Breakpoints and Forecasting with R

Question

I am new in R and Timeseries analysis and forecasting. I have 2 questions.

1. I am detecting three change points in my dataset.

   ts <- ts(y)
   bp <- breakpoints(ts~1) #three breakpoints are detected
   

Can I somehow conclude that any of the breakpoints is not significant and will not change my forecasting? If no, how can I adjust two out of three breakpoints into my forecast dataset?

2. My timeseries has trend and seasonality. I implement an ARIMA model with auto.arima() function. Do I have to detrend and decompose my series? Is auto.arima() valid if I don't? The code I use:

   fit <- auto.arima(ts2, stationary=FALSE, seasonal = TRUE, trace=TRUE, ) pred <- forecast(fit, h=59) plot(pred, lty = c(1,3), xlab='week', ylab='index', main='Timeseries - Prediction')

Lastly, can I check for a max h for forecast?

EDIT Timeseries plot with breakpoints

Answer 1

1. The breakpoints() function you have specified is for a mean change (the ~1). If you plot the resulting estimated mean you will see that you have misspecified the model and that is why 3 changepoints have been detected. I am guessing this is why you are asking whether "they are significant". If you believe that your data, within each segment, is generated from a trend+seasonal arima model then that is the model you need to put into the breakpoints() function (if you can, I don't think it handles time series errors, although you could make AR covariates to get an approximation).

2. Yes, the auto.arima() model is not appropriate if there are changes within the data. It will likely fit an integrated model to deal with the changes as the difference data is stationary except at the changepoint locations.

I'm not sure on your background but the following paper describes different stages to fit changepoints in a modelling pipeline and their influence on the forecasting ability: https://onlinelibrary.wiley.com/doi/10.1002/qre.2712

If your only aim is to forecast and the changepoint is a nuisance then the best approach is to estimate the changes, correct for them and then fit a model to the corrected series. In your example it is clear that there is a steady mean prior to the first change identified. Following this it looks like a slow (and unsteady) return to a new lower steady-state (around 900). You would need more data to see if the return is just over a longer period though or maybe there is knowledge of the specific problem that might help in assessing this?

For the "return to equilibrium" part you might be interested in this recent paper which models a trend followed by equilibrium after a changepoint: https://arxiv.org/pdf/2007.09417.pdf