)$

# Typically, you would use pred $+/-1\mathrm{.}96*$se for $95\%$ confidence interval

# Adjust the multiplier as needed for different confidence levels

lines$($predictions$pred $+1\mathrm{.}96*$predictions$se$,$ col $=$ "blue",Ity $=$ "dashed"$)$

lines$($predictions$pred $-1\mathrm{.}96*$predictions$se$,$ col $=$ "blue",Ity $=$ "dashed"$)$

f $<-$ predictions$pred

plot$($f$,$ main $=$"ARIMA Forecasted values",xlab $=$ "Time",ylab $=$ "Value",col $=$"blue" $)$

# Initialize the multivariate ARIMA model

# The relationship between the predictor$($input$)$ variables and forecasted variable$($Load$)$ is initialized through this model.

# InitializedModel $=$ arima$($Yts$,$ order $=$ c$(4,1,5),$xreg$=$pastset$[1$:$2184,$c$(3,4,5,6,7)])$ #add command xreg for multivariate

# Predict the next day load$-$next $24$ samples

# Single day has been selected $($July $31,2015)-$forecast & validate the performance of the proposed model

# Prediction$=$forecast$($InitializedModel$,$ h$=24,$ xreg$=$dataset$[2185$:$2208,$c$(3,4,5,6,7)])$ #add xreg for multivariate

# plot$($Prediction$)$

# Prediction$mean

# plot$($Prediction$mean$)$

# f$=$Prediction$mean

# plot$($f$)$

# f

# Mape $-$ ARIMA

mape $=$ mean$($abs$($dataset$Actual$[2185$:$2208]-$f$)/$dataset$Actual$[2185$:$2208])$

mape

## Random forest$($RF$)$

# Ensemble based Method $-$ use multiple learning algorithms$-$

# the ensembles use the small portion of the larger dataset, it is extremely effective in handling the large dataset

# achieve good accuracy as well as overcoming the over$-$fitting problem.

# Training Dataset$-$Load

pastset $<-$dataset$[1$:$2184,]$

# Training the RF Model

rf $<-$randomForest$($Actual~P$.$DD$\mathrm{.}1+$P$.$DD$\mathrm{.}6+$Temp$+$irradiance$+$windspeed,data$=$pastset,importance$=$TRUE,ntree$=1000,$mtry$=2)$

# mtry: Number of variables randomly sampled as candidates at each split

# ntree: Number of trees to grow

# Larger number of trees produce more stable models and covariate importance estimates, but require more memory and a longer run time.

# For larger datasets, $500$ or more may be required.

# For regression models, mtry is the number of predictor variables divided by $3.$

# Test dataset $-$ Forecast day $($July $30,2015)$

forecastset $<-$dataset$[2185$:$2208,]$

forecastset

attach$($forecastset$)$

# The database is attached to the R search path.

# This means that the database is searched by R when evaluating a variable,so objects in the database can be accessed by simply giving their names.

# Predict the next day load$-$ next $24$ samples

RF$.$pred $<-$predict$($rf$,$ newdata$=$data.frame$($P$.$DD$\mathrm{.}1,$P$.$DD$\mathrm{.}6,$data$=$forecastset$))$

RF$.$pred

# Plot the Rf predictions

plot$(1$:$24,$RF$.$pred, type $="1",$ main$=$"Random Forest Forecasted Values", xlab$=$"Time",ylab$=$"Predicted Value",col$=$"darkgreen"$)$

# MAPE RF

mape$=$mean$($abs$($dataset$Actual$[2185$:$2208]-$RF$.$pred$)/$dataset$Actual$[2185$:$2208])$

mape

### Support Vector Machines$-$ supervised learning model that analyzes data for regression in ths work

# Training Dataset$-$Load

pastset $<-$dataset$[1$:$2184,]$

# Training the SVM Model

svm$.$model $<-$ksvm$($Actual ~ P$.$DD$\mathrm{.}1+$ P$.$DD$\mathrm{.}6,$data $=$ pastset,kernel$=$"vanilladot"$)$

# vanilladot helps in fitting a linear SVM

# Fit non$-$linear SVM with Gaussian$($rbf$=$ radial basis function$),$ then kernel $=$ "rbfdot"

# Test dataset $-$Forecast day$($July $30,2015)$

forecastset $<-$dataset$[2185$:$2208,]$

attach$($forecastset$)$

# Predict the next day load$-$next $24$ samples

SVM$.$pred $<-$predict$($svm$.$model,newdata$=$data.frame$($P$.$DD$\mathrm{.}1,$P$.$DD$\mathrm{.}6,$Temp,irradiance,windspeed,data$=$forecastset$))$

SVM$.$pred

plot$(1$:$24,$SVM$.$pred, type$="1",$main$="$SVM Forecasted Values",xlab$=$"Time",ylab$=$"Predicted Value",col$=$"darkred"$)$

# MAPE$-$SVM

mape$=$mean$($abs$($dataset$Actual$[2185$:$2208]-$SVM$.$pred$)/$dataset$Actual$[2185$:$2208])$

mape

I run into this error message anytime I run the arima model. Any help will be appreciated.

$>$InitializedModel $=$ arima$($Yts$,$order$=$ c$(4,1,5),$xreg $=$ pastset$[1$:$2184,$c$(3,4,5,6,7)])$

Error in solve.default$($res$hessian$*$n$.$used, A$)$:

system is computationally singular: reciprocal condition number $=8\mathrm{.}18369$e$-32$