0
$\begingroup$

I'm trying to forecast data that has an hourly and weekly pattern. The model I made using predictors created using seasonaldummy does a nice job of picking up the hourly weekly pattern, but it takes a long time to train the model. I tried to create a similar forecast using fourier function, but it doesn't seem to be picking up the hourly pattern as well. Am I setting up fourier correctly to try to achieve the effect I've gotten with seasonaldummy? Should the frequency in ts be something other than 168? My data is hourly. I've provided some sample data below.

My end goal is to combine the predictors for the hourly weekly pattern with other predictors, that's why I'm not just using tbats. I've provided examples below of how I'm trying to combine dummy variables for the hourly weekly pattern with other predictors.

Code:

##BoxCox

TTTlambda <- BoxCox.lambda(tsData)

##Partitioning Time Series
EndTrain<-1344
ValStart<-EndTrain+1
ValEnd<-ValStart+336

tsTrain <-tsData[1:EndTrain]
tsValidation<-tsData[ValStart:ValEnd]
tsTest <- tsData[TestStart:TestEnd]

##Predictors
xregTrain<-dfPredictors[1:EndTrain,]
xregVal<-dfPredictors[ValStart:ValEnd,]
xregTest<-dfPredictors[TestStart:TestEnd,]

##Seasonal Dummies
x=ts(tsData,freq=168) 
dummies=seasonaldummy(x)
xreg2Train<-dummies[1:EndTrain,]
xreg2Val<-dummies[ValStart:ValEnd,]
xreg2Test<-dummies[TestStart:TestEnd,]


##Fourier Terms

tsTTT<-ts(tsData, freq=168)

bestfit <- list(aicc=Inf)
for(i in 1:25)
{
  fit <- auto.arima(tsTTT, xreg=fourier(tsTTT, K=i), seasonal=FALSE)
  if(fit$aicc < bestfit$aicc)
    bestfit <- fit
  else break;
}

bestfit$coef ## K=2

xreg3<-fourier(tsTTT,2)

xreg3Train<-xreg3[1:EndTrain,]
xreg3Val<-xreg3[ValStart:ValEnd,]
xreg3Test<-xreg3[TestStart:TestEnd,]


##hourly weekly
Arima.fit_D <- auto.arima(tsTrain, lambda = TTTlambda, xreg=xreg2Train, stepwise=FALSE, approximation = FALSE, seasonal = FALSE )

Arima.fit_D_P <- auto.arima(tsTrain, lambda = TTTlambda, xreg=cbind(xreg2Train,xregTrain$Predictor), stepwise=FALSE, approximation = FALSE, seasonal = FALSE )

##Fourier hourly weekly
Arima.fit_F <- auto.arima(tsTrain, lambda = TTTlambda, xreg=xreg3Train, stepwise=FALSE, approximation = FALSE, seasonal = FALSE )

Arima.fit_F_P <- auto.arima(tsTrain, lambda = TTTlambda, xreg=cbind(xreg3Train,xregTrain$Predictor), stepwise=FALSE, approximation = FALSE, seasonal = FALSE )

##Forecast Model

Acast_D<-forecast(Arima.fit_D,xreg=xreg2Val, h=336)

Acast_D_P<-forecast(Arima.fit_D_P,xreg=cbind(xreg2Val,xregVal$Predictor), h=336)

Acast_F<-forecast(Arima.fit_F,xreg=xreg3Val, h=336)

Acast_F_P<-forecast(Arima.fit_F_P,xreg=cbind(xreg3Val,xregVal$Predictor), h=336)

