IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2303.01863.html
   My bibliography  Save this paper

Constructing High Frequency Economic Indicators by Imputation

Author

Listed:
  • Serena Ng
  • Susannah Scanlan

Abstract

Monthly and weekly economic indicators are often taken to be the largest common factor estimated from high and low frequency data, either separately or jointly. To incorporate mixed frequency information without directly modeling them, we target a low frequency diffusion index that is already available, and treat high frequency values as missing. We impute these values using multiple factors estimated from the high frequency data. In the empirical examples considered, static matrix completion that does not account for serial correlation in the idiosyncratic errors yields imprecise estimates of the missing values irrespective of how the factors are estimated. Single equation and systems-based dynamic procedures that account for serial correlation yield imputed values that are closer to the observed low frequency ones. This is the case in the counterfactual exercise that imputes the monthly values of consumer sentiment series before 1978 when the data was released only on a quarterly basis. This is also the case for a weekly version of the CFNAI index of economic activity that is imputed using seasonally unadjusted data. The imputed series reveals episodes of increased variability of weekly economic information that are masked by the monthly data, notably around the 2014-15 collapse in oil prices.

Suggested Citation

  • Serena Ng & Susannah Scanlan, 2023. "Constructing High Frequency Economic Indicators by Imputation," Papers 2303.01863, arXiv.org, revised Oct 2023.
  • Handle: RePEc:arx:papers:2303.01863
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2303.01863
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Breitung, Jörg & Tenhofen, Jörn, 2011. "GLS Estimation of Dynamic Factor Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1150-1166.
    2. Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation of Non-Stationary Large Approximate Dynamic Factor Models," Papers 1910.09841, arXiv.org.
    3. Santos Silva, J. M. C. & Cardoso, F. N., 2001. "The Chow-Lin method using dynamic models," Economic Modelling, Elsevier, vol. 18(2), pages 269-280, April.
    4. Doz, Catherine & Giannone, Domenico & Reichlin, Lucrezia, 2011. "A two-step estimator for large approximate dynamic factor models based on Kalman filtering," Journal of Econometrics, Elsevier, vol. 164(1), pages 188-205, September.
    5. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    6. Catherine Doz & Domenico Giannone & Lucrezia Reichlin, 2012. "A Quasi–Maximum Likelihood Approach for Large, Approximate Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1014-1024, November.
    7. Bańbura, Marta & Giannone, Domenico & Modugno, Michele & Reichlin, Lucrezia, 2013. "Now-Casting and the Real-Time Data Flow," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 195-237, Elsevier.
    8. Christiane Baumeister & Lutz Kilian, 2016. "Forty Years of Oil Price Fluctuations: Why the Price of Oil May Still Surprise Us," Journal of Economic Perspectives, American Economic Association, vol. 30(1), pages 139-160, Winter.
    9. Arlene Naranjo & A. Alexandre Trindade & George Casella, 2013. "Extending the State-Space Model to Accommodate Missing Values in Responses and Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 202-216, March.
    10. Jushan Bai & Serena Ng, 2021. "Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1746-1763, October.
    11. Itkonen, Juha & Juvonen, Petteri, 2017. "Nowcasting the Finnish economy with a large Bayesian vector autoregressive model," BoF Economics Review 6/2017, Bank of Finland.
    12. Joshua C. C. Chan & Aubrey Poon & Dan Zhu, 2021. "Efficient Estimation of State-Space Mixed-Frequency VARs: A Precision-Based Approach," Papers 2112.11315, arXiv.org.
    13. Aruoba, S. BoraÄŸan & Diebold, Francis X. & Scotti, Chiara, 2009. "Real-Time Measurement of Business Conditions," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 417-427.
