How can you use regression models to forecast economic trends?

A "regression" is one subjective projection, out of many possible projections with n correlated variables. There is no analysis involved and you can forget about "prediction."

regression analysis is a powerful tool for understanding and quantifying relationships between variables.I would encourage you to think of regression as a tool that helps uncover patterns and make predictions based on data.

Regression models by themselves test associations not causation. Causation requires designed experiments or causal inference. The latter is very complex.

Regression analysis is a great tool to ensure that policies are based upon data and not opinion. However, a better question to ask is how can you use the economic trend data from regression models to inform policy? While it may be more common to use data around decisions of monetary policy, data is not often sufficiently leveraged in other types of policy decisions. Especially during emergencies, ineffective policies can be pushed through too hastily. It's better to do analysis ahead of time and identify thresholds for taking action.

Estudiar los errores ayuda a identificar términos o variables faltantes. Por ejemplo, un error con forma cuadratica es indicativo de la falta de términos de dicho orden. Otro ejemplo, si hay errores con ciertos patrones (fin de semana o festivo) indica que se debe a?adir dichas variables dummies para tratarlos.

Data will most probably be time series data which requires special treatment. While working with any kind of data that also has a time component, we have to be extremely careful with autocorrelation and stationarity. If this period's data is significantly correlated with the previous period's data and/or if the data has drift and seasonality then we have to treat these features carefully. We have to check the Autocorrelation and Partial Autocorrelation plots to determine what kind of process the dataset follows.

Building a regression model involves several key steps and considerations to ensure a robust and meaningful analysis. These include data exploration, feature selection, validating assumptions, model selection, evaluation, addressing overfitting/underfitting, model interpretation, reporting, validation/robustness, ethical considerations, and iteration. Flexibility and adaptability are essential when building regression models. By following these steps, you can develop a regression model that provides valuable insights and accurate predictions.

To create this model we hence do EDA with two fold goal - a) identify predictor variables that influence the outcome b) remove repetitive influencers as they do not contribute in explaining the outcome

Start by gathering data on variables you suspect are connected. Split it into two sets: one to teach your model (training set) and another to test its predictions (test set). Choose a regression type—like linear if expecting a straight-line relationship. Train your model with the training set, letting it learn the patterns. Evaluate on the test set to see how well it predicts. Fine-tune the model for better accuracy. It's a bit like teaching your model to recognize patterns in a game—train it well, and it becomes your reliable player in predicting future outcomes!

From an academic perspective, one from economic theory, I would also emphasize that theory should match your model. As much as regression analysis or even Econometrics as a whole is largely statistical and mathematical, for economic modelling the regression should lend itself to theory. For instance, there are always apriori expectations of variables and how they are correlated according to their theoretical model. If the data shows correlations that are unexpected, it should be interrogated against theory. If indeed it shows unexpected results, there are more advanced methods to test the robustness of those results such as the Zivot-Andrews test.

We cannot use random split for test data because it will break the "equal time step" principle of time series data. Our test data should be a block from the most recent periods. With this approach, we can successfully test the model and compare forecasts with actual outcomes. I suggest using ARMA, ARIMA, or SARIMA models with external regressors. These algorithms come with a number of assumptions and we have to check them one by one to get reliable forecasts. There are other models like Prophet, LSTM, DeepAR built for time series forecasting. I personally prefer these algorithms instead of simple or multiple linear regression.

We can forecast using regression model by creating lagged variables of the response and feature variables. That will allow us to capture the impact of value of the response variable in previous time periods on the current time period. This allows us to capture the seasonality and holiday periods. For example if there is more sale in end of the quarter, then lagged response variable 3 months back will have a stronger relationship with current period. Also we can capture trend by adding a trend variable as another feature. Trend variable can have values 1, 2, 3 and so on. This will allow us to capture a linear trend. One can also capture a quadratic trend through creation of a quadratic trend variable.

Regression models have pros and cons for forecasting. The pros include interpretable results, quantitative predictions, flexibility, incorporation of multiple factors, and assessment of variable significance. The cons include assumptions of linearity and stationarity, limited extrapolation, sensitivity to outliers, overfitting, data quality and assumptions, and limited causality. Understanding these factors is crucial for effectively using regression models in forecasting.