Data:

dput(tsData[1:1681])

c(11, 14, 17, 5, 5, 5.5, 8, NA, 5.5, 6.5, 8.5, 4, 5, 9, 10, 11, 7, 6, 7, 7, 5, 6, 9, 9, 6.5, 9, 3.5, 2, 15, 2.5, 17, 5, 5.5, 7, 6, 3.5, 6, 9.5, 5, 7, 4, 5, 4, 9.5, 3.5, 5, 4, 4, 9, 4.5, 6, 10, NA, 9.5, 15, 9, 5.5, 7.5, 12, 17.5, 19, 7, 14, 17, 3.5, 6, 15, 11, 10.5, 11, 13, 9.5, 9, 7, 4, 6, 15, 5, 18, 5, 6, 19, 19, 6, 7, 7.5, 7.5, 7, 6.5, 9, 10, 5.5, 5, 7.5, 5, 4, 10, 7, 5, 12, 6, NA, 4, 2, 5, 7.5, 11, 13, 7, 8, 7.5, 5.5, 7.5, 15, 7, 4.5, 9, 3, 4, 6, 17.5, 11, 7, 6, 7, 4.5, 4, 4, 5, 10, 14, 7, 7, 4, 7.5, 11, 6, 11, 7.5, 15, 23.5, 8, 12, 5, 9, 10, 4, 9, 6, 8.5, 7.5, 6, 5, 8, 6, 5.5, 8, 11, 10.5, 4, 6, 7, 10, 11.5, 11.5, 3, 4, 16, 3, 2, 2, 8, 4.5, 7, 4, 8, 11, 6.5, 7.5, 17, 6, 6.5, 9, 12, 17, 10, 5, 5, 9, 3, 8.5, 11, 4.5, 7, 16, 11, 14, 6.5, 15, 8.5, 7, 6.5, 11, 2, 2, 13.5, 4, 2, 16, 11.5, 3.5, 9, 16.5, 2.5, 4.5, 8.5, 5, 6, 7.5, 9.5, NA, 9.5, 8, 2.5, 4, 12, 13, 10, 4, 6, 16, 16, 13, 8, 12, 19, 19, 5.5, 8, 6.5, NA, NA, NA, 15, 12, NA, 6, 11, 8, 4, 2, 3, 4, 10, 7, 5, 4.5, 4, 5, 11.5, 12, 10.5, 4.5, 3, 4, 7, 15.5, 9.5, NA, 9.5, 12, 13.5, 10, 10, 13, 6, 8.5, 15, 16.5, 9.5, 14, 9, 9.5, 11, 15, 14, 5.5, 6, 14, 16, 9.5, 23, NA, 19, 12, 5, 11, 16, 8, 11, 9, 13, 6, 7, 3, 5.5, 7.5, 19, 6.5, 5.5, 4.5, 7, 8, 7, 10, 11, 13, NA, 12, 1.5, 7, 7, 12, 8, 6, 9, 15, 9, 3, 5, 11, 11, 8, 6, 3, 7.5, 4, 7, 7.5, NA, NA, NA, NA, 6.5, 2, 16.5, 7.5, 8, 8, 5, 2, 7, 4, 6.5, 4.5, 10, 6, 4.5, 6.5, 9, 2, 6, 3.5, NA, 5, 7, 3.5, 4, 4.5, 13, 19, 8.5, 10, 8, 13, 10, 10, 6, 13.5, 12, 11, 5.5, 6, 3.5, 9, 8, NA, 6, 5, 8.5, 3, 12, 10, 9.5, 7, 24, 7, 9, 11.5, 5, 7, 11, 6, 5.5, 3, 4.5, 4, 5, 5, 3, 4.5, 6, 10, 5, 4, 4, 9.5, 5, 7, 6, 3, 13, 5.5, 5, 7.5, 3, 5, 6.5, 5, 5.5, 6, 4, 3, 5, NA, 5, 5, 6, 7, 8, 5, 5.5, 9, 6, 8.5, 9.5, 8, 9, 6, 12, 5, 7, 5, 3.5, 4, 7.5, 7, 5, 4, 4, NA, 7, 5.5, 6, 8.5, 6.5, 9, 3, 2, 8, 15, 6, 4, 10, 7, 13, 14, 9.5, 9, 18, 6, 5, 4, 6, 4, 11.5, 17.5, 7, 8, 10, 4, 7, 5, 9, 6, 5, 4, 8, 4, 2, 1.5, 3.5, 6, 5.5, 5, 4, 8, 10.5, 4, 11, 9.5, 5, 6, 11, 21, 9.5, 11, 13.5, 7.5, 13, 10, 7, 9.5, 6, 10, 5.5, 6.5, 12, 10, 10, 6.5, 2, 8, NA, 10, 5, 4, 4.5, 5, 7.5, 12, 22, 5, 