Time series analysis is a powerful inferential statistical tool used to forecast economic trends by observing data points systematically collected over time. It allows analysts to grasp and forecast patterns such as trends, seasonality, and cyclical fluctuations that are characteristic of economic series. These time trends include series like gross domestic product, unemployment rates, and stocks (Box, Jenkins, & Reinsel, 2015). They are dynamic and maintain their shape over time. Time series models rely on a series of observations to learn from (Hamilton, 1994). Year-on-year values from GDP or unemployment rates are such examples. They model the path that variables will take in the future.

These temporal dependencies are critical for forecasting, policy, investment, and resource allocation. Their ability to incorporate signals and noises from past behaviors improves their predictive power compared to static or cross-sectional methods. Among these, autoregressive integrated moving average (ARIMA) models are widely used for economic forecasting. This class of models combines autoregression, differencing from the error, and the faster smoothing of noise through time, which makes it suitable for many economic time series like the cycle of growth and contraction (Hamilton, 1994). Another model of ARIMA is SARIMA, which explicitly includes seasonality. This is essential for time series data like GDP, which have high seasonality due to factors such as holidays and fiscal quarters. Univariate studies show that this model has parameters that give the past values and errors of past observations to future ones for scenario analysis (Hamilton, 1994).

Accordingly, estimation memory is a key feature of ARIMA and SARIMA. However, these models assume linearity, which can limit their forecasting performance in dynamic economic environments. More sophisticated types of time series models include new methods like machine learning or VAR and state space models (Lütkepohl, 2005; Durbin & Koopman, 2012). VAR models are good for complex economies with several sectors and long-term economic growth rates. These models allow interactions among the outputs, which account for the industries. VAR models also examine how changes in one variable affect others.

They resolve path-dependent anticipation, thereby giving credence to complex interactions (Lütkepohl, 2005). State space models use time-varying parameters to estimate unobserved components in the economic data. Using different mathematical models, they capture the effect of economic shocks or regime changes on time series data (Durbin & Koopman, 2012). They are therefore integral to economic forecasting. In conclusion, time series analysis in empirical economic forecasting is a fundamental requirement for many decision-makers in the public and private sectors.

References

Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley.

Durbin, J., & Koopman, S. J. (2012). Time Series Analysis by State Space Methods (2nd ed.). Oxford University Press.

Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.

Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.

Time series analysis enables economists to identify, model, and forecast dynamic behavior in economic variables over time. Techniques such as ARIMA, VAR, and exponential smoothing are used to uncover patterns like trends, cycles, and seasonality. These models help forecast inflation, GDP growth, exchange rates, etc., by leveraging historical data to predict future values. Critically, stationarity checks, model diagnostics (ACF/PACF, residual analysis), and out-of-sample validations are essential for robust forecasting. The power of time series lies in its ability to inform policy by anticipating economic turning points with reasonable accuracy.

Time series analysis cannot forecast future trends. It is a term for a set of statistical methods to test (specified) models. It can e.g. be used to discover present(?) trends or seasonal or cyclical fluctuations. Its mainly use is to find-out relations (not only linear ones) between variables. But I doubt that it can find-out turning points. An application of complicated econometric methods without careful specification of the model (unfortunately often done) is senseless.

Time series analysis examines patterns in economic data collected over time—such as GDP, inflation, or unemployment—to model trends, seasonality, and cycles, allowing economists to generate forecasts and evaluate the likely future impact of policy or external shocks.

You can use ARMA modeling via difference equations

I presume that you are asking about the use of time series models such as ARMA to forecast various economic time series.

The principle is to select a parsimonious ARMA model that mimics the persistence in the model (Autoregressive or AR component) and the extended effect of shocks over several periods after the shock (Moving Average or MA component of the shock). The actual process being forecast does not follow the ARMA process. The parameters of the ARMA process can not be used for structural or causal inference.

The values of the parsimonious ARMA process are forecast assuming that there are no further shocks to the system. It has been found that, under certain conditions, the values of the forecast ARMA process provide good short-term forecasts of the real process.

The question is too general to give precise answers. One of the easiest tasks is to "find-out" trends (better: to extract trends from time series data). That is a theory-less matter, one needs no specification except the assumption of a (quasi-)systematic relation between a variable and time.

What concerns ARMA: One should differentiate between an economic model and the estimation method. Often, "economists" spare themselves the trouble of carefully specifying the model (equation) and feed a program with data they have not analysed before. They present a plenty of results without examining whether they are reasonable and without interpretation.

Estimados Joseph Ozigis Akomodi , Emmanuel Aklinu , Anton Rainer y John C Frain, su discusión sobre el uso del análisis de series temporales en la previsión económica es muy rica y abarca desde el potencial hasta las limitaciones. Mi visión se alinea con la utilidad de estas herramientas, pero enfatizando una aplicación crítica y contextualizada.

Coincido con Joseph y Emmanuel en que el análisis de series temporales es una herramienta estadística poderosa para identificar patrones como tendencias, estacionalidad y ciclos en variables económicas como el PIB, la inflación o el desempleo. Modelos como ARIMA y SARIMA son fundamentales para pronósticos a corto plazo, especialmente cuando las series presentan estacionalidad marcada (el PIB de muchos países exhibe patrones estacionales, influenciados por trimestres fiscales o festividades).

