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What are the advantages and disadvantages of using vector autoregression for forecasting?

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Vector autoregression (VAR) is a statistical method that models the relationship between multiple time series variables. It can be used for forecasting, impulse response analysis, and testing causal hypotheses. In this article, you will learn about the advantages and disadvantages of using VAR for forecasting, and some tips on how to apply it effectively.

本文章的要点总结

Optimal lag selection:

Choosing the right number of lags is crucial for VAR to be effective. Use criteria like Akaike information criterion to decide, so your forecasts are more accurate and less biased.
Exogenous variable path:

When using VAR for policy analysis, select a suitable path for exogenous variables. This ensures your forecasts are conditional and relevant rather than just replicating expected historical dynamics.

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Nerys Ramírez Mordán

Economista en Banco Central de la…
Tavishi Jaglan

Data Science Manager @Publicis Sapient…

1 What is VAR?

VAR is a system of equations that expresses each variable as a linear function of its own past values and the past values of other variables. For example, if you want to forecast the inflation rate and the unemployment rate, you can use a VAR model that includes both variables and their lags. The coefficients of the VAR model can be estimated using ordinary least squares or maximum likelihood methods.

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Tavishi Jaglan

Data Science Manager @Publicis Sapient | 4xGoogle Cloud Certified | Gen AI | LLM | RAG | Graph RAG | LangChain | ML | Mlops |DL | NLP | Time Series Analysis
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What is VAR,??? In very Simple term VAR is like trying to predict what will happen next in a story by looking at the past actions of multiple characters, instead of just one. It uses the history of several related things to forecast their future. Imagine you're trying to predict tomorrow's weather. Instead of just using today's temperature, you also consider today's humidity, wind speed, and other factors. So, you're using multiple variables to make your prediction. That's a bit like what VAR does, but for time series data.

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Akhilesh Pandey

Backend Engineering Expertise in Java, Springboot, Microservices | Proficient with Docker, Kubernetes, GCP | Exploring the Frontiers AI
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VAR model is like a weather forecast but for multiple things at once like predicting rain and temperature together. It looks at past data to make these predictions. For example, imagine a shop owner using VAR to predict both ice cream sales and soda sales for the next week. By looking at past sales of both items, the model can tell if, when ice cream sales go up, soda sales also tend to go up, helping the owner stock up accordingly

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Daniel Alor Minaya

PhD (e) en Economía | MBA en Administración Estratégica y Finanzas Internacionales | Psicólogo e investigador en Economía Conductual | Econometría, machine learning e investigación científica.
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Un modelo VAR podría plantear que la "inflación" en un período actual depende de los valores rezagados del "desempleo" y de la misma "inflación". Y del mismo modo, el "desempleo" en período actual depende de los valores rezagados de la "inflación" y del mismo "desempleo". De esa manera se genera un sistema de ecuaciones, donde hay un vector de variables dependientes ("inflación" y "desempleo") que dependen de ellas mismas en sus valores rezagados. Es decir, un modelo de un vector autorregresivo: eso es un modelo VAR.

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2 Why use VAR for forecasting?

One of the main advantages of using VAR for forecasting is that it can capture the dynamic interactions and feedback effects among multiple variables. For instance, if you want to forecast the impact of a monetary policy shock on the economy, you can use a VAR model to trace how the shock affects interest rates, output, inflation, and unemployment over time. Another advantage of VAR is that it does not impose any restrictive assumptions on the structure or the distribution of the data. You can use VAR for forecasting any time series variables that are stationary or cointegrated.

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Akhilesh Pandey

Backend Engineering Expertise in Java, Springboot, Microservices | Proficient with Docker, Kubernetes, GCP | Exploring the Frontiers AI
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Why use VAR for forecasting? Imagine trying to predict a soccer game's outcome. Instead of just looking at one team's past performance, VAR lets us consider both teams histories together, since they affect each other. Similarly, in forecasting, some things are interconnected. VAR helps predict multiple related things at once by considering how they have influenced each other in the past.

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Santosh Kumar Puvvada

Data Scientist- NTT Data | Tata Motors | Godrej | IIM Mumbai | BITS Pilani
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Most time series algorithms impose a unidirectional relationship. For ex: Temperature influences ice cream sales. However, ice cream sales don't influence the temperatures. So, when we try to forecast ice cream sales, taking temperature as an exogenous variable & generating demand will give a good output. But what if there is a bidirectional relationship eg: per-capita income & per-capita expenditure. If per capita income increases, per capita expenditure will likely increase in future & if per capita expenditure is decreasing it indicates that people anticipate tougher times going ahead & per-capita income is likely to decrease. This kind of bidirectional/feedback relationship is allowed in VAR & in these situations VAR is advisable.

