DAT320: Forecasting Techniques

Introduction to Forecasting

• Norwegian University of Life Sciences (NMBU) course DAT320: Forecasting, covering multivariate extensions of ARIMA models.
• Course taught by Kristian Hovde Liland, autumn 2024.

Forecasting Methods

• Dynamic Regression: Models with lagged predictors.
• Multivariate ARIMA: Multivariate extensions of ARIMA.
• Granger Causality: A concept for determining if one time series predicts another, particularly relevant when dealing with multiple time series.

Airquality Dataset Overview

• The airquality dataset is used for illustrative examples.
• Includes time series data for Ozone, Wind, and Temperature.
• Data visualized as time series plot showing ozone, wind, and temperature levels over time.

ARIMAX Model

• ARIMAX models extend ARIMA models by incorporating exogenous input variables.
• ARIMAX models are essential for forecasting scenarios involving an influential factor beyond the time series itself.
• A variable of interest is being modeled.
• Additional contributing factors are identified as exogenous inputs.

ARIMAX Model-Equation and Interpretation

• ARIMAX models' mathematical representation is provided in equations representing the relationship between a variable being predicted and other factors.
• Interpretation of model parameters (ß, θ) and the underlying meaning of these parameters in relation to model's predictions are presented.

Weaknesses of the ARIMAX Model

• Limited interpretability of model constants: specifically comparing, the interpretation with other regression algorithms.

Dynamic Regression with ARIMA Errors

• Models combining classical regression with ARIMA error models.
• These models consider potential autocorrelation in the regression errors, allowing the errors to be correlated.
• Differencing techniques enable input variables to be stationary.

Dynamic Regression Model with Lagged Predictors

• Models that incorporate past values of predictor variables into the regression equation.
• A dynamic regression with lagged predictors, in addition to present values of predictor variables, uses past values of those variables as predictors.

Distributed Lag Model (DLM)

• A forecasting model that explicitly incorporates the relationship of lagged predictor variables.
• This approach separates the complexity of a dynamic regression from the need of considering the underlying complex structure.

Multivariate Forecasting with VARIMA

• VARIMA models (Vector Autoregressive Integrated Moving Average) can be utilized for multiple time series involving interdependent variables, particularly in forecasting and time series analysis.
• The variables within the VARIMA model are assumed to be intercorrelated.

Granger Causality Concept

• Granger causality is a method for measuring the predictive relationship between time series in a system.
• A cause precedes an effect in time.
• It is presented within the context of time series analysis.

Granger Causality: Problem

• The limitations of the Granger causality approach in accounting for real-world scenarios with potential confounding factors.
• Instances wherein the causality may appear spurious (e.g. rooster crows -> sunrise) rather than causal.

Further Reading - Resources

• A list of web links referencing academic and practical resources for the studied topics.

Literature Cited

• List of identified reference texts for scholarly work and academic foundations.

Explore the key forecasting methods including dynamic regression and multivariate ARIMA models, as taught in the Norwegian University of Life Sciences course DAT320. This quiz covers the application of techniques using the airquality dataset, focusing on time series analysis. Gain insights into ARIMAX models and their importance in forecasting.