Original link:tecdat.cn/?p=18493
Original source:Tuo End number according to the tribe public number
In this paper, we use four time series models to model the weekly temperature series. The first is obtained by auto. Arima, then two are the SARIMA model, and the last is the Buys-Ballot method.
We use the following data
k=620
n=nrow(elec)
futu=(k+1):n
y=electricite$Load[1:k]
plot(y,type="l")
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We started to model the temperature series (which has a great influence on the power load)
y=Temp
plot(y,type="l")
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abline(lm(y[ :k]~y[( :k)-52]),col="red")
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Time series are autocorrelated at order 52
acf(y,lag=120)
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model1=auto.arima(Y)
acf(residuals(model1),120)
Copy the codeWe save this model in the workspace and look at its predictions. Let’s try SARIMA here
C (Y,order = c(0,0,0))Copy the codeThen let’s try using seasonal unit roots
C = c(0,0,1) c = c(0,0,1) c = c(0, 1)Copy the codeThen, we can try the Buys-Ballot model
lm(Temp~0+as.factor(NumWeek),
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Make predictions about the model
plot(y,type="l",xlim=c(0,n )
abline(v=k,col="red")
lines(pre4,col="blue")
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plot(y,type="l",xlim=c(0,n))
abline(v=k,col="red")
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plot(y,type="l",xlim=c(0,n))
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plot(y,type="l",xlim=c(0,n))
abline(v=k,col="red")
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Finally, the results of the four models are compared
lines( MODEL$y1,col="
lines( MODEL$y2,col="green")
lines( MODEL$y3,col="orange")
lines( MODEL$y4,col="blue")
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Then, we can try a weighted average to optimize the model, instead of figuring out which of the four models is “optimal”, y ^ T = ∑ I ωiy ^ T (I) where ω= (ω I), ω1+… + omega k = 1. Then, we want to find the “best” weights. We will calibrate our four models on the first m value, and then compare the predicted combinations of 111 values (and true values),
We use the first 200 values.
Then, we fit four models on these 200 values
And then we make predictions
y1=predict(model1,n.ahead = 111)$pred,
y2=predict(model2,n.ahead = 111)$pred,
y3=predict(model3,n.ahead = 111)$pred,
y4=predict(model4,n.ahead = 111)$pred+
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A =rep(1/4,4) y_pr = as. Matrix (DOS[,1:4]) %*% aCopy the codeTherefore, we visualize the four predictions, their linear combinations (with equal weights) and their observations
To find the “best” value for the weights and minimize the sum of squares of error, we use the following code
function(a) sum( DONN[,1:4 %*% a-DONN[,5 )^2
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Optim (par = c (0, 0), erreur2) $parCopy the codeThen, we need to ensure the convergence of the two algorithms: the SARIMA parameter estimation algorithm and the weight parameter research algorithm.
If (inherits(TRY, "try-error") arima(y,order = c(4,0,0) seasonal = list(order = c(1,0,0))Copy the codeThen, we look at the weight change over time.
Get the figure below, where pink is Buys-Ballot, pink is SARIMA model, green is seasonal unit root,
barplot(va,legend = rownames(counts)
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We found that the model with the highest weight was the Buys Ballot model.
We can change the loss function, for example, we use 90% of the quantile,
tau=.9
function(e) (tau-(e<=0))*e
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This time, the two most heavily weighted models are SARIMA and Buys-Ballot.
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