Iteratively applying auto.arima (forecast package) to multiple time series in R

Question

I have the following time series:

ts<-data.frame(Date=c('2017-01-01','2017-01-02','2017-01-03','2017-01-04','2017-01-05','2017-01-06','2017-01-07','2017-01-08','2017-01-09','2017-01-10'),
               A=c(15,37,29,18,12,8,2,24,42,10),
               B=c(16,22,5,6,22,12,13,7,20,36))

ts

      Date    A  B
1  2017-01-01 15 16
2  2017-01-02 37 22
3  2017-01-03 29  5
4  2017-01-04 18  6
5  2017-01-05 12 22
6  2017-01-06  8 12
7  2017-01-07  2 13
8  2017-01-08 24  7
9  2017-01-09 42 20
10 2017-01-10 10 36

I would like to iterative apply auto.arima function from forecast package on time series A & B.

I need help in having a functional approach which first creates a forecast function having the following setup (this function will loop through the multiple series):

1. splits data into train:test in 80:20 ratio
2. Trains auto.arima model on the train set
3. Model evaluation using the test set (rmse metric)
4. optional----> cross-validation with 1 time step
5. generates forecast (horizon=2) with the error metric as below:

  series    Date         rmse    pt_forecast_1 pt_forecast_2
1    A   2017-01-11      0.21       12            13
2    B   2017-01-12      0.11       36            34

Need help here. Thanks

Answer 1

I wrote data_gen_func() to do what you need. I hope it helps. The output is almost the same as what you need. You need to have the forecast and the CombMSC packages installed. the following code will do the job if you do not have it installed.

I also show how you can use and I describe the parameters that you need to pass to data_gen_func().

if(!require(forecast)){
  install.packages("forecast")
}

if(!require(CombMSC)){
  install.packages("CombMSC")
}


#' @param dta a multiple time series
#' @param h final forecast horizon
#' @param test_size how many observation to use for test
#' @param start_fc_date Startind date of forecast. Note you can change it. this method was the fist came to my mind.
#' @param ts_frequency A character string, containing one of "day", "week", 
#' "month", "quarter" or "year". 
#' This can optionally be preceded by a (positive or negative) 
#' integer and a space, or followed by "s".
#' @param error masure of error. 
#' It can be one of the following: ME , RMSE, MAE, MPE, MAPE, MASE, ACF1.

data_gen_func <- function(dta, h, test_size, start_fc_date, ts_frequency, 
                          error = "RMSE"){
  
  if(!"Date" %in% class(start_fc_date)){
    stop(" 'start_fc_date' must have class of 'Date'")
  }
  
  if(!"mts" %in% class(dta)){
    stop("dta must be an mts")
  }
  
  nts <- ncol(dta)
  
  fc <- data.frame(matrix(nrow = h, ncol = nts))
  
  acc <- data.frame(matrix(nrow = 1, ncol = nts))
  
  
  train_length <- nrow(dta) - test_size
  
  for (i in 1:nts) {
    
    d_list <- CombMSC::splitTrainTest(dta[,i], train_length)
    
    train <- d_list$train
    test <- d_list$test
    
    point_fc <- forecast(auto.arima(train), h = test_size)$mean
    
    acc[,i] <- accuracy(point_fc, test)[,paste0(error)]
    
    colnames(acc)[i] <- colnames(dta)[i]
    
    fc[,i] <- forecast(auto.arima(dta[,i]), h = h)$mean
    
    colnames(fc)[i] <- colnames(dta)[i]
  }
  
  acc <- tidyr::pivot_longer(acc, everything(),names_to = "series", 
                             values_to = paste0(error))
  
  fc$date <- seq(from = start_fc_date, length.out = h, by = ts_frequency)
  
  tidyr::pivot_longer(fc, -date,names_to = "series", 
                      values_to = "fc")%>%
    tidyr::pivot_wider(names_from = date, values_from= fc)-> fc
  
  output <- dplyr::left_join(fc,acc)
  
  return(output)
}


# usage -------------------
library(forecast)
library(CombMSC)

my_data <-  ts(data.frame(
  AA = arima.sim(list(order=c(1,0,0), ar=.5), n=50, mean = 12), 
  AB = arima.sim(list(order=c(1,0,0), ar=.5), n=50, mean = 12), 
  AC = arima.sim(list(order=c(1,0,0), ar=.5), n=50, mean = 11),
  BA = arima.sim(list(order=c(1,0,0), ar=.5), n=50, mean = 10),
  BB = arima.sim(list(order=c(1,0,0), ar=.5), n=50, mean = 14)), 
  start = c(2010, 1), frequency = 12)

end(my_data)


out1 <- data_gen_func(dta = my_data, h = 2, test_size = 1, start_fc_date = as.Date("2014-03-01"),
                     ts_frequency = "month", error = "MAPE")
out1

the output for 5 time series looks like this

    # A tibble: 5 x 4
  series `2014-03-01` `2014-04-01`  MAPE
  <chr>         <dbl>        <dbl> <dbl>
1 AA             23.6         23.4  3.38
2 AB             24.2         24.4  1.18
3 AC             21.1         21.3  4.31
4 BA             19.9         20.1  1.47
5 BB             27.3         27.7  3.54

If you set error = "RMSE" the results will look like this :

# A tibble: 5 x 4
  series `2014-03-01` `2014-04-01`  RMSE
  <chr>         <dbl>        <dbl> <dbl>
1 AA             24.0         24.0 1.05 
2 AB             23.2         23.3 0.160
3 AC             22.2         22.2 0.851
4 BA             19.4         19.7 1.59 
5 BB             27.5         27.9 1.04 

with your example data: it is short hence you will get some warning

my_ts <-data.frame(Date=c('2017-01-01','2017-01-02','2017-01-03','2017-01-04','2017-01-05','2017-01-06','2017-01-07','2017-01-08','2017-01-09','2017-01-10'),
               A=c(15,37,29,18,12,8,2,24,42,10),
               B=c(16,22,5,6,22,12,13,7,20,36))



my_ts <- stats::ts(my_ts[,-1], start = c(2017,1), frequency = 7)


out2 <- data_gen_func(dta = my_ts, h = 2, test_size = 2, 
                      start_fc_date = as.Date("2017-01-10"),
              ts_frequency = "day", error = "MAPE")

out2

The output:

# A tibble: 2 x 4
  series `2017-01-10` `2017-01-11`  MAPE
  <chr>         <dbl>        <dbl> <dbl>
1 A              19.7         19.7  69.0
2 B              15.9         15.9  49.9

you can also transform the data if you are not happy with output.

tidyr::pivot_longer(out2, -c(series,MAPE), names_to = "date", 
                    values_to= "point_fc")

The output after pivoting

# A tibble: 4 x 4
  series  MAPE date       point_fc
  <chr>  <dbl> <chr>         <dbl>
1 A       69.0 2017-01-10     19.7
2 A       69.0 2017-01-11     19.7
3 B       49.9 2017-01-10     15.9
4 B       49.9 2017-01-11     15.9