ETS vs ARIMA in R: Which Forecasting Model Should You Use?

ETS and ARIMA are the two workhorse forecasting model families in R, and both run in a single line with the forecast package. ETS builds a forecast from a series' structure (its level, trend, and seasonality), while ARIMA builds one from the correlations between a value and its own recent past. This guide shows how each works, why you must never compare them with AICc, and how a fair accuracy test picks the winner.

What is the core difference between ETS and ARIMA?

Give R a monthly time series and two single lines produce two finished forecasters. But which one should you trust? Before you can compare them, you need to see what each model is actually doing. Let's fit both to the same classic dataset, read off the models they choose, and then unpack why those two choices are so different.

We'll use AirPassengers, a dataset built into R: monthly totals of international airline passengers from 1949 to 1960. It has a clear upward trend and a strong yearly season (summer peaks, winter dips), so it is a perfect stress test for any forecaster. Both functions we use here, ets() and auto.arima(), live in the forecast package and pick their own model automatically.

Two lines, two very different answers. ets() returned a label made of letters, ETS(M,Ad,M). auto.arima() returned a set of integer orders that read as ARIMA(2,1,1)(0,1,0)[12]. We will decode both labels in the next two sections. For now, the point is that they describe the same data in completely different languages.

Here is the intuition behind that difference. ETS looks at the series and asks "what is the current level, is it trending, and what is the seasonal pattern?" It then extrapolates that structure forward. ARIMA asks a different question: "after I remove the trend and season by differencing, how does each value relate to the values just before it?" It then models those leftover correlations. One works from the visible shape of the series; the other works from the correlations between each value and the ones just before it.

Figure 1: ETS and ARIMA start from the same series but model it in opposite ways.

How does ETS model a time series?

ETS stands for Error, Trend, Seasonal, the three ingredients it uses to build a forecast. The label ETS(M,Ad,M) is just those three ingredients described one at a time: the error is Multiplicative, the trend is Additive and damped, and the season is Multiplicative. Each slot can be A (additive), M (multiplicative), or N (none), which is how one function covers dozens of model shapes.

What does "multiplicative" mean here? It means the seasonal swings and the error grow in proportion to the level of the series. Look at AirPassengers and you can see it: the summer peaks in 1960 are much taller than the peaks in 1949, because the whole series is bigger. A multiplicative season captures that "swings scale with size" behaviour, which additive models cannot.

The engine underneath ETS is exponential smoothing. Its simplest form updates a running estimate of the level after every new observation:

$$\ell_t = \alpha \, y_t + (1 - \alpha)\, \ell_{t-1}$$

Where:

• $\ell_t$ = the smoothed level at time $t$ (the model's current sense of "where the series is")
• $y_t$ = the actual value observed at time $t$
• $\ell_{t-1}$ = the previous level estimate
• $\alpha$ = the smoothing weight, between 0 and 1

The single idea to take away: $\alpha$ decides how much the newest observation matters. A high $\alpha$ trusts recent data and reacts fast; a low $\alpha$ leans on the past and stays smooth. Trend and season have their own smoothing weights, $\beta$ and $\gamma$. If the equation is not your thing, skip it, the printed parameters below tell the same story.

Let's print the fitted model to see those weights R estimated.

Read the smoothing parameters top to bottom. alpha = 0.7096 is fairly high, so the level tracks recent months closely. beta = 0.0204 is tiny, meaning the trend changes very slowly and steadily. gamma = 1e-04 is almost zero, which says the seasonal shape is stable year to year and barely needs updating. The Initial states block holds the starting level l, starting trend b, and the twelve seasonal factors s (one per month). At the bottom sit the information criteria, including AICc, which we return to shortly.

There is a fourth parameter, phi = 0.98. That is the damping factor, the d in Ad.

How does ARIMA model a time series?

ARIMA describes a series through its own past values instead of through visible structure. Its label has three numbers for the non-seasonal part and three more for the seasonal part: ARIMA(p,d,q)(P,D,Q)[m]. Here is what each letter counts, using our fitted ARIMA(2,1,1)(0,1,0)[12]:

• p (here 2): autoregressive terms, how many recent values feed into the prediction.
• d (here 1): how many times the series is differenced to remove trend.
• q (here 1): moving-average terms, how many recent forecast errors feed in.
• P, D, Q (here 0, 1, 0): the same three ideas applied to the seasonal pattern.
• m (here 12): the season length, twelve months for monthly data.

