I have a dataset with columns that represent lagged values of predictors. To illustrate with a simple example, suppose we had car sales data for 3 years and the only predictors available were income and population for a number of car dealers, the dataset could be represented as follows,
ID IncLag1 PopLag1 SalesLag1 IncLag2 PopLag2 SalesLag2 IncCurrent PopCurr SalesCurr a 100 1000 200 150 2000 300 500 2500 450 b 10 300 50 60 900 80 90 1000 100
k 30 60 10 200 2000 60 80 800 ??
My dependent variable is SalesCurr - i.e., given a history of past sales and corresponding Income and Population values (which we can use as the train-test data), predict what the Sales will be in the current year (SalesCurr).
My question is as follows -- Using R or GRETL, how is it possible to create an ARIMA/TimeSeries model with the above data to predict the SalesCurrent variable. Using simple Linear Regression, one could simply have a formula such as say,
lm (SalesCurrent ~ ., data=mytable), but it would not be a time-series model since it does not take into account the relationship between the different variables.
Alternatively, I am quite familiar with Machine Learning models and wanted to get your thoughts on how such a dataset could be modeled using say, randomForest, GBM, etc.
Thanks in advance.