Different method for parameter estimation auto.arima

by Michieldo   Last Updated October 10, 2018 20:19 PM

I am trying to fit a multivariate time series with the auto.arima() function in R. Since my time series has seasonality I included Fourier approximation and used the following method proposed by Rob J Hyndman

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

Aside from adding more variables that will increase estimation, it fits well based on the methods used by the package. In my understanding estimation is done by "CSS-ML". However, I am forecasting demand of products where the error is measured by a pinball loss function similar to:

\begin{align} L(q_a, y) = \begin{cases}(1 - a/100) (q_a - y), & \text{if $y< q_a$};\\ a/100 (y - q_a), & \text{if $y\ge q_a$}; \end{cases} \end{align}

I would like to estimate my parameters by minimizing a pinball loss function like the one above for the auto.arima() function. It does not specifically has to be this function, but minimizing a loss function in combination with the auto.arima() function would be great. Does anyone has a suggestion how to do this?

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