The middle letter, the "I" for Integrated, is the key to ARIMA. Differencing means replacing each value with the change from the value before it. Do that once and a rising trend flattens out. d = 1 here means one round of ordinary differencing, and D = 1 means one round of seasonal differencing (each month minus the same month last year). ARIMA needs the series to be stationary first: no trend, no season, and a roughly constant mean and spread over time. Differencing is how it gets there.

Let's print the full fitted ARIMA to see its estimated coefficients.

The Coefficients block lists the estimated weights: two autoregressive terms (ar1, ar2) and one moving-average term (ma1), each with a standard error underneath. sigma^2 is the estimated variance of the model's one-step errors, and the bottom row shows the information criteria. Notice there is no alpha or gamma here; ARIMA speaks entirely in AR and MA coefficients, not in smoothing weights. That is the same series as before, described in a totally different vocabulary.

Why can't you compare ETS and ARIMA with AICc?

Here is the trap that catches almost everyone. Both models print an AICc value, and lower AICc means a better model, so it feels obvious to fit both, compare the two AICc scores, and keep the smaller one. That reasoning is wrong, and it will steer you to the worse forecaster.

Let's look at the two numbers side by side.

By this logic ARIMA (1018) crushes ETS (1401), so you would throw ETS away without a second thought. Do not. These two numbers are not measured on the same ruler.

AICc is built from each model's likelihood (a measure of how well the model fits the data it was trained on), and the two families compute that likelihood in different ways. Our ETS model uses multiplicative errors, so its likelihood is defined on the relative scale of the data. The ARIMA model works on the differenced series, so its likelihood is defined on that transformed scale. Comparing the two AICc values is like comparing a temperature in Celsius to one in Fahrenheit by their raw numbers. AICc is genuinely useful, but only for ranking models inside one family: ETS against other ETS models, or ARIMA against other ARIMA models.

How do you fairly compare ETS and ARIMA in R?

If AICc cannot referee this match, what can? The answer is the same test you would trust for any forecaster: hide the most recent part of the series, forecast it, and measure the error against the values the model never saw. This is a train and test split, and it is the fair comparison every serious forecaster uses.

We'll train both models on AirPassengers up to the end of 1958, then ask each to forecast the final two years, 1959 and 1960, which they were never shown. The window() function slices a time series by date.

Now the comparison is honest, because both models are judged on the exact same unseen data. Here is what each column means in plain terms:

• RMSE (root mean squared error): typical error size in passengers, punishing big misses harder. Lower is better.
• MAE (mean absolute error): average error size in passengers. Lower is better.
• MAPE (mean absolute percentage error): average error as a percentage of the actual value. Lower is better.
• MASE (mean absolute scaled error): error scaled against a naive seasonal forecast, so it carries no units. Lower is better.

On every single metric, ETS wins: lower RMSE (72.55 versus 74.25), lower MAE, lower MAPE, and lower MASE. Remember that ARIMA had the far better AICc? On the data that actually matters, the held-out future, ETS is the better forecaster here. That is exactly why AICc could not be trusted to choose between them.

A picture makes the difference concrete. Let's plot both forecasts against the real 1959-1960 values.

The chart (which draws when you run the block) shows both coloured forecast lines tracking the black actual series, with ETS staying a little closer through the seasonal peaks. Seeing the forecasts overlaid is often more convincing than any single error number.

When should you use ETS vs ARIMA?

You now have the honest workflow: fit both, and let a holdout decide. But you often want a starting instinct before running the test. This table sums up where each family tends to shine.

A widespread myth says ARIMA is the more general, more powerful family, so it must be the safer default. It is not true. As the diagram below and the numbers above both show, the right choice depends on the series, not on a ranking.

Figure 2: A quick heuristic for which model to reach for first.

The two families genuinely overlap, though. Some simple ETS models are exactly equal to specific ARIMA models, which is why they often forecast alike. These equivalences come from the forecasting textbook by Hyndman and Athanasopoulos:

But the overlap is only partial. Multiplicative ETS models, like the ETS(M,Ad,M) we fit, have no ARIMA equivalent at all. And many stationary ARIMA models have no ETS equivalent, because every ETS model is non-stationary by design. Neither family contains the other, which is the real reason you should try both.

One practical move often beats picking a single winner: average the two forecasts. Let's average the ETS and ARIMA predictions on our AirPassengers holdout and score the blend.