8.5, 2.5, 3, 10.5, 4, 7, 13, 4, 3, 5, 6.5, 3, 9, 9.5, 16, NA, 4, 12, 4.5, 7, 5.5, 8, 14, 3, 8, 12, 14, 7, 8, 6, 8.5, 6, 6.5, 15.5, 13, 3.5, 12, 7, 6, NA, 3, 5.5, 8.5, 9, 12, 13, 8, 6.5, 8, 3, 5, 16.5, 2, 7, 6, 2, 5, 6.5, 3, 3, 7, 2, NA, 13, 7, 16, 13, 12.5, 12, 7, 13, 11, 21.5, 16, 20, 3, 4, 5, 7, 11, 7, 9, 11, 7, 13, 4, 14, 5, 12, 6, 7, 9, 12, 7, 12.5, 6.5, 16, 5, 12, 9, 9.5, 9, 7, 9.5, 3, 13, 8, 7, 7, 7, 9, 6, 6, 11, 15, 9, 6, 19, 10.5, 4, 6, 14.5, 9, 17, 14, 4, 16, 5, 6.5, 10, 9, 17, 11.5, 3, 5, 9, 8, 16, 10, NA, 7, 5, 12.5, 12, 11, 3, 3, 3.5, 14, 12, 7, 4, NA, 6, NA, 6, 10, 8, 10, 2, NA, 4, 5.5, 14, 4, 4.5, 8.5, 13, 21, 10, 11.5, 18, 5, 3, 2, 6, 11, 3, 7.5, 6, 3, 5, 9, 7.5, 7.5, 5, 9, 17, 3, 9.5, 5.5, 9.5, 15, 14.5, 10, 9, 13.5, 12, 12, 3, 11, 6, 4, 8, 17.5, 7.5, 7.5, NA, 7, 4, 6, 6, 6, 6, 6, 5, 8.5, 6, 6, 5, 6, 7, 5, 5, 5, 5, 7, 6, 8, 14, 6.5, 9.5, 5, 18.5, 5, 8, 10, 16, 12, 13, 7, 6, 13, 9, 18, 17, 8, 7, 3, 8, 2, 9, 11, 5, 2, 5.5, 6.5, 7, 10, 2, 3, 2, 3, 5, 4, 5, 6, 3, 5, 3.5, 5, 4, 9, NA, 10.5, 16, NA, 11, 8.5, 13, 4, 12.5, 12, 13, 18.5, 21, 5, 9, 4.5, 3, 3, 4, 3, 4, 4, 2, 8, 4.5, 4, 5, 9, 5, 4.5, 4, 7.5, 6, 7, 22, 5, 8, 5, 7, 4, 8, 5.5, 3, 8, 7, 6, 7.5, 6, 15, 13.5, 10, 7, 2.5, 7.5, 9, 9.5, 8, 19, 8, 8, 10, 6, 9, 5, 4.5, 9, 3.5, 4, 3.5, 8, 5, 3.5, 8.5, 9, 12.5, 7, 8, 10.5, 10, 1.5, 5, 10, 9, 2, 5, 8, 11, 3, 4.5, 2, 8.5, 4, 8, 2, 3, 4, 5.5, 2, 4, 6, 4.5, 6, 6.5, 0, 2, 3.5, 10, 7, 14, 14, 12.5, 3, 7, 8, 3, 7, 12, 12.5, 2, 2.5, 3, 9, 10.5, 8, 6, 6.5, 8.5, 5, 10.5, 9, 3.5, 7, 5, 8, 5, 5, 5.5, 4, 9, 8, 5.5, 5, 6, 10.5, 4, 9, 6, 5, 11, 10.5, 10.5, 4, 11.5, 11, 6, 2, 9, 5, 9, 5, 5.5, 7, 4, 10, 5, 3, 9, 9, 19.5, 13, 6, 15, 7, 10, 8, 10.5, 8, 16, 7, 10.5, 8.5, 10.5, 8, 8, 7, 5, 5, 6, 6, 5, 4, 9, 6.5, 4, 7, 7, 5, 4, 7, 6, 3, 6, 8.5, 8.5, 4, 5.5, 7, 8, 5, 6, 3, 9, 12, 6, 7.5, 4, 3, 5.5, 2, 5.5, 7, NA, 8.5, 2, 5, 8, 8, 4, 3, 6, 4, 4.5, 5, 3, 7.5, 9, 13, 8, 10, 12, 6.5, 3, 3.5, 8.5, 9, NA, 12, 8, 9, 4, 6, 8, 8, 9.5, 8, 6, 5, 4, 10.5, 6.5, 4, 3.5, 5, 7, 7, 5, 9, 6, NA, 6, 6, 5, 10, 7, 9, 9, 5, 4, 5, 4, 6, 8, 5, 3, 2.5, 2.5, 13, 4.5, 2.5, 2, 3, 9.5, 3, 5.5, 6, 10, 9, 