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Macroeconomic Forecasting Evaluation of MIDAS Models

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Theory and Applications of Time Series Analysis (ITISE 2022)

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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Abstract

We compare the nowcasting and forecasting performance of different variants of MIDAS models (ADL-MIDAS, TF-MIDAS and U-MIDAS) when predicting the GDP growth of the four largest Euro Area economies between 2011Q4 and 2020Q3. We consider various high-frequency indicators, horizons and sub-periods, each of the latter with a distinct level of uncertainty. A meta-regression, with an average error metric as exogenous variable, is estimated to account for potential differences in performance by country, indicator, sample period or method. The results obtained with the whole sample do not reveal any difference in the predictive accuracy of the models under comparison. The findings are robust to the forecasting error metric used, RMSFE or MAFE.

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Notes

  1. 1.

    The Exponential Almon weighting function was proposed in [24], and it has the following expression, with Q shape parameters:

    $$\begin{aligned} b(j;\boldsymbol{\theta })=\dfrac{\exp (\theta _{1}j+...+\theta _{Q}j^{Q})}{\sum _{j=0}^{K_{\max }}\exp (\theta _{1}j+...+\theta _{Q}j^{Q})},\text { where } \boldsymbol{\theta } = \left\{ \theta _1,\theta _2,\dots ,\theta _Q \right\} . \end{aligned}$$
    (2)

    Beta weighting function, proposed for the first time in [23], includes only two shape parameters:

    $$\begin{aligned} b(j;\boldsymbol{\theta })=\dfrac{\beta (\dfrac{j}{K_{\max }};\theta _{1},\theta _{2})}{\sum _{j=0}^{K_{\max }}\beta (\dfrac{j}{K_{\max }};\theta _{1},\theta _{2})},\text { where } \boldsymbol{\theta } = \left\{ \theta _1,\theta _2\right\} , \end{aligned}$$
    (3)

    and \(\beta (\cdot )\) is the Beta probability density function.

  2. 2.

    In order to keep focused on the models’ performance evaluation and comparison, we do not present in this chapter the ML function and its corresponding Kalman filter equations, as these are standard in the state space models literature. However, for readers unfamiliar with this type of formulations, all the equations needed to compute the ML can be found in [7], Sect. 5.3.2, where expression (5.50) specifically shows the log-likelihood function used.

  3. 3.

    Notice that the polynomial \(\hat{\theta }(Z)\) does not include the unit term as \(\hat{\epsilon }_{kT_q+es}\) is not known at period \({T_q k + es}\).

  4. 4.

    GDP data were downloaded from the webpage: https://ec.europa.eu/eurostat/web/national-accounts/data/database.

  5. 5.

    Volume Index of Industrial Production indicators were downloaded from the webpage: https://ec.europa.eu/eurostat/databrowser/view/sts_inpr_m/default/table?lang=en

    Consumer Confidence Indicators were downloaded from the webpage: https://ec.europa.eu/info/business-economy-euro/indicators-statistics/economic-databases/business-and-consumer-surveys/download-business-and-consumer-survey-data/time-series_en.

  6. 6.

    In some specific cases, probably due to the presence of outliers, data was adjusted in order to not alter subsequent results and conclusions. In practice, the detection and treatment of these extreme nowcasts/forecasts would be easily addressed by an analyst. In summary, less than 0.9\(\%\) of predictions were adjusted, most of them corresponding to Italy and Spain. Regarding the methods applied, the adjustments distribute uniformly, except for U-M\(_{3}\) and ADL-M\(_{3}\) that account for half of the adjusted values corresponding to each one of the rest of the methods. The exact same estimations have been calculated without these corrections and conclusions do not vary significantly.

  7. 7.

    Matlab code to estimate TF-MIDAS model is available from the authors.

  8. 8.

    The analogous figure for MAFE can be found in [3]. The main conclusions do not differ significantly from those for RMSFE.

  9. 9.

    Analogous figures for RMSFE by countries, indicators and horizons can be found in [3].

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Author information

Authors and Affiliations

  1. Banco de España, Madrid, Spain

    Nicolas Bonino-Gayoso

  2. DANAE and ICAE, Universidad Complutense de Madrid, Madrid, Spain

    Alfredo Garcia-Hiernaux

Authors
  1. Nicolas Bonino-Gayoso
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  2. Alfredo Garcia-Hiernaux
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Corresponding author

Correspondence to Nicolas Bonino-Gayoso .

Editor information

Editors and Affiliations

  1. Faculty of Sciences, University of Granada, Granada, Spain

    Olga Valenzuela

  2. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Fernando Rojas

  3. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Luis Javier Herrera

  4. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Héctor Pomares

  5. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Ignacio Rojas

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Bonino-Gayoso, N., Garcia-Hiernaux, A. (2023). Macroeconomic Forecasting Evaluation of MIDAS Models. In: Valenzuela, O., Rojas, F., Herrera, L.J., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis. ITISE 2022. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-40209-8_10

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