## Nowcasting Growth Using the Bayesian Structural Time Series Model: Application to Tanzania — Sections II–VI

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---

### Context and Motivation
- Need for short-term monitoring amid recent global shocks and increased external volatility.
- Official quarterly GDP figures:
  - absent in over 60 countries.
  - lag exceeds one quarter for about 20 countries in sub-Saharan Africa.
- Growing availability of high-frequency economic indicators (including novel data from new technologies and expanded official statistics) enables higher-frequency assessment of economic activity than official releases allow.

### BSTS Model: Role, Advantages, and Cautions
- Key features and mechanics
  - State-space framework with observational and state equations (example random walk in noise):
    - yt = μt + εt, εt ~ N(0, σε2)
    - μt = μt−1 + ut, ut ~ N(0, σu2)
  - Uses the Kalman filter for estimation: prior beliefs → fitted values → update parameter distribution → iterate simulation → posterior distribution → forecasts.
  - Variable selection via Spike and Slab prior:
    - Prior assumes majority of regression coefficients exactly zero.
    - Prior inclusion probability: e.g., expected model size = 1 yields prior inclusion probability 1/n for each of n indicators.
  - Provides full predictive distributions (not just point estimates).
- Advantages in developing-economy contexts
  - Accommodates sparse and irregular growth data.
  - Transparent attribution of forecast drivers to observable indicators.
  - Gradual reweighting toward indicators that become more informative as more data accumulate.
  - Adaptable to longer forecast horizons and to changing economic relationships via dynamic regressors.
- Cautions and trade-offs
  - Flexibility requires careful specification to ensure reliable performance.
  - Computational demands rise with predictors.
  - Sparsity prior may exclude informative indicators in short samples.
  - Forecasts sensitive to prior assumptions and require calibration.
  - Bayesian model averaging and averaging of selected models recommended to improve robustness.

### Model Components, Trend and Seasonality, and Priors
- Local linear trend with quarterly seasonality (tested):
  - yt = μt + τt + β′xt + εt, εt ~ N(0, σε2)
  - μt = μt−1 + δt−1 + ut, ut ~ N(0, σu2)
  - δt = δt−1 + νt, νt ~ N(0, σν2)
  - τt = −∑τt−s (s=1 to S−1) + ωt (S = 4 for quarterly)
- Robust (student) local linear trend:
  - μt = μt−1 + δt−1 + εt, εt ~ Tνμ(0, σμ2)
  - δt = δt−1 + ηt, ηt ~ Tνδ(0, σδ2)
  - Tail thickness parameters νμ and νδ provide resilience to outliers.
- Expected model size (k) and priors
  - 0<k<1 is the prior probability (share) of regressors with nonzero coefficients.
  - Informative priors can force inclusion of key indicators.
  - Example: with local linear trend + quarterly seasonality + 130 NDVI series, lower k places more weight on trend and seasonality.
- Model selection and evaluation
  - Grid over priors for σu and σν based on response variable and user input; grid size adjustable.
  - One-period-ahead predictive performance assessed with out-of-sample RMSE using expanding window of N quarters.
  - For each t = T−n+1 with n = N,...,1, generate one-period-ahead prediction using data up to t; use mean prediction error to compute RMSE.