Sin embargo, comparto las cautelas de Anton y John C. Frain. Es crucial reconocer que el análisis de series temporales, por sí solo, no puede "predecir" el futuro con certeza absoluta ni identificar puntos de inflexión con total precisión. Su poder radica en la modelización de la persistencia y los efectos de los choques pasados (como señala John). Por ejemplo, aunque el modelo ARIMA pudo haber pronosticado el crecimiento del PIB de México en 2023 basándose en datos históricos, no habría anticipado con precisión el impacto de una guerra comercial sorpresiva o una nueva pandemia. El crecimiento del PIB de México en 2023 fue del 3.2% (Fuente: INEGI, 2024), una cifra que se pudo pronosticar con cierta fiabilidad usando estas herramientas, pero que también dependió de eventos exógenos.

Desde una perspectiva personal, el valor real de los modelos de series temporales no reside en la "predicción perfecta", sino en su capacidad para informar políticas públicas y la asignación de recursos, permitiendo a los gobiernos y empresas anticipar escenarios y preparar respuestas. Modelos más sofisticados como VAR son valiosos para entender las interacciones complejas entre variables macroeconómicas (por ejemplo, cómo un cambio en la tasa de interés afecta el desempleo y la inflación). Sin embargo, su aplicación debe ir acompañada de un sólido fundamento teórico y una especificación cuidadosa del modelo, evitando el "uso de métodos econométricos complicados sin una especificación cuidadosa" (Anton).

Puedo concluir que el análisis de series temporales es una herramienta indispensable para la previsión económica, pero su eficacia depende de un uso consciente de sus limitaciones. No es una bola de cristal, sino un instrumento para comprender mejor las dinámicas pasadas y proyectar tendencias futuras bajo supuestos razonables. Su verdadero poder se maximiza cuando se combina con un profundo conocimiento económico y una interpretación crítica, informando decisiones que busquen la estabilidad y el bienestar.

@Anton Rainer the question is a research question. A research aught to be open ended that is what encourages creativity in answering a research question

Joseph Ozigis Akomodi, if you want to make causal conclusions about a process, you must design a proper random experiment or survey. In this design, the explanatory variables are pre-assigned, and the process is randomised over other explanatory variables. Such an experimental design is often feasible in engineering, the sciences, medicine, and other disciplines. It is generally not possible in areas such as economics and the social sciences.

Data that is simply observed or is not the output of a properly designed randomised experiment is known as observational data. In general, it is not possible to make causal conclusions with observational data. You must have a theoretical model of your process that contains some causal links. You then collect an observational data set covering the variables in your model. You do various misspecification tests. If the data and the model are consistent, you can proceed to estimate the model and evaluate the causal links. Your results are conditional on the correctness of the model.

If you just put your observational data into an econometric or statistical package and find a model that fits the data, you can not make any causal conclusions from your estimates. This does not work.

It is just a simple matter that the open-ended statistical approach that you propose is not valid.

John C Frain If you took your time to read my researched submission above you will note that it is possible. First of all read the research and tell me again it is not possible. Then I will prove you wrong! You are looking at factual research data of the trends of events over time.

Joseph, what is a research question? I have never heard this expression.

John, one should be careful to speak of causality in economics (in other sciences, too). Is income the cause of consumption? Of course, not! In causality tests, by causality one means a clear effect (in one direction) of a variable on another. You are right about the theory-less (or should one say: brainless) application of statistical methods, which I have criticized in my former answer concerning ARMA.

BTW, I do not understand why an ARMA sort of economic model must be linear (see Josph’s answer to his own question). I see the general form of such a model like Y=f(lagged Y’s)+g(lagged X’s) with f and g functions or transformations and + stands for any operation. Maybe, that such a specified model could be difficult to estimate by a (linear) ARMA method, but mostly it is possible to approximately linearize the specification.

It seems that time series analyses are, by far preferred to cross-sections ones. In fact, it depends. Counter-example: In the Austrian Ministry of Finance, my division had the task of forecasting tax revenues (for all Federal taxes). If you want to e.g. forecast wage tax revenue, one should, of course, not recur to a time series estimate, which would bring very poor results (especially when there were considerable changes of the tax law in the year before). We took the latest wage tax statistics (clearly cross-section) to build a model for the forecast assuming a realistic increase of wages and salaries. Another example: For the forecast of private consumption, one may take a time-series-estimate C=C(Net Income). This would not be a good approach for the calculation of the effect of a change of the income tax scheme, which may concern different incomes differently. One needs an estimation of income specific propensities to consume (again a cross-section matter).

@Joseph Ozigis Akomodi, I did read what I believe you considered a "research submission". To me, it reads like part of the recommended reading list for an advanced time series course. The four books are on my bookshelf, and I use them, along with others, for reference. If I were presented with this as a research proposal, I would ask the presenter to clarify.

I have made two previous comments.

You would benefit from reading Scott Cunningham's book Causal Inference: The Mixtape. An online version is available at

https://mixtape.scunning.com/