10, 13, 14.5, 9, 7, 6, 5, 4, 4, 4, 5, 6.5, 11, 13.5, 11, 12, 3, 3, 14, 11, 6, 8, 5.5, 9, 8, 8, 7, 7, 5.5, 3.5, 10.5, 6, 5.5, 8, 8, 15, 6.5, 8, 9.5, 6.5, 5, 7, 6, 4, 14.5, 4, 2.5, 5, 8, 18, 13, 10, 6, 7, 18, 4.5, 7, 6.5, 5, 17, 7, 3, 5.5, 4, 6.5, 5.5, 6, 8, NA, 9.5, 14, 9, 11, 8, 7, 17, 7, 8, 8, 9, 2, 2, 4, 3, 8, 4, 9, 6, 9, 11, 13, 7.5, 8.5, 6, 6, 10, 17.5, 18.5, 14, 8.5, 4, 5, 6, 3, 2, 4, 4, 12, 11, 5, 2.5, 8, 6, 10, 5, 8, 8, 10.5, 14, 7, 16, 15, 6, 4.5, 10, 19, 3, 3, 4.5, 6.5, 4, 7.5, 8, 6, 20, 6, 7, 13, 13, 4, 10, 6, 5, 4.5, 6, 10, 6, 4, 8.5, 7.5, 3, 3.5, 3, 2, 2, 20.5, 6, 18, 5.5, 7.5, 5, 3.5, 8, 6, 6.5, 3, 4, 8, 5, 15.5, 4, 5, 8, 5, 3, 4, 5, 3, 3, 3, 6, 4, 12, 8, 10, 12, 5.5, 9.5, NA, 5, 4.5, 7, 16, 7, 4.5, 5, 5, 10, 6, 19, 8, 15, 7, 19.5, 10, 7.5, 9, 9, 7, 8, 3, 6, 5.5, 6, 7, 8, 14, 8, 13, 5.5, 3.5, 5, 9, 4.5, 4, 4, 3, 7.5, 4, 5, 6.5, 9, 4, NA, 12, 5.5, 6, 12.5, 6.5, 6.5, 5, 11, 4.5, 8, 2, 4, 5, 5, 3, 2.5, 6, 7, 4, 17, 4, 3, 5, 6, 2, 8, 8.5, 6.5, 4, 10, 12.5, 11, 6.5, 9, 12.5, 5.5, 5, 7.5, 16, 11.5, 4, 5.5, 3.5, 4, 3, 6, 4, NA, 5, 6, 7, 3, 4.5, 7, 5.5, 4, 7, 11, 7, 3, 3, 4, 3.5, 9, 4.5, 8, 5, 6, 8, 5, 5.5, 8, 5, 9, 8, 8, 6.5, 6, 10, 7, 7, 9, 12, 8, 13, 6.5, 6, 4, 5.5, 6, 3, 7, 8, 15, 10, 8, 3, NA, 5, 7, 7, 6, 9, 19, 13, 7, 7.5, 11, 8.5, 4, 7.5, 6, 13.5, 17, 9, 5, 6.5, 6, 4, 5, NA, 3, 6, 10.5, 6, 14, 6, 9.5, 6, 10, 11, 10, 3, 7, 9, 16.5, 5.5, 12.5, 8, 5, 10, 6, 1, 5, 6.5, 10, 8.5, 5, NA, 9.5, 13, 10, 10, 20, 7, 8, 5, 3, 3, 4.5, 3.5, 2, 5, 11, 3, 7.5, NA, 5.5, NA, 6, 6, 11, 12, 7, 5, 15, 11, 6, 17.5, 13.5, 16, 16.5, 5, 4, 3, 5.5, 3, 8, 11, 8, 12, 14, NA, 10, 6, 4, 5, 8, 10, 12.5, 6, 3, 6, 5, 8, 6, 11, 12.5, 7, 6, 9.5, 2, 8.5, 9.5, 8, 8, 2, 7.5, NA, 6, 2.5, 4, 5, 5, 6, 9, 4, 7, 6, 2, 4.5, 3, 4, 4, 5, 4, 3, 7.5, 8.5, NA, 12, 9, 11, 9, 3, 2.5, 7, 4, 4, 7, 8.5, 12.5, 3.5, 6.5, 10, 6, 8, 7, 13, 13.5, 12, 13, 8, NA, 8, 9, 15, NA, 4, 3.5, 2, 7, 8, 7.5, 9.5, 1.5, 5, 4, 8, 11, 5, 12, 4, 3, 11, 8, 7.5, 5.5, 13, 11, NA, 12, 7, 8, 6, 13, 8, 5, 4, 7, 8, 2, 3, 4, 4, 5, 5.5, 5.5, 6, 5, 6, 14, 12, 6, 11.5, 13, 5, 5, 8, 9, 2, 5, 6, 10, 4.5, 4, 7, 7.5, 7, 4, 10, 6.5, 6, 10)