    14. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    15. Ke-Hai Yuan & Linda Marshall & Peter Bentler, 2002. "A unified approach to exploratory factor analysis with missing data, nonnormal data, and in the presence of outliers," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 95-121, March.
    16. Cimadomo, Jacopo & Giannone, Domenico & Lenza, Michele & Monti, Francesca & Sokol, Andrej, 2022. "Nowcasting with large Bayesian vector autoregressions," Journal of Econometrics, Elsevier, vol. 231(2), pages 500-519.
    17. Palm, Franz C & Nijman, Theo E, 1984. "Missing Observations in the Dynamic Regression Model," Econometrica, Econometric Society, vol. 52(6), pages 1415-1435, November.
    18. repec:wrk:wrkemf:38 is not listed on IDEAS
    19. Jushan Bai & Kunpeng Li, 2016. "Maximum Likelihood Estimation and Inference for Approximate Factor Models of High Dimension," The Review of Economics and Statistics, MIT Press, vol. 98(2), pages 298-309, May.
    20. Litterman, Robert B, 1983. "A Random Walk, Markov Model for the Distribution of Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 169-173, April.
    21. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    22. Foroni, Claudia & Marcellino, Massimiliano & Stevanovic, Dalibor, 2022. "Forecasting the Covid-19 recession and recovery: Lessons from the financial crisis," International Journal of Forecasting, Elsevier, vol. 38(2), pages 596-612.
    23. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    24. Chow, Gregory C & Lin, An-loh, 1971. "Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series," The Review of Economics and Statistics, MIT Press, vol. 53(4), pages 372-375, November.
    25. Frank Schorfheide & Dongho Song, 2015. "Real-Time Forecasting With a Mixed-Frequency VAR," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 366-380, July.
    26. Michael Healy & Michael Westmacott, 1956. "Missing Values in Experiments Analysed on Automatic Computers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 5(3), pages 203-206, November.
    27. Marta Bańbura & Michele Modugno, 2014. "Maximum Likelihood Estimation Of Factor Models On Datasets With Arbitrary Pattern Of Missing Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(1), pages 133-160, January.
    28. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    29. Roberto S. Mariano & Yasutomo Murasawa, 2003. "A new coincident index of business cycles based on monthly and quarterly series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 427-443.
    30. Jingheng Cai & Zhibin Liang & Rongqian Sun & Chenyi Liang & Junhao Pan, 2019. "Bayesian analysis of latent Markov models with non-ignorable missing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(13), pages 2299-2313, October.
    31. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
    32. Hauber, Philipp & Schumacher, Christian, 2021. "Precision-based sampling with missing observations: A factor model application," Discussion Papers 11/2021, Deutsche Bundesbank.
    33. repec:hal:journl:peer-00844811 is not listed on IDEAS
    34. Petrella, Ivan & Antolin-Diaz, Juan & Drechsel, Thomas, 2021. "Advances in Nowcasting Economic Activity: Secular Trends, Large Shocks and New Data," CEPR Discussion Papers 15926, C.E.P.R. Discussion Papers.
    35. Jin, Sainan & Miao, Ke & Su, Liangjun, 2021. "On factor models with random missing: EM estimation, inference, and cross validation," Journal of Econometrics, Elsevier, vol. 222(1), pages 745-777.
    36. Jungbacker, B. & Koopman, S.J. & van der Wel, M., 2011. "Maximum likelihood estimation for dynamic factor models with missing data," Journal of Economic Dynamics and Control, Elsevier, vol. 35(8), pages 1358-1368, August.
    37. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    38. Clements, Michael P & Galvão, Ana Beatriz, 2008. "Macroeconomic Forecasting With Mixed-Frequency Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 546-554.
    39. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    40. Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
    41. Foroni, Claudia & Marcellino, Massimiliano, 2014. "A comparison of mixed frequency approaches for nowcasting Euro area macroeconomic aggregates," International Journal of Forecasting, Elsevier, vol. 30(3), pages 554-568.
