Point Estimates using forecast in R for Multi-Step TS Forecast -- Sometimes Same/Sometimes Not -- Why?

Question

I am using the simple forecast(data, h = 6) function in R - as I work through Hyndman's 'Forecasting: Principles and Practice" textbook - which returns forecasts from the ETS algorithm.

I'm not breaking into training/test or doing any tuning -- just taking a very straightforward approach to start as I learn.

My question --

Why is it that with the forecast() function, the point estimate - in a multi-step forecast - is sometimes the same across the periods I'm forecasting for (6 in this case for the remainder of 2021) and in other cases, it's different.

I'm questioning the validity of the output of this function considering in some cases, the algorithm is providing different point estimates by month and in some cases, it's almost taking a naive approach and providing the last actual for the next six periods in the forecast horizon.

Any guidance would be much appreciated!

Two Examples:

Dataset A: produces differing point estimates - and to your point, @Chris Haug, appears to be showing a strong upward trend.

Date	Budget
2020-01-01	6204
2020-02-01	1706
2020-03-01	5293
2020-04-01	6015
2020-05-01	12680
2020-06-01	10641
2020-07-01	16247
2020-08-01	14368
2020-09-01	12567
2020-10-01	14323
2020-11-01	35675
2021-12-01	45106
2021-01-01	21960
2021-02-01	19144
2021-03-01	37446
2021-04-01	32807
2021-05-01	45950
2021-06-01	31009

Dataset B: produces the same point estimates over next six periods.

Date	Budget
2020-01-01	83668
2020-02-01	73967
2020-03-01	94079
2020-04-01	119222
2020-05-01	320785
2020-06-01	375266
2020-07-01	497954
2020-08-01	728576
2020-09-01	809110
2020-10-01	439066
2020-11-01	469127
2021-12-01	175535
2021-01-01	362897
2021-02-01	1536035
2021-03-01	954311
2021-04-01	1248185
2021-05-01	1063065
2021-06-01	784101

I've considered removing Jan-April 2020 (COVID) and looking only at 2021 as well.

Answer 1

Consumers of forecasts often express the belief that forecasts should "look like the data". Producers of model-based forecasts, on the other hand, are not typically trying to replicate exactly what the data looks like, but rather trying to find a balance by including important, useful features only when their effect can be reliably estimated, in an attempt to find the most objectively accurate model. For example, if the data looks kind of seasonal, but the seasonality is so noisy that you might predict a peak when a trough occurs and vice-versa, ignoring seasonality and aiming for the "center" can result in more accurate forecasts on average.

The result is that objectively accurate models frequently produce forecasts that look "too simple" to forecast consumers. The constant forecast usually elicits the strongest reaction, but there's nothing intrinsically wrong with it. Sometimes, it's the best that can be done.

In your case, you have very limited data (18 periods). You will not be able to support reliable estimates of even moderately complicated models, so you will have to use very simple models. In particular, since you don't have two full yearly cycles, you can't disentangle seasonality from other effects (e.g. was December 2020 high because all Decembers are high, or was that a fluke? Hard to tell when you've never seen any other Decembers). So, you are limited to non-seasonal ETS models.

In your first series, there is a very clear trend that is easy to see even with few points. It makes sense that the best ETS model has a trend. In the second case, it's a lot less clear. It's vaguely trending upwards, sometimes down for a few months, but it's also almost flat except for the jump in February 2021. You can see how a model with an upward trend would have been pretty wrong in the last 5 months. All this to say that if this thing has a trend, it's pretty hard to estimate precisely from this limited amount of data, so our best model isn't going to include one, and our forecast will be flat.

That's not to say that we believe series B is actually going to be constant; if we did, the prediction interval would not be constantly widening as we increase the horizon, reflecting increasing uncertainty. This is just our best guess.