dput(dfPredictors$Predictor[1:1681])

c(2, 6, 3, 5, 3, 2, 2, NA, 2, 6, 12, 11, 9, 10, 13, 9, 11, 7, 12, 8, 6, 4, 10, 6, 2, 7, 2, 1, 3, 2, 1, 3, 8, 7, 7, 8, 13, 13, 13, 11, 12, 4, 12, 18, 12, 7, 5, 4, 6, 4, 3, 3, NA, 4, 2, 8, 8, 8, 7, 3, 5, 3, 7, 8, 7, 7, 11, 8, 10, 3, 10, 6, 5, 5, 3, 1, 2, 1, 1, 3, 4, 8, 8, 5, 9, 12, 12, 11, 8, 5, 9, 10, 7, 8, 4, 6, 4, 1, 3, 1, 3, NA, 2, 1, 4, 10, 7, 13, 6, 9, 6, 16, 12, 11, 10, 12, 9, 7, 7, 7, 6, 2, 3, 1, 1, 2, 2, 3, 11, 10, 9, 8, 9, 13, 6, 6, 10, 9, 11, 10, 8, 7, 6, 4, 2, 3, 5, 3, 2, 4, 4, 4, 8, 5, 12, 8, 7, 12, 9, 12, 12, 12, 13, 12, 9, 8, 9, 10, 4, 7, 4, 2, 2, 4, 1, 7, 6, 6, 8, 11, 11, 5, 7, 6, 9, 12, 15, 9, 11, 5, 10, 5, 4, 4, 2, 3, 3, 2, 5, 4, 7, 8, 6, 6, 5, 12, 10, 8, 10, 10, 4, 13, 12, 6, 8, 6, 3, 1, 4, 2, NA, 4, 3, 2, 6, 5, 8, 10, 4, 13, 2, 13, 8, 11, 13, 8, 9, 10, 9, 5, 1, NA, 1, 1, 2, NA, 1, 7, 6, 10, 7, 8, 12, 12, 9, 5, 6, 8, 13, 13, 13, 8, 8, 1, 5, 7, 6, 2, NA, 2, 1, 2, 7, 9, 12, 12, 10, 10, 10, 6, 8, 2, 8, 3, 4, 5, 6, 2, 2, 1, 4, 1, NA, 3, 1, 3, 8, 8, 11, 11, 12, 5, 7, 14, 9, 10, 14, 11, 8, 6, 8, 7, 5, 4, 3, 4, 9, NA, 2, 4, 5, 8, 2, 12, 8, 15, 12, 8, 9, 12, 9, 9, 12, 7, 7, 8, 7, 5, 4, NA, 1, NA, NA, 4, 9, 8, 8, 8, 12, 13, 7, 11, 8, 14, 12, 13, 15, 8, 6, 4, 4, 5, 2, NA, 2, 5, 4, 5, 6, 15, 11, 10, 16, 10, 5, 5, 10, 13, 10, 9, 8, 7, 5, 4, 5, 6, NA, 2, 5, 4, 1, 6, 5, 8, 4, 3, 10, 11, 8, 12, 10, 10, 10, 12, 10, 10, 7, 5, 7, 3, 4, 3, 3, 3, 3, 8, 4, 8, 10, 5, 10, 10, 10, 11, 10, 11, 7, 10, 7, 6, 7, 7, 3, 3, NA, 3, 6, 5, 3, 3, 5, 6, 6, 13, 14, 14, 7, 13, 9, 10, 4, 9, 10, 8, 3, 6, 10, 5, 2, 1, NA, 3, 4, 4, 12, 12, 11, 12, 11, 13, 10, 9, 11, 11, 14, 10, 13, 10, 7, 11, 1, 3, 1, 4, 1, 2, 2, 3, 9, 6, 9, 9, 8, 9, 7, 12, 17, 13, 9, 10, 8, 8, 10, 2, 3, 3, 6, 2, 2, 1, 6, 8, 7, 9, 5, 11, 8, 8, 12, 13, 14, 10, 7, 5, 11, 11, 8, 5, 7, 3, 2, 3, 5, NA, 1, 3, 3, 4, 9, 12, 12, 3, 5, 12, 10, 9, 14, 15, 