### Application to Nowcasting Tanzania’s Growth — Data and Main Results
- Data and context
  - Variable of interest: log level of real GDP (nowcasts converted to year-over-year growth for reporting).
  - Test period for evaluation: expanding test window of 16 quarters spanning from 2021Q1 to 2024Q4; full sample from 2008Q1 onward.
  - Sector shares (selected):
    - Agriculture: about 27 percent of GDP in 2023; about 65 percent of total employment in 2021.
    - Industry and construction: approximately 30 percent of GDP in 2023.
    - Services: accounted for 39 percent of GDP in 2022.
  - High-frequency indicators included (examples): monthly rainfall, Agricultural Stress Index, cash crop exports, industrial raw materials imports, service receipts, credit to private sector, monetary/fiscal/exports/imports indicators.
- Forecasting performance and diagnostics
  - Benchmarks: naïve model, AR(1), and 5-year quarterly averages.
  - RMSE results (one-period-ahead, averaged BSTS estimates over 16-quarter test window):
    - RMSE of averaged BSTS estimates = 0.46.
    - RMSE of benchmark AR(1) model = 0.8.
  - Diebold-Mariano test p-values:
    - BSTS vs AR(1): 0.009.
    - BSTS vs naïve model: 0.002.
  - Estimation precision improves toward end of sample due to expanding window and data quality improvements.
- Sensitivity analysis and prior calibration
  - Key priors varied: trend variance (level, slope), seasonal variance, expected model size.
  - Practical calibration guidance:
    - Calibrating standard deviation parameters to roughly 2 to 5 percent of the standard deviation of the observed series yields stable results for Tanzania.
    - Expected model size of roughly 50-60 percent of the indicator set worked well for near-term forecasting in this application.
    - Forecast performance most responsive to variance priors in the trend slope; moderate values deliver lowest out-of-sample RMSE.
    - Increasing prior model size yields modest RMSE improvement with diminishing returns and added noise beyond a threshold.
- Model outputs used for interpretation
  - Component contributions:
    - Trend is the major contributor to growth forecasts (model estimated in log GDP levels).
    - Seasonality captures intra-year patterns (agriculture, fiscal execution, tourism); pattern shifts observed since 2020 (more frequent peaks in Q3).
    - Regressors refine latent trend and explain short-run deviations; regression contribution fluctuated and was marginal post-Covid recovery.
  - Inclusion probabilities (top predictors, averaged across top specifications):
    - Emerging markets PMI (composite and manufacturing) and Developing Markets PMI: each exceeding 40 percent inclusion probability.
    - Monetary aggregates (M3, Monetary Base), oil prices (Brent), private credit, Agricultural Stress Index, commodity prices show moderate to prominent inclusion probabilities.
  - Time variation in inclusion probabilities:
    - General decline in importance of most regressors over the sample, except external indicators which remain robust.
    - Temporary decline in external demand indicator inclusion during Covid-pandemic followed by re-establishment.

### Extensions: Multi-period Forecasts and Dynamic Regressors
- Multi-period forecasts (three-period-ahead findings)
  - Method: expanding window; generate p-period-ahead forecasts and compute out-of-sample RMSE where actual data available p periods ahead; average nowcasts from specifications with lowest RMSE.
  - Test window: 16 quarters.
  - Findings:
    - Performance increasingly sensitive to trend specification at longer horizons.
    - Preferred multi-period specifications characterized by higher trend variance priors and smaller effective model sizes (marginal value of regressors diminishes with horizon).
  - Selected example rows reported in Table 2 (PRIOR GUESS, POSTERIOR DISTRIBUTION, IN-SAMPLE RESULTS) include:
    - 0.77 4 0.075 0.014 0.04 1.4 0.048 0.003 0.027 0.017 0.023
    - 0.79 4 0.067 0.011 0.03 0.5 0.042 0.003 0.021 0.015 0.020
    - 0.79 6 0.006 0.003 0.03 1.1 0.006 0.007 0.018 0.016 0.021
    - 0.80 2 0.019 0.003 0.03 0.2 0.015 0.005 0.019 0.015 0.020
    - 0.80 2 0.075 0.008 0.05 0.6 0.048 0.005 0.032 0.015 0.019
- Dynamic regressors and climate-related dynamics
  - Dynamic regressors specification:
    - Time-varying coefficient: βi,t+1 = βi,t + εt, with εt ∼ N(0, σi2 variance_xi).
    - Dynamic regressors are always incorporated (not selected via spike-and-slab).
  - Motivation: relationships (e.g., rainfall–growth) can change due to sectoral transformation or changing climate patterns (floods/droughts).
  - Tanzania rainfall evidence:
    - Trends show changes in annual mean precipitation and increases in number of floods.
  - Empirical results with rainfall as dynamic regressor:
    - Re-estimated over test window 2021Q1–2024Q4.
    - In-sample performance gain concentrated in early sample period.
    - Estimated dynamic rainfall coefficient behavior:
      - Negative in earlier periods (rainfall as disruptive shock during flooding episodes).
      - Turns positive beginning 2016 (rainfall supporting agricultural output under normal conditions).
      - From 2017 onward the relationship weakens and becomes intermittently negative (structural transformation and increasing rainfall volatility).
  - Diagnostics reported: one-period-ahead prediction comparisons (baseline vs dynamic regressors), cumulative absolute one-period-ahead forecast errors, and dynamic coefficient time series.

