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Faculdade de Ciências e Tecnologia

Forecasting Techniques



Academic unit

Faculdade de Ciências e Tecnologia


Departamento de Engenharia Mecânica e Industrial



Teacher in charge

Ana Paula Ferreira Barroso

Weekly hours


Total hours


Teaching language



The emphasis of the course is on the application of forecasting techniques for decision making by management. Provides an introduction to the theory, the methods, and the concerns of forecasting. It makes extensive use of examples, case study analysis and problems solving. The learning goals associated with this course are to:

  • Provide an understanding of common statistical methods used in business and economic forecasting;
  • Provide students with an overview of a broad range of techniques and an understanding of the strengths and weaknesses of each approach;
  • Develop computer skills for forecasting from business and economics time series data;
  • Provide insights into the problems of implementing and operating large scale forecasting systems for use in production and services management.

Subject matter

1           Planning and Forecasting

1.1         Financial and Strategic Importance of Forecasting

1.2         Forecasting Methods 

1.3         Common Time Series Patterns: Trend, Seasonal, Cyclical, …

1.4         Quantitative and Qualitative Forecasting Methods

1.5         Time Series Forecasting Methods and Causal Forecasting Methods

2           Statistical Fundamentals for Forecasting

2.1         Adjusting Outliers in Time Series with and without Seasonal Pattern 

2.2         Descriptive Statistics

2.3         Measuring Forecast Error: Mean Squared Errors, Mean Absolute Deviation

2.4         Fitting versus Forecasting: Absolute and Relative Measures of Error

2.5         Relative Measures of Linear Association: Correlation Coefficient and Autocorrelation

2.6         Autocorrelation and ACF (k)

2.7          ACFs of several Time Series: Random Series, Random-Walk Series, Trending Series, Seasonal Series, …

3           Univariate Methods to Model Time Series without Trend or Seasonality

3.1         Simple Smoothing Methods: Simple Moving Averages, Weighted Moving Averages, Exponential Smoothing 

3.2         Exponential Smoothing Applied to Seasonal Data

3.3         Estimating the Smoothing Constant 

3.4         Estimating the Smoothing Constant based on RSE

3.5         Adaptive Response-Rate Exponential Smoothing

4           Univariate Methods to Model Time Series with Trend or Seasonality

4.1          Classical Decomposition Method

4.1.1        Multiplicative versus Additive Models

4.1.2        Multiplicative Decomposition Method: Seasonal variation, Interpreting Seasonal Indexes, Deseasonalizing values and using Simple Linear Regression to Forecast Trend

4.1.3        Additive Decomposition Method: Seasonal variation, Interpreting Seasonal Indexes, Deseasonalizing values and using Simple Linear Regression to Forecast Trend

4.1.4        Decomposition using Regression Models: Additive Seasonal Regression Models and Multiplicative Seasonal Regression Models

4.1.5        Disadvantages

4.1.6         Advantages 

4.1.7        Applications

4.2          Trend-Seasonal Smoothing 

4.2.1        Estimating Trends with Differences: Advantages and Disadvantages

4.2.2        Nonlinear Trends and Second Differences

4.2.3        Seasonal Differences to Model Seasonality and Trend

4.2.4        Double Moving Averages: Advantages and Disadvantages

4.2.5        Brown’s Double Exponential Smoothing

4.2.6        Holt’s Model

4.2.7        Winters’ Model: Initialization of Starting Values, Additive and Multiplicative Factors, Data Requirements, Advantages and Disadvantages

5           Univariate ARIMA Models

5.1         ARIMA Notation

5.2         ARIMA Processes

5.3         ARIMA Model Identification

5.4         Integrated Stochastic Process (0, 1, 0)

5.5         Autoregressive Processes

5.6         Moving Average Processes

5.7         ARIMA (p, d, q) Models

6 ARIMA Applications


  1. Hanke, J. E. and  Wichern, D. W. (2009). Business Forecasting. Pearson International Edition.
  2. Wilson, J.H., Keating, B. e Galt, J. (2009). Business Forecasting with ForecastX. McGraw Hill.
  3. Hoshmand, A. R. (2010). Business Forecasting. A practical approach. Routledge, Taylor & Francis Group.
  4. DeLurgio, S. A. (1998). Forecasting Principles and Applications. Irwin McGraw-Hill.
  5. Box, G.E.P., Jenkins G.M. and  Reinsel, G. C. (1994). Time Series Analysis, Forecasting and Control. 3th ed., Englewood Cliffs, Prentice-Hall.
  6. Tavares, L., Oliveira, R., Themido, I. and Correia, F. (1996). Investigação Operacional, Alfragide, McGraw-Hill de Portugal, Lda.

Evaluation method

Regular attendance is expected and considered mandatory.

Course grades are affected by several components. The contribution that each component makes to the final grade is: Participation in class activities and discussions (10%), Projects (50%), Assignments (10%) and 3 Mid-term mini tests(30%).