    42. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    43. Serena Ng, 2017. "Opportunities and Challenges: Lessons from Analyzing Terabytes of Scanner Data," NBER Working Papers 23673, National Bureau of Economic Research, Inc.
    44. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    2. Junting Duan & Markus Pelger & Ruoxuan Xiong, 2023. "Target PCA: Transfer Learning Large Dimensional Panel Data," Papers 2308.15627, arXiv.org.
    3. Chan, Joshua C.C. & Poon, Aubrey & Zhu, Dan, 2023. "High-dimensional conditionally Gaussian state space models with missing data," Journal of Econometrics, Elsevier, vol. 236(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    2. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    3. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    4. Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Papers 1910.03821, arXiv.org, revised Sep 2024.
    5. Bańbura, Marta & Giannone, Domenico & Lenza, Michele, 2015. "Conditional forecasts and scenario analysis with vector autoregressions for large cross-sections," International Journal of Forecasting, Elsevier, vol. 31(3), pages 739-756.
    6. Karim Barhoumi & Olivier Darné & Laurent Ferrara, 2014. "Dynamic factor models: A review of the literature," OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2013(2), pages 73-107.
    7. Hindrayanto, Irma & Koopman, Siem Jan & de Winter, Jasper, 2016. "Forecasting and nowcasting economic growth in the euro area using factor models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1284-1305.
    8. Kaufmann, Daniel & Scheufele, Rolf, 2017. "Business tendency surveys and macroeconomic fluctuations," International Journal of Forecasting, Elsevier, vol. 33(4), pages 878-893.
    9. Alain Galli, 2018. "Which Indicators Matter? Analyzing the Swiss Business Cycle Using a Large-Scale Mixed-Frequency Dynamic Factor Model," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 14(2), pages 179-218, November.
    10. Matteo Barigozzi, 2023. "Quasi Maximum Likelihood Estimation of High-Dimensional Factor Models: A Critical Review," Papers 2303.11777, arXiv.org, revised May 2024.
    11. Proietti, Tommaso, 2008. "Estimation of Common Factors under Cross-Sectional and Temporal Aggregation Constraints: Nowcasting Monthly GDP and its Main Components," MPRA Paper 6860, University Library of Munich, Germany.
    12. Simona Delle Chiaie & Laurent Ferrara & Domenico Giannone, 2022. "Common factors of commodity prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 461-476, April.
    13. Tóth, Peter, 2014. "Malý dynamický faktorový model na krátkodobé prognózovanie slovenského HDP [A Small Dynamic Factor Model for the Short-Term Forecasting of Slovak GDP]," MPRA Paper 63713, University Library of Munich, Germany.
    14. Juho Koistinen & Bernd Funovits, 2022. "Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization," Papers 2202.00310, arXiv.org, revised Feb 2022.
    15. Jin, Sainan & Miao, Ke & Su, Liangjun, 2021. "On factor models with random missing: EM estimation, inference, and cross validation," Journal of Econometrics, Elsevier, vol. 222(1), pages 745-777.
    16. Antolín-Díaz, Juan & Drechsel, Thomas & Petrella, Ivan, 2024. "Advances in nowcasting economic activity: The role of heterogeneous dynamics and fat tails," Journal of Econometrics, Elsevier, vol. 238(2).
    17. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    18. Rusnák, Marek, 2016. "Nowcasting Czech GDP in real time," Economic Modelling, Elsevier, vol. 54(C), pages 26-39.
    19. Lippi, Marco & Deistler, Manfred & Anderson, Brian, 2023. "High-Dimensional Dynamic Factor Models: A Selective Survey and Lines of Future Research," Econometrics and Statistics, Elsevier, vol. 26(C), pages 3-16.
    20. Monica Defend & Aleksey Min & Lorenzo Portelli & Franz Ramsauer & Francesco Sandrini & Rudi Zagst, 2021. "Quantifying Drivers of Forecasted Returns Using Approximate Dynamic Factor Models for Mixed-Frequency Panel Data," Forecasting, MDPI, vol. 3(1), pages 1-35, February.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2303.01863. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.