12, 7, 8, 7, 3, 4, 1, 5, 6, 4, NA, 5, 9, 6, 7, 8, 15, 13, 9, 12, 9, 7, 7, 6, 7, 8, 8, 6, 4, 5, 4, 1, 5, 1, NA, 5, 4, 12, 7, 20, 12, 14, 10, 11, 11, 12, 6, 6, 11, 5, 6, 7, 4, 7, 5, 1, 2, NA, 2, 7, 16, 9, 4, 12, 14, 12, 9, 8, 12, 7, 6, 11, 9, 15, 9, 4, 4, 3, 3, 2, 5, 2, 1, 6, 8, 3, 12, 11, 14, 9, 6, 3, 12, 11, 10, 14, 10, 10, 12, 2, 3, 3, 5, 3, 2, 3, 3, 5, 9, 5, 10, 14, 9, 14, 11, 9, 12, 9, 15, 13, 12, 15, 11, 4, 7, 3, 3, 3, 2, 5, 5, 11, 4, 2, NA, 3, 6, 10, 8, 5, 9, 9, 10, 11, 8, 9, 8, NA, 3, NA, 1, 1, 4, 3, 3, NA, 4, 8, 3, 9, 6, 12, 9, 7, 11, 6, 6, 12, 5, 4, 11, 7, 1, 2, 3, 2, 4, 8, 2, 6, 5, 9, 3, 7, 8, 8, 8, 14, 10, 12, 5, 12, 9, 13, 7, 3, 5, 3, 4, 2, 4, 2, NA, 5, 5, 9, 8, 7, 11, 9, 5, 6, 10, 13, 10, 9, 16, 11, 7, 5, 6, 2, 5, 3, 5, 2, 2, 6, 5, 11, 7, 13, 6, 10, 7, 9, 7, 8, 9, 12, 7, 7, 5, 3, 5, 3, 3, 5, 3, 1, 2, 10, 11, 8, 1, 9, 10, 14, 12, 7, 11, 11, 10, 7, 5, 9, 8, 6, NA, 4, 2, NA, 3, 4, 4, 6, 10, 9, 6, 8, 9, 10, 9, 14, 12, 8, 11, 16, 16, 13, 8, 7, 4, 4, 1, 3, 4, 2, 2, 5, 9, 9, 3, 8, 12, 6, 11, 10, 6, 8, 15, 12, 12, 7, 6, 7, 3, 2, 1, 3, 2, 2, 5, 7, 11, 8, 3, 4, 5, 5, 9, 6, 10, 9, 7, 17, 12, 3, 8, 6, 4, 4, 4, 3, 4, 2, 1, 4, 7, 12, 5, 4, 8, 7, 15, 8, 6, 6, 10, 5, 10, 7, 3, 4, 4, 1, 5, 3, 4, 5, 2, 1, 8, 6, 8, 9, 7, 13, 11, 11, 6, 9, 9, 9, 9, 8, 1, 8, 1, 3, 2, 2, 1, 3, 2, 3, 8, 9, 10, 12, 6, 9, 12, 7, 8, 8, 14, 10, 10, 8, 10, 4, 4, 4, 4, 3, 2, 4, 2, 3, 16, 3, 9, 8, 15, 9, 11, 10, 12, 12, 7, 15, 13, 8, 9, 3, 8, 1, 2, 2, 3, 3, 3, 10, 7, 5, 10, 4, 8, 8, 10, 8, 9, 9, 6, 7, 7, 4, 6, 8, 4, 5, 5, 1, 1, 1, 5, 7, 3, 3, 12, 8, 7, 10, 7, 12, 11, 7, 6, 14, 13, 9, 14, 3, 4, 6, 3, 2, 3, NA, 2, 3, 7, 6, 9, 7, 5, 9, 8, 10, 7, 7, 6, 11, 11, 9, 7, 5, 2, 3, 2, 2, 5, NA, 2, 5, 6, 7, 8, 14, 11, 6, 9, 10, 10, 9, 8, 16, 9, 6, 6, 3, 2, 5, 1, 1, NA, 3, 3, 2, 5, 10, 9, 10, 13, 11, 8, 17, 13, 5, 11, 10, 11, 6, 9, 6, 4, 5, 6, 5, 2, 4, 1, 2, 5, 9, 12, 10, 