在R中的ARIMAX模型中预测转换后的时间序列的实际值

Question

I am fitting an ARIMAx model to my time series data. The "data" includes "Rate" as the outcome and x1, x2, and x3 as covariates and I have transformed the outcome using Box-Cox transformation. My data is split into a train and a test set and I want to forecast the test set with the actual values and not the transformed values. I have done the following:

data.train <- ts(data[1:24, ] , frequency = 4, start = c(2011, 4)  
data.test <- ts(data[25:28, ], frequency = 4, start = c(2017, 4)) 

covariates <- c("x1", "x2", "x3")
xreg.train <- data.train[, covariates] 
xreg.test <- data.test[, covariates] 

outcome <- data.train[, "Rate"]
lambda <- BoxCox.lambda(outcome)
outcome.trans <- BoxCox(outcome, lambda) 

fit <- auto.arima(outcome.trans, xreg = xreg.train, trace = TRUE, stepwise = FALSE, seasonal = TRUE)

Now I want to forecast the test set with the actual values and not the transformed values:

 forecast.test <- predict(fit, newxreg = xreg.test, lambda = lambda)

Now the PROBLEM is that this predict function produces a forecast of the transformed values and not the actual values. How can I get the forecast of the actual values without doing the transformation myself.

Answer 1

The forecast package does all this for you. But you need to use the forecast() function, not the predict() function.

data.train <- ts(data[1:24,] ,frequency=4, start=c(2011,4)  
data.test <- ts(data[25:28,], frequency=4, start=c(2017,4)) 

covariates <- c("x1","x2","x3")
xreg.train <- data.train[, covariates] 
xreg.test <- data.test[, covariates] 

outcome <- data.train[,"Rate"]
lambda <- BoxCox.lambda(outcome)

fit<- auto.arima(outcome, xreg=xreg.train, lambda=lambda,
  trace=TRUE, stepwise=FALSE, seasonal=TRUE, lambda=lambda)

forecast.test <- forecast(fit, xreg=xreg.test, lambda=lambda)