Forecasting using support vector regression in R - r

Question

I want to forecast the future energy consumption using support vector regression in R.I have this code but I'am not sure weather it is correct or not.
`#gathering the data
data<-read.csv("C:\\2003_smd_hourly.csv",header=TRUE) #these are the values which are used to train the given model#
data
#data1<-read.csv("C:\\pr.csv",header=TRUE)#this file/ddata is used for checking the accuracy of prediction#
#data1
#y1<-data1[,15]
#x0<-data1[,2]
y<-data[,15] #sysload
x1<-data[,2] #houroftheday
x2<-data[,13] #drybulb temp(actualtemp)
x3<-data[,14] #dewpnttemp
#train<-sample(744,447)
#train
library(e1071)
model<-svm(y~x1+x2+x3,data=data[1:48,],cost=2.52*10^11,epsilon=0.0150,gamma=1)
model
#pr<-data[-train,]
#pr
predict1<-predict(model,newdata=data[49:72,])
predict1
par(mfrow=c(2,2))
plot(x1,y,col="red",pch=4)
#par(new=TRUE)
plot(x1,predict1,col="blue",pch=5) #plotting the values that have been predicted
#par(new=TRUE)
plot(x0,y1,col="black",pch=1)
error=y1-predict1
error
mae <- function(error)
{
mean(abs(error))
}
mae(error)
error <- y1 - predict1
error
rmse <- function(error)
{
sqrt(mean(error^2))
}
svrPredictionRMSE <- rmse(error)
svrPredictionRMSE
max(error)
min(error)
mape <- function(y1,predict1)
mape
mean(abs((y1 - predict1)/y1))*100
mape
`Eg:data can be found here http://pastebin.com/MUfWFCPM

Answer 1

Use the newdata parameter for prediction (you newdata for test should have the same set of features as the training data). e.g., with mtcars dataset
library(e1071)
model<-svm(mpg~wt+disp+qsec,data=mtcars[1:24,],cost=512,epsilon=0.01)
model
predict1<-predict(model,newdata=mtcars[25:32,])
predict1 # prediction for the new 8 data points
Pontiac Firebird Fiat X1-9 Porsche 914-2 Lotus Europa Ford Pantera L Ferrari Dino Maserati Bora Volvo 142E
28.514002 31.184527 23.022863 22.603601 6.228431 30.482475 6.801507 22.939945

Answer 2

If you want to predict what happens in the next two days, you have to train a model to predict two days ahead. Let's pick a simple example, then I'll move to an SVR. Suppose we use a linear AR-direct forecasting model and, through some method we determined that two lags are enough. So we have this model:
y_{t+h} = alpha + phi_1 y_{t} + phi_2 y_{t-1} + e_{t+h}
The literature in economics calls this an AR-direct forecast because it directly ouputs y_{t+h}, as opposed to indirectly producing y_{t+h} by providing a recursive relationship across forecasts. Say that 'y' is the temperature in celcius degrees, so you want to forecast the temperature in two days using temperature data up until -- and including -- today. Suppose we use daily temperatures of the last month.
We know that ordinary least squares is a convergent estimator of alpha, phi_1 and phi_2, so we can form a matrix, X, containing a column of ones, one column of temperatures lagged h times and a column of temperatures lagged h + 1 times. Then, compute a linear projection of our temperature vector, y, on X like so: estimated [alpha, phi_1, phi_2] = (X'X)^-1X'Y.
Now, we have estimated parameters for the whole sample. If I want to know y_{t+h}, I need a constant (we arbitrarily picked '1' to estimate the model, so we'll use '1'), the temperature today and the temperature yesterday. Suppose h=2 here:
predicted temperate in two days = alpha + phi_1 x temperature today + phi_2 x temperature yesterday
You see, the difference between training the model and applying the model lies in a simple shift: y_{t} = alpha + phi_1 y_{t-h} + phi_2 y_{t-h-1} + e_{t} is what we fitted in the training sample. The last in-sample prediction we made using this model is the temperate today, using the temperatre 3 and 4 days ago, respectively. We also produced least square forecasts for all other observed temperatures, except the first three observations -- to forecast with this model, we need two observations plus a two day gap.
Now, with SVMs and SVRs, the point is very similar. Your predicted output is a real-valued label in the case of a regression problem. Suppose we also want to forecast the temperature, also two days in advance, using the same data and using the same regressors. Then, the input space of our SVR is defined by two vectors -- the same two lagged vectors of temperatures we used.
When we train the SVR on the whole dataset, we produce forecasts for each observations in the dataset -- again, except for the first three observations.
For e-insensitive SVR, let K() be the kernel we use, x_i is a support vector (it's one point in the y_{t}, y_{t-1} space) and n_sv is the number of support vectors:
y_{t+h} = sum_{i=1}^{n_sv} (alpha_i - alpha_i*) K(x_i, x)
Forecasting y_{t+h} is like asking what is the real-valued label of x: you input the last p (in this case, p=2) observations in the trained decision rule of the SVR and it gives you a label. If it was a support vector machine for classification, the training would result in a sperating hyperplane and you would decide on the label of any point which has coordinates in the input space by asking 'on what side of the plane is it?'... It's the exact same thing here, except you are looking for a real value.
So, programming-wise, you just need to provide a vector with the right dimension to 'predict': predict(best_model_you_picked, newdata=appropriate_input_space_vector)
Note that if you trained your model on the 'whole sample', but some of the variables you used are lagged variables, the model is not fitted on the last few observations of the non-lagged variables... just like the AR model estimated by OLS does not use the last h observations to forecast in-sample.