# What is the distinction between short term and long term forecasting?

I often see forecasting methods described as long term or short term methods.

I assume the difference between short term and long term forecasting cannot just be the amount of time. I assume this because the sampling frequency and the rate at which the series changes is also significant. Also some series are timeless i.e. those derived form equations.

So what defines a short term and long term forecast?

Many thanks

• Could you edit your question to give examples for methods described as long term or short term methods? – Stephan Kolassa Nov 20 '14 at 14:58
• I was under the impression that ARIMA was a short term method. But after a quick Google I can't find anything which says that so I may have dreamt it. @Zhanxiong's comment appears to indelicate that it is though. – Andy T Nov 20 '14 at 15:21
• Careful: Zhanxiong talks about ARMA. Once you add differencing and move to ARIMA, you have trends, which are not dampened (as is frequently done in Exponential Smoothing). And of course AR(I)MA as such does not model external drivers, so I'd say Zhanxiong's answer looks at the problem from an orthogonal angle than I do. – Stephan Kolassa Nov 20 '14 at 16:20

Interesting question, although there probably is no clear-cut correct answer.

I would say that any difference between short- and long-term forecasting lies in which causal factors dominate at the different forecasting horizons.

• For instance, in electric load forecasting, short term forecasts will be dominated by weather (driving air conditioning/heating use), whereas long term forecasts will be dominated by economic development and political decisions (building offshore wind parks will yield different load distributions than power plants in the middle of the country).
• In the retail business, short term forecasts will be driven by promotions and price changes on existing products. Medium term forecasts will be driven by product substitutions, and long term forecasts again by economic developments and politics.

Methods will need to model these driving factors.

I think that the sampling frequency is less important. You will usually try to get data at the highest possible frequency, anyway, since you can always throw data away. However, for long term forecasting you will likely not be interested in the higher frequencies. For electricity forecasting, you are interested in data in 15 minute buckets for the short term (next days), but probably only in bigger buckets when deciding where to build new high voltage power lines, for which you need multi-year ahead forecasting.

• That's roughly what I suspected. "I would say that any difference between short- and long-term forecasting lies in which causal factors dominate at the different forecasting horizons." - though how do we choose which forecast horizons are long term and which are short term? It sounds like its not formally defined. Thanks – Andy T Nov 20 '14 at 15:07
• It certainly is not formally defined, at least not in the forecasting textbooks I am familiar with. Which is why I was so interested in examples for "short term forecasting methods". It appears to me like this distinction is used in a very ad hoc manner by different authors. – Stephan Kolassa Nov 20 '14 at 22:20

The following paragraph is excerpted from Brockwell, Davis: Time series: theory and application, section 13.2:

An ARMA process $\{X_t\}$ is often referred to as a short memory process since the covariance (or dependence) between $X_1$ and $X_{1+k}$ decreases rapidly as $k \to \infty$. In fact we know from Chapter 3 that the autocorrelation function is geometrically bounded, i.e. $$\left|\rho(k)\right| \leq Cr^k \quad k = 1, 2, ...$$ where $C > 0$ and $0 < r < 1$. A long memory process is a stationary process for which $$\rho(k) \sim Ck^{2d-1} \text{ as } k \to \infty$$ where $C \neq 0$ and $d < .5$.

Intuitively, the "short memory (or term, in your words)" and "long memory" time series correspond to the correlation between two observations with lag $k$ are "small" (with geometric decreasing order) and "large" (with power function order, but is still decreasing to zero slowly), respectively.

Consequently, a short/long term forecasting is the forecasting for which the underlying time series model is short/long memory time series.

• That's my personal understanding. – Zhanxiong Nov 20 '14 at 15:05

I think short term forecasting is usually used in short term objectives covering less than one year for example material requirement planning, scheduling, budgeting e.t.c while long term forecasting is usually used to predict the the long term objectives covering more than five years for example product diversification, sales and advertisement e.t.c.

• A good practical answer, but are there any mathematical concepts that are fundamentally different between the two? And what about forecasting in a non-business application? – JDL Nov 8 '16 at 14:43