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Daniel Alor Minaya

PhD (e) en Economía | MBA en Administración Estratégica y Finanzas Internacionales | Psicólogo e investigador en Economía Conductual | Econometría, machine learning e investigación científica.
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?Qué sucede cuando queremos saber si el comportamiento de una variable en el tiempo influye en el comportamiento de otra variable en el tiempo? Los modelos VAR (a través de su análisis de "impulso - respuesta") permite establecer si los cambios ("shocks") de una variable en un momento determinado genera cambios en otra variable en otro momento determinado. Un ejemplo sería analizar el impacto de la tasa de interés sobre el consumo o inversión. Un cambio de la tasa de interés debería generar un cambio en la inversión en un tiempo posterior.

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3 What are the challenges of using VAR for forecasting?

One of the main disadvantages of using VAR for forecasting is that it requires a large amount of data and a careful selection of the lag length. If you have too few observations or too many lags, you may overfit the model and produce inaccurate forecasts. If you have too many variables or too few lags, you may omit important information and produce biased forecasts. Another challenge of using VAR for forecasting is that it may not account for structural changes or nonlinearities in the data. You may need to test for stability, heteroscedasticity, and nonlinearity, and use alternative methods such as structural VAR, threshold VAR, or vector error correction models.

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Nerys Ramírez Mordán

Economista en Banco Central de la República Dominicana
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En el análisis de política, usualmente estamos interesados en estimar pronósticos condicionados, por tanto, debemos elegir la senda adecuada para las variables exógenas. Por que de lo contrario, el VAR solo recrea la dinámica histórica esperada.

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Daniel Alor Minaya

PhD (e) en Economía | MBA en Administración Estratégica y Finanzas Internacionales | Psicólogo e investigador en Economía Conductual | Econometría, machine learning e investigación científica.
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Hay que recordar que en el modelo VAR (simple), es probable que los errores estén autocorrelacionados, dado que se trata de un sistema parecido a ecuaciones simultáneas. Aparte, el VAR simple usualmente no permite implicar mucha teoría económica. Ante ello el VAR estructural permite definir el modelo con restricciones que ameritan mayor carga teórica al modelo.

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4 How to use VAR for forecasting effectively?

To use VAR for forecasting effectively, you need to follow some steps and guidelines. First, you need to identify the variables and the data sources that are relevant for your forecasting problem. Second, you need to check the stationarity and the cointegration of the variables, and apply appropriate transformations or differencing if needed. Third, you need to choose the optimal lag length based on criteria such as the Akaike information criterion or the Schwarz criterion. Fourth, you need to estimate the VAR model and evaluate its goodness of fit and diagnostic tests. Fifth, you need to generate the forecasts and the confidence intervals, and compare them with other methods or benchmarks.

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Daniel Alor Minaya

PhD (e) en Economía | MBA en Administración Estratégica y Finanzas Internacionales | Psicólogo e investigador en Economía Conductual | Econometría, machine learning e investigación científica.
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Una ruta resumida para elaborar un modelo VAR sería: - Definir las variables. - Evaluar la estacionariedad (requisito básico) y cointegración. Aquí es posible que necesitemos transformar las variables. - Definir el número de rezagos (usar Akaike) - Estimar el Var. Con los parámetros (betas) hallados, podemos realizar diagnósticos.

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5 What are some examples of using VAR for forecasting?

VAR is employed in many areas, such as economics, finance, marketing, and ecology, for forecasting. For instance, a VAR model with exogenous variables or dummy variables can be used to forecast macroeconomic variables and policy responses in different scenarios. Similarly, a VAR model with GARCH errors or a multivariate GARCH model can be used to forecast stock market returns and volatility. Additionally, a VAR model with seasonal dummies or a vector autoregressive moving average model can be utilized to forecast sales and advertising effects. Lastly, a VAR model with spatial lags or a spatial vector autoregressive model can be employed to forecast population dynamics and environmental factors.

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6 What are some resources for learning more about VAR for forecasting?

If you’re interested in learning more about VAR for forecasting, there are various resources available. Enders (2015) has a textbook on time series analysis and forecasting that covers the theory and applications of VAR models in detail. Pfaff (2008) has a tutorial on how to implement VAR models in R with examples and codes for estimating, testing, and forecasting. Tsay (2014) has a course on econometrics and forecasting that introduces the concepts and methods of VAR models as well as other advanced topics. Lastly, Lütkepohl (2020) has a website on VAR models with lectures, slides, exercises, and data sets.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are the advantages and disadvantages of using vector autoregression for forecasting?

1

2

3

4

5

6

7

1 What is VAR?

2 Why use VAR for forecasting?

3 What are the challenges of using VAR for forecasting?

4 How to use VAR for forecasting effectively?

5 What are some examples of using VAR for forecasting?

6 What are some resources for learning more about VAR for forecasting?

7 Here’s what else to consider

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What are the advantages and disadvantages of using vector autoregression for forecasting?

1

2

3

4

5

6

7

1 What is VAR?

2 Why use VAR for forecasting?

3 What are the challenges of using VAR for forecasting?

4 How to use VAR for forecasting effectively?

5 What are some examples of using VAR for forecasting?

6 What are some resources for learning more about VAR for forecasting?

7 Here’s what else to consider

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