When we have the relation between the outcome and predictive variables to be linear ( check correlation curves) we do a linear regression or regression based decision trees. If the relations is nonlinear (I.e. like a repetitive up and down curve) we will do a polynomial regression

I like to use ARIMA for forecasting It’s a powerful tool that incorporates autoregressive and moving average components When using ARIMA it’s important to choose the parameters wisely and check model fit statistics

To test validity of a regression model we use specific tests to check whether the assumptions of linear regression holds. We check whether assumptions of linearity, homoscedasticity, goodness of fit and normality hold. However I give highest priority to accuracy metric. If the accuracy is high consistency with different training and test datasets, then I will chose the linear regression model and relax some of the linearity, homoscedasticity, goodness of fit assumptions. We need to remember that in real life we have to take calls/informed decisions when selecting a model.

There are several ways to check the validity of a model. There are pre-estimation (e.g stationarity) and post estimation diagnostic tests (e.g CUSUM test for normality). However the simplest way to understand this is : At the core of valid models is the concept of the error term. In any time series, a variable at time 't' is correlated with a variable in time 't-1'. Simply put today is correlated with yesterday. E.g inflation today is related to yesterday's; wages today are related to yesterday's, etc. So it is important to arrest this error term to make sure that it doesn't create this 'chaos' in our models. Therefore the basic model must fulfill what is called OLS assumptions to be valid. (Please Google - not enough characters).

To ensure the validity of a regression model, consider these key steps: Residual Analysis: Examine differences between observed and predicted values. Outlier Detection: Identify and address outliers that can impact model validity. Influential Observations: Identify data points that significantly influence model parameters. Collinearity: Assess and address multicollinearity among independent variables.Model Stability: Check if coefficients are stable over time or subsets of data. Alternative Models: Compare regression model with alternative approaches. Heteroscedasticity: Be aware of varying levels of error dispersion.

We basically look at the error of the prediction to understand how good is our model - we can use techniques like regularisation where we add penalty in MSE calculations

La validité d'un modele de regression se verifie à l'aide des tests effectués sur les residus du modèles et celui effectué sur la significativé des coefficients de chaque variable.

Mejorar modelos implica abordar el sobreajuste y la falta de generalización. La regularización, como Ridge (L2) y LASSO (L1), es clave. Ridge penaliza cuadrados de coeficientes, útil para correlaciones. LASSO penaliza valores absolutos, eliminando algunos coeficientes y favoreciendo la relevancia de variables. Estas técnicas evitan la sobreponderación, mejorando la adaptación a patrones generales y facilitando la generalización a nuevos datos. La elección depende de la naturaleza del problema. Ajustar parámetros, como \(\alpha\), equilibra la complejidad del modelo y su adaptabilidad. Encuentra el equilibrio para un modelo preciso y generalizable.

Improving a regression model requires a combination of techniques and considerations. Key factors include addressing data quality issues, feature engineering, regularization, cross-validation, model selection, hyperparameter tuning, residual analysis, handling multicollinearity and outliers, ensuring model interpretability, feature selection, time series considerations, handling imbalanced data, incorporating domain knowledge, robustness testing, and regular model maintenance. It's crucial to strike a balance between model complexity and interpretability while ensuring generalization to unseen data.

To enhance a regression model, adjust variable selection by adding relevant variables or removing insignificant ones. Transform variables for better linearity and normalize distributions. Choose appropriate model types, like nonlinear or logistic, for better fit. Incorporate interaction terms for complex relationships and use diagnostic checks for model accuracy. Employ cross-validation and regularization techniques to reduce overfitting. Continuously update the model with new data and apply domain expertise for real-world relevance. Finally, use advanced statistical software for robust analysis.

Un modèle de régression s'améiore par l'ajout et ou le retrait de certanies variables explicatives. Cela se fait en regardant le coefficient de correlation pour eviter l'effet de multi colinéarité.

Many a times using a step by step forward variable selection provides a good model as it takes into account the mathematics and the domain knowledge for the particular problem in hand Other techniques like normalising data and adding dummies to account for less than 5% outlier outcomes

Despite its limitations, I think the VAR, VARMAX and VEC models are the best for groups of time series with complex interactions. With regard to assessing macroeconomic impacts to a given variable of interest, the IRF functions built from those models give strong insights of those interactions.

Regression provides y=f(x), where the x's are independent variables. Forecasting provides y=f(t), where t is time. I would discourage including time as an independent variable in regression. Time Series Analysis should be used when modeling and issuing forecasts with y=f(t). If interested in y=f(x,t), consider using Time Series Analysis with transfer functions.

Make sure that the regression model can scale efficiently with the size of the data and that it keeps providing adequate solutions.