### Conclusion — Practical Takeaways, Recommendations, and Limitations
- Main conclusions
  - BSTS is a useful tool for nowcasting in data-constrained environments: flexible treatment of trends and seasonality, inclusion of high-frequency indicators, and capacity for dynamic regressors.
  - Application to Tanzania produced reliable forecasts that outperformed simple benchmarks (RMSE 0.46 vs AR(1) 0.8; DM p-values 0.009 and 0.002).
  - Model yields diagnostic outputs (predictive distributions, component decompositions, inclusion probabilities) valuable for operational monitoring and policy interpretation.
- Practical recommendations for operational use
  - Regular re-estimation on a limited set of calibrated specifications as new high-frequency releases arrive.
  - Use the posterior mean as a central nowcast and monitor widening forecast bands and tail risks.
  - Track stability in posterior inclusion probabilities and shifts in indicator importance as early signals of evolving macro relationships.
  - Perform robustness checks and sensitivity analysis focused on trend flexibility and variable selection priors.
  - Begin with broad prior grids and refine based on model performance and data-specific sensitivity; calibrate trend standard deviations roughly to 2 to 5 percent of the series’ standard deviation for Tanzania-like settings, but adjust for higher intrinsic volatility.
- Limitations and avenues for future work
  - Computational scaling limits as predictor set grows; spike-and-slab sparsity may under-select in short samples.
  - Forecast sensitivity to prior assumptions warrants careful calibration and economic judgment.
  - Future extensions: time-varying volatility, alternative shrinkage priors, while preserving operational simplicity for surveillance and policymaking.

*Source: IMF working paper (content unit: wpiea2026049-source-pdf — Sections II–VI, Annex).*

### References .............................................................................................................

### wpiea2026049-source-pdf - References .............................................................................................................

### Figures and Tables Inventory (as listed)
- Figures
  - Figure 1. Contribution to predictions by components, different priors of expected model size k
  - Figure 2. Tanzania: Real GDP growth (year-over-year, percentage)
  - Figure 3. Tanzania: Real GDP growth Decomposition
  - Figure 4. One-period-ahead Mean Predictions, Real GDP Growth of Tanzania (year-over-year, percentage)
  - Figure 5. Robustness checks
  - Figure 6. Contribution by Components
  - Figure 7. Inclusion Probability of Regressors
  - Figure 8. Inclusion Probability over the Sample Period, Selected Indicators
  - Figure 9. Distribution of Mean Predictions, Three-period-ahead Forecasts
  - Figure 10. Tanzania: Rainfall Patterns
  - Figure 11. One-period Ahead Predictions, Dynamic Regressors
  - Figure 12. Cumulative Absolute One-period Ahead Forecast Errors, Percentage Points
  - Figure 13. Dynamic Coefficient over the Sample Period
- Tables
  - Table 1. Prior and Posterior Distribution of Model Parameters and In-sample Prediction Errors
  - Table 2. Prior and Posterior Distribution of Model Parameters and In-sample Prediction Errors, Three-period-ahead Forecasts
  - Table A 1. High-frequency Economic Indicators

### Context and Motivation
- There is a growing need for monitoring short-term economic fluctuations amid recent global shocks and increased external volatility affecting economies.
- Official quarterly GDP figures:
  - are absent in over 60 countries.
  - are often subject to delays; in sub-Saharan Africa, the lag exceeds one quarter for about 20 countries.
- Improved availability of high-frequency economic indicators (including novel data from new technologies and expanded official statistics) enables higher-frequency assessment of economic activity than official releases allow.

### Nowcasting Approaches and Literature
- Univariate models:
  - Bridge and Mixed Data Sampling (MIDAS) models are noted for simplicity and effectiveness with limited indicators (Clements and Galvao (2007); Armesto et al. (2010)).
- Multivariate approaches:
  - Vector Auto-regressive Models (VAR) and Dynamic Factor Models (DFM) account for interdependencies among variables and suit larger datasets (D'Agostino et al. (2010); Mariano and Murasawa (2010); Giannone et al. (2008); Banbura et al. (2011)).
  - DFMs handle high-dimensional data and non-fundamental shocks.
- Machine learning advances:
  - Enable modeling of nonlinear relationships and processing of big data, improving forecast accuracy and reliability (Barhoumi et al. (2022); Woloszko (2020)).

