In short, for the purposes of forecasting, it is often convenient and even beneficial to ignore economic theory. The restrictions implied by economic theory is necessary for inference when the question of interest is causal in nature (e.g., when you want to understand the underlying causal relationships). However, if the forecast you're interested is more of the variety of a sophisticated extrapolation, then something simple like ARIMA may be more helpful and more accurate.
I think the following are helpful references.
Why would I not be interested in the underlying causal relationship?
Consider the following example from "Introduction to Econometrics" (3rd Edition), by Stock and Watson (p. 517).
The simplest regression model in Chapter 3 related test scores to the
student-teacher ration (STR): \begin{equation} \widehat {Test Score} = 989.9 - 2.28 \times STR \tag{14.1} \end{equation} As was discussed in Chapter 6, a school superintendent, contemplating hiring more teachers
to reduce class sizes, would not consider this equation to be very
helpful. The estimated slope coefficient in Equation (14.1) fails to
provide a useful estimate of the causal effect on test scores of the
student-teacher ratio because of probable omitted variable bias
arising from omission of school and student characteristics that are
determinant of test scores and that are correlated with the
student-teacher ratio.
In contrast, as was discussed in Chapter 9, a parent who is
considering moving to a school district might find Equation (14.1)
more helpful. Even though the coefficient does not have a causal
interpretation, the regression could help the parent forecast test
scores in a district for which they are not publicly available. More
generally, a regression model can be useful for forecasting even if
none of its coefficients has a causal interpretation. From the
perspective of forecasting, what is important is that the model
provides as accurate a forecast as possible.
Along these same lines, this is a point that is brought up frequently
when discussing Machine Learning. Machine Learning may not be so useful in helping to understand underlying causal relationships. However, often we are more interested in the predictions/forecasts. Sendhil Mullainathan in this talk on "Machine Learning and Prediction in Economics and Finance" gives the useful "rule of thumb" rubric---are you more interested in the $\hat y$ or the $\hat beta$?
Why would something like ARIMA forecast better than a model that better reflected economic theory?
Consider this useful passage from "A Guide to Econometrics" (6th Edition) by Peter Kennedy (p. 333).
The main competitors to econometric models for forecasting purposes
are Box-Jenkins, or ARIMA (autoregressive integrated moving average),
models explained in some detail in chapter 19. Univariate Box-Jenkins
models are sophisticated extrapolation methods, using only past values
of the variable being forecast to generate forecasts; they ignore the
many explanatory variables that form the foundation of econometric
models. There are several reasons why forecasters should be interested
in these naive models: thanks to improved computer software, they are
easy and cheap to produce; the extra information required to estimate
a proper econometric model may be expenÂsive to obtain ; forecasts
from such models can serve as a useful benchmark for comÂparison
purposes; forecasts from this process can be combined with other
forecasts to produce improved forecasts ; and they are useful as a
preliminary step for further modeling---they clarify the nature of the
data and make clear what behavior patterns require explanation.
During the 1970s controversy raged over the relative forecasting
merits of econoÂmetric models and ARIMA models, prompted by studies
claiming the superiority of the ARIMA models. As noted in chapter 19,
this led to a synthesis of the two approaches, and prompted the
development of models, such as error-correction models (ECMs), which
paid more attention to dynamics. In retro spect, the reason why
econometric models performed so poorly in these comparisons was
because of misspecification errors in the econometric models,
primarily with respect to their dynamic structure. It is generally
acknowledged that whenever specification or conditioning errors
renÂder econometric models impractical (which some claim is most of
the time), the Box-Jenkins approach has considerable merit for
forecasting. It is also recognized that if an econometric model is
outperformed by an ARIMA model, this is evidence that the econometric
model is misspecified.
Can a univariate model like ARIMA represent a rational expectations equilibrium?
Not really. Most economics theory employ rational expectations that lead to a nonlinear system of equations (in multiple variables) that describe the model's dynamics. Often, these are approximated (e.g., log-linear approximation), so that they can be solved and estimated using something like a linear state space model---but many still require multiple variables (here, arranged in a vector) to describe the full dimensionality of the model. For an example of one particular model that uses rational expectations, see p. 30 of "Recursive Models of Dynamic Linear Economics" by Hansen and Sargent.
Consider a stochastic process $\{p_t\}$ related to a stochastic process $\{m_t\}$ via
\begin{equation}
p_t = \lambda E_t p_{t+1} + \gamma m_t \tag{(2.4.38)}
\end{equation}
where
\begin{equation}
m_t = G x_t \tag{(2.4.39)}
\end{equation}
and $x_t$ is governed by
$$
x_{t+1} = A x_t + C w_{t+1}, \text{ for } t = 0,1,2,...
$$
...
Collecting results, we have that $(p_t, m_t)$ satisfies
\begin{align*}
\begin{bmatrix}{p_t \\ m_t }\end{bmatrix}
&=
\begin{bmatrix}
\gamma G(I - \lambda A)^{-1} \\ G
\end{bmatrix}
x_t
\\
x_{t+1} &= A x_t + C w_{t+1}.
\end{align*}
[This system] embodies the cross-equation restrictions associated with
rational expectations models: note that the same parameters in $A,G$ that pin > down the stochastic process for $m_t$ also enter the equation that determines > $p_t$ as a function of the state $x_t$.
This equation, written flexibly, allows for many state variables and many (possibly orthogonal) shocks. As such, this cannot be represented by a simple univariate model like ARIMA.
Many other examples can be found in "Structural Econometrics" by Dejong and Dave or more in "Recursive Models of Dynamic Linear Economics", by Hansen and Sargent. Some will only have a single dimensional state space. Some will have much larger state spaces.
However, again, describing the model in full may not be necessary if you're only interested in simple forecasting. Hence, something like ARIMA is an attractive option.