10, 18, 9, 13, 16, 8, 13, 5, 16, 11, 8, 10, 3, 6, 3, 1, 2, 2, 6, 2, 12, 9, 5, 8, 10, 11, 4, 10, 9, 9, 9, 19, 11, 8, 9, 4, 4, 4, 7, 5, 2, 2, 1, 2, 6, 10, 11, 12, 9, 9, 12, 9, 8, 14, 8, 5, 3, 5, 7, 6, 3, 4, 6, 3, 3, NA, 2, 2, 7, 12, 11, 14, 7, 10, 10, 13, 12, 5, 8, 8, 9, 10, 4, 9, 4, 5, 3, 1, 4, 2, 1, 7, 9, 10, 10, 11, 9, 8, 6, 3, 8, 10, 9, 9, 10, 8, 11, 4, 1, 1, 3, 1, 1, 3, 6, 2, 3, 10, 4, 9, 6, 10, 11, 6, 7, 8, 6, 11, 8, 4, 8, 5, 5, 1, 7, 1, 3, 3, 3, 6, 6, 8, 8, 9, 7, 6, 10, 9, 10, 6, 13, 10, 20, 7, 9, 2, 6, 3, 2, 1, 1, 2, 1, 3, 13, 7, 6, 7, 11, 7, 9, 7, 9, 10, 9, 10, 6, 11, 7, 5, 5, 5, 4, 6, 4, NA, 4, 4, 11, 11, 9, 8, 9, 9, 12, 8, 11, 12, 3, 9, 12, 10, 8, 7, 3, 5, 2, 2, 3, 2, 3, 4, 8, 13, 6, 8, 7, 4, 7, 13, 10, 9, 11, 10, 10, 5, 12, 4, 3, 7, NA, 2, 2, 1, 6, 2, 8, 8, 9, 6, 11, 7, 7, 9, 11, 9, 6, 8, 11, 10, 6, 5, 3, 5, 5, 1, 1, 2, 2, 5, 7, 13, 11, 7, 17, 10, 4, 10, 9, 10, 6, 5, 8, 4, 6, 6, 3, 5, NA, 5, 1, 3, 1, 5, 3, 8, 11, 6, 8, 9, 7, 11, 5, 12, 10, 10, 8, 9, 8, 7, 3, 2, 4, 5, 1, 3, 1, 2, 9, 10, 4, 7, 10, 11, 6, 11, 8, 8, 7, 10, 9, 9, 11, 9, 2, 3, 4, 3, NA, 2, 5, 5, 8, 13, 7, 14, 11, 4, 7, 10, 15, 10, 15, 8, 6, 9, 5, 4, 2, 1, 3, NA, 1, 1, 2, 3, 13, 6, 8, 6, 12, 10, 13, 5, 14, 11, 14, 14, 10, 10, 5, 3, 4, 2, 4, 2, 3, 2, 2, NA, 10, 9, 6, 14, 10, 7, 7, 12, 3, 13, 12, 12, 14, 8, 11, 3, 6, NA, 2, NA, 3, 2, 5, 5, 11, 3, 5, 7, 7, 12, 8, 5, 11, 5, 2, 8, 9, 6, 7, 3, 3, 1, 1, NA, 1, 3, 1, 3, 5, 10, 10, 7, 3, 5, 8, 11, 9, 11, 7, 9, 9, 10, 5, 10, 4, 3, 3, 1, 2, NA, 3, 4, 6, 6, 7, 11, 9, 11, 9, 6, 6, 8, 7, 9, 12, 12, 9, 5, 4, 3, NA, 1, 2, 1, 2, 2, 2, 6, 9, 8, 8, 8, 12, 8, 13, 7, 12, 7, 8, 12, 8, 5, 5, 1, NA, 4, 3, 1, NA, 5, 6, 10, 7, 15, 12, 12, 6, 11, 12, 12, 10, 16, 10, 8, 11, 8, 5, 4, 2, 1, 2, NA, 5, 2, 8, 9, 7, 9, 14, 7, 13, 3, 6, 9, 13, 10, 8, 6, 4, 6, 4, 5, 1, 3, 3, 2, 1, 4, 4, 9, 11, 4, 8, 9, 11, 8, 8, 9, 19, 9, 7, 7, 11, 6, 8)