### Bayesian Structural Time Series (BSTS) Model: Role and Advantages
- Introduced by Scott and Varian (2014).
- Key features:
  - Modular state-space framework allowing flexible inclusion of trend, seasonality, and regression components.
  - Spike-and-slab priors for automatic variable selection without relying on latent factor estimation.
  - Provides full posterior distributions (not just point estimates) for richer uncertainty analysis.
- Advantages in developing-economy contexts:
  - Accommodates sparse and irregular growth data.
  - Offers transparent attribution of forecast drivers to observable indicators.
  - Gradually shifts weight toward indicators that become more informative as more data accumulate.
  - Can be adapted to longer forecast horizons and to changing economic relationships via dynamic regressors that allow predictor–outcome relationships to evolve over time.
- Cautions:
  - Model flexibility requires careful specification to ensure reliable performance.
  - Bayesian model averaging during estimation and averaging of selected models improve robustness.

### Application to Tanzania (purpose and framing)
- The paper applies the BSTS framework to estimate quarterly GDP growth in Tanzania.
- Builds on:
  - Previous applications of BSTS for economic forecasting (Pérez (2018); Kohns and Bhattacharjee (2023)).
  - Existing nowcasting initiatives for Tanzania and Sub-Saharan Africa (Barhoumi et al. (2022); Akbal et al. (2023)).
  - Central bank forecasting frameworks for Tanzania.
- Paper structure preview:
  - Section 2: overview of model components.
  - Section 3: methodology and application to Tanzania.
  - Section 4: model outputs.

### Referenced Notes (as cited in the source text)
- Note 2: See Bear, Guerreiro, and Silungwe (2022).
- Note 3: See Akbal, Choi, Narita, and Yao (2023).

*Source: wpiea2026049-source-pdf - References .............................................................................................................*

### Section 5 illustrates the extensions with multi-period forecasts and dynamic regressors; and Section 6

### wpiea2026049-source-pdf - Section 5 illustrates the extensions with multi-period forecasts and dynamic regressors; and Section 6

### II. Model Components and Features
- Model structure
  - BSTS is a state-space model with an observational equation and state equations.
  - Example state-space (random walk observed in noise):
    - 푦푡 = 휇푡 + 휀푡, 휀푡 ~ 푁(0, 휎휀2)
    - 휇푡 = 휇푡−1 + 푢푡, 푢푡 ~ 푁(0, 휎푢2)
- Key features
  - Uses the Kalman filter for estimation: prior beliefs → fitted values → update parameter distribution → iterate simulation → posterior distribution → forecasts.
  - Variable selection via Spike and Slab prior:
    - Prior assumes majority of regression coefficients exactly zero.
    - Prior inclusion probability: e.g., expected model size = 1 yields prior inclusion probability 1/n for each of n indicators.
    - Combined with Bayesian model averaging to mitigate spurious relationships.
  - Produces full predictive distributions (not single point estimates): users may focus on mean, median, or ranges.
- Comparative strengths and trade-offs
  - Strengths: interpretability, indicator-level attribution, transparency; useful when indicator set includes noisy or weakly informative series.
  - Differences vs DFMs: BSTS relies on spike-and-slab sparsity and preserves attribution to individual indicators; DFMs scale better to very large, dense data and can handle substantial data irregularities.
  - Trade-offs: computational demands rise with predictors; sparsity prior may exclude informative indicators in short samples; forecasts sensitive to prior assumptions and require calibration.

### III. Model Inputs and Methodology
- Trend and seasonality assumptions
  - Tested local linear trend with quarterly seasonality.
  - Local linear trend equations:
    - 푦푡 = 휇푡 + 휏푡 + 훽′푥푡 + 휀푡, 휀푡 ~ 푁(0, 휎휀2)
    - 휇푡 = 휇푡−1 + 훿푡−1 + 푢푡, 푢푡 ~ 푁(0, 휎푢2)
    - 훿푡 = 훿푡−1 + 휈푡, 휈푡 ~ 푁(0, 휎휈2)
    - 휏푡 = −∑휏푡−푠 (s=1 to S−1) + 휔푡 (S = 4 for quarterly)
  - Robust (student) local linear trend:
    - 휇푡 = 휇푡−1 + 훿푡−1 + 휖푡, 휖푡 ~ 푇νμ(0, 휎μ2)
    - 훿푡 = 훿푡−1 + 휂푡, 휂푡 ~ 푇νδ(0, 휎δ2)
    - Tail thickness parameters νμ and νδ allow resilience to outliers.
- Expected model size (k) and priors
  - 0<k<1 is the prior probability (share) of regressors with nonzero coefficients.
  - Informative priors on inclusion probabilities can force inclusion of key indicators.
  - Example: model with local linear trend + quarterly seasonality + 130 NDVI series as regressors; lower k places more weight on trend and seasonality.
- Model selection and evaluation
  - Grid over priors for standard deviations 휎푢 and 휎휈 based on response variable and user input; grid size adjustable.
  - One-period-ahead predictive performance assessed with out-of-sample RMSE using expanding window of N quarters.
  - For each t = T−n+1 with n = N,...,1, generate one-period-ahead prediction using data up to t; use mean prediction error to compute RMSE.