The blended RMSE is 72.70, sitting between ETS (72.55) and ARIMA (74.25). On this particular series the average did not beat ETS alone, which is an honest and useful lesson: averaging often helps, but it is not a guaranteed free win. You still have to measure it on held-out data, exactly as with any single model.

Practice Exercises

These pull together everything above: you fit both families, hold out the most recent data, then score them on real out-of-sample error. Use fresh variable names so you do not overwrite the tutorial objects.

Exercise 1: Judge both models on a new series

Repeat the fair comparison on USAccDeaths. Train both ets() and auto.arima() on all data up to the end of 1977, forecast the twelve months of 1978, and print each model's test-set RMSE. Which family wins on this series?

Exercise 2: Write a reusable model picker

Write a function pick_model(y, h) that takes any time series y and a horizon h, holds out the last h observations, fits both families on the rest, and returns a small data frame of each model's test MASE. Run it on AirPassengers with h = 24.

Exercise 3: Test whether averaging beats both

Using USAccDeaths from Exercise 1, average the ETS and ARIMA forecasts and compare the blend's test RMSE against each single model. Does the average win here?

Frequently Asked Questions

Should I always use ETS instead of ARIMA because it won here? No. ETS was the better forecaster on AirPassengers, but ARIMA won on USAccDeaths in Exercise 1. There is no family that is better in general, so the honest habit is to fit both and let a holdout decide for the series in front of you.

Can I use ETS or ARIMA if my series has no seasonality? Yes, both handle non-seasonal data. On a series with no repeating yearly pattern, ets() returns N in its seasonal slot (for example ETS(A,A,N)), and auto.arima() simply leaves the seasonal orders at zero. You call the two functions exactly the same way you did above.

My data has an extra predictor like price or temperature. Which model takes it? ARIMA does, through the xreg argument of auto.arima(), which lets you add outside variables alongside the series' own past. Plain ets() has no equivalent, so when an outside predictor matters to your forecast, ARIMA is the family that can use it.

How much history does ARIMA need before it will difference the season? Seasonal differencing (D = 1) needs at least two full seasonal cycles to estimate, so roughly two years of monthly data or two years of quarterly data at a minimum. On a shorter series auto.arima() will usually leave D at zero because there is not enough repetition to measure a stable season.

Why did auto.arima() pick a model that lost my test-set comparison? auto.arima() chooses the model with the lowest in-sample AICc, which rewards fit on the training data, not accuracy on future data it has never seen. Those two goals often agree, but not always, which is exactly why you still run a train and test holdout before trusting a model.

Summary

ETS and ARIMA are two different languages for describing the same time series, and the only fair way to choose between them is an out-of-sample accuracy test.

Key takeaways:

• Fit both, it is cheap. ets() and auto.arima() each take one line and choose their own model.
• Never compare their AICc. The two likelihoods live on different scales, so a lower AICc across families means nothing.
• Judge on held-out data. Split the series, forecast the tail, and compare RMSE or MASE on the part neither model saw.
• The winner is data-dependent. ETS won on AirPassengers; ARIMA won on USAccDeaths. Test every time.
• Consider averaging. Blending the two forecasts sometimes beats either alone, but confirm it on a holdout.

References

1. Hyndman, R.J. & Athanasopoulos, G. - Forecasting: Principles and Practice, 3rd ed. Section 9.10: ARIMA vs ETS. Link
2. Hyndman, R.J. & Athanasopoulos, G. - Forecasting: Principles and Practice, 3rd ed. Chapter 8: Exponential smoothing. Link
3. Hyndman, R.J. & Athanasopoulos, G. - Forecasting: Principles and Practice, 3rd ed. Chapter 9: ARIMA models. Link
4. Hyndman, R.J. et al. - Forecasting with Exponential Smoothing: The State Space Approach. Springer (2008). Link
5. Hyndman, R.J. - forecast package reference (ets, auto.arima, accuracy, tsCV). CRAN. Link
6. R Core Team - R datasets documentation (AirPassengers, USAccDeaths). Link

Continue Learning

• ETS Models in R: Error, Trend, and Seasonal Components - the full ETS letter system and how ets() chooses each component.
• Exponential Smoothing in R: ses() and the Alpha Parameter - the smoothing engine underneath ETS, one parameter at a time.
• Choosing a Forecasting Model in R - the broader workflow for picking among all the common forecasting methods.