Forecasting in R using Holt's Linear model

Question

I am trying to forecast data with a downward trend. I understand that Holt's linear model might be the better way to do it, but am unsure how I can implement it in R.

The data is as follows:

   day  saleRep
1    1 1001.104
2   11 1000.944
3   21 1000.734
4   31 1000.642
5   41 1000.517
6   51 1000.468
7   61 1000.425
8   71 1000.377
9   81 1000.286
10  91 1000.306
11 101 1000.285
12 111 1000.170

Plotting it gives:

I am trying to achieve a few things:

1. Conduct a train test split to create a forecast model that I can evaluate on the test set
2. Using the model, obtain the predicted sale values for the 250th and 500th day.

How can I implement it in R?

Use this to reproduce the code:

day <- seq(1,111, by = 10)
saleRep <- c(1001.104, 1000.944, 1000.734, 1000.642, 1000.517, 1000.468, 1000.425, 1000.377, 1000.286, 1000.306, 1000.285, 1000.170)
df <- data.frame(day, saleRep)

Thank you.

Answer 1

I will use the forecast package and go step-by-step. Load the forecast package and generate an example daily time-series data

require(forecast)

The toy data

x <- c(120:1 + rnorm(120, 12, 3)) 

Convert data to a ts object

x <- ts(x, frequency = 7, #daily data with no yearly seasonalty
          start = 1)
  
  autoplot(x)

Split train and test

train <- window(x, end = c(17,1))
  test <- window(x, start = c(17,2))

fit and forecast an hw model

fc <- forecast::hw(x, h = 7) # h = 7 the lenght of test set
  

Plot the forecast

  autoplot(fc)