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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
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.
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.
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.
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.