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    $\begingroup$ Can you provide all of your data? $\endgroup$ – Rob Hyndman Apr 8 '16 at 5:19
  • $\begingroup$ I was about to suggest looking at earlier answers on "multiple seasonalities" until I saw that you want "to combine the predictors for the hourly weekly pattern with other predictors". Could you give a few details on what you have in mind here? $\endgroup$ – Stephan Kolassa Apr 8 '16 at 6:24
  • $\begingroup$ @RobHyndman Hi Professor Hyndman, thank you for looking at this, and for your online textbook, and blog. I've been teaching myself time-series and forecasting from your textbook, blog, and forum posts. I'm in the US, I would love a chance to take an online forecasting class from you. Do you have any online courses available or planned in the future? I've added more sample data, along with code examples of how I'm trying to combine the dummy variables with other predictors. $\endgroup$ – ndderwerdo Apr 8 '16 at 17:09
  • $\begingroup$ @StephanKolassa Hi Stephan, thank you for looking at this. I've edited the post and added examples of how I'm trying to combine the dummy variables with other predictors. I found the SO post below which has an example using a tbats model in an auto.arima model with predictors. I was wondering if that might work for my case. I've created a tbats forecast and compared it to the forecast I get using seasonaldummy, their very similar. Post: stats.stackexchange.com/questions/176129/… $\endgroup$ – ndderwerdo Apr 8 '16 at 17:34
  • $\begingroup$ @StephanKolassa Example from SO post: y <- msts(ts, c(7,365)) # multiseasonal ts fit <- auto.arima(y, seasonal=F, xreg=fourier(y, K=c(3,30))) fit_f <- forecast(fit, xreg= fourierf(y, K=c(3,30), 180), 180) $\endgroup$ – ndderwerdo Apr 8 '16 at 17:35

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