### IV. Application to nowcasting Tanzania’s growth — data and main results
- Data and context
  - Variable of interest: log level of real GDP (nowcasts converted to year-over-year growth for reporting).
  - Test period for evaluation: expanding test window of 16 quarters spanning from 2021Q1 to 2024Q4; full sample from 2008Q1 onward.
  - Sector shares (selected):
    - Agriculture: about 27 percent of GDP in 2023; about 65 percent of total employment in 2021.
    - Industry and construction: approximately 30 percent of GDP in 2023.
    - Services: accounted for 39 percent of GDP in 2022.
  - High-frequency indicators included (examples): monthly rainfall, Agricultural Stress Index, cash crop exports, industrial raw materials imports, service receipts, credit to private sector, monetary/fiscal/exports/imports indicators. (Table A 1 lists full set.)
  - Real-time evaluation used pseudo-real-time alignment and standard transformations for missing edge data.
- Forecasting performance and diagnostics
  - Benchmarks: naïve model, AR(1), and 5-year quarterly averages.
  - RMSE results:
    - RMSE of averaged BSTS estimates over the 16-quarter test window = 0.46.
    - RMSE of benchmark AR(1) model = 0.8.
  - Diebold-Mariano test p-values:
    - BSTS vs AR(1): 0.009.
    - BSTS vs naïve model: 0.002.
  - Estimation precision improves toward end of sample due to expanding window and data quality improvements.
- Sensitivity analysis and prior calibration
  - Key priors varied:
    - Trend variance (level, slope)
    - Seasonal variance
    - Expected model size
  - Practical calibration guidance:
    - Calibrating standard deviation parameters to roughly 2 to 5 percent of the standard deviation of the observed series yields stable results for Tanzania.
    - Expected model size of roughly 50-60 percent of the indicator set worked well for near-term forecasting in this application.
    - Forecast performance most responsive to variance priors in the trend slope; moderate values deliver lowest out-of-sample RMSE.
    - Increasing prior model size yields modest RMSE improvement with diminishing returns and added noise beyond a threshold.
- Model outputs used for interpretation
  - Component contributions:
    - Trend is the major contributor to growth forecasts (model estimated in log GDP levels).
    - Seasonality captures intra-year patterns (agriculture, fiscal execution, tourism); pattern shifts observed since 2020 (more frequent peaks in Q3).
    - Regressors refine latent trend and explain short-run deviations; regression contribution fluctuated and was marginal post-Covid recovery.
  - Inclusion probabilities (top predictors, averaged across top specifications):
    - Emerging markets PMI (composite and manufacturing) and Developing Markets PMI: each exceeding 40 percent inclusion probability.
    - Monetary aggregates (M3, Monetary Base), oil prices (Brent), private credit, Agricultural Stress Index, commodity prices show moderate to prominent inclusion probabilities.
  - Time variation in inclusion probabilities:
    - General decline in importance of most regressors over the sample, except external indicators which remain robust.
    - Temporary decline in external demand indicator inclusion during Covid-pandemic followed by re-establishment.

### V. Extensions
- Multi-period forecasts
  - Method: same model selection approach using expanding window; generate p-period-ahead forecasts and compute out-of-sample RMSE where actual data available p periods ahead; average nowcasts from specifications with lowest RMSE.
  - Findings for three-period-ahead forecasts:
    - Test window remained 16 quarters.
    - Performance increasingly sensitive to trend specification at longer horizons.
    - Preferred multi-period specifications characterized by higher trend variance priors and smaller effective model sizes (marginal value of regressors diminishes with horizon).
  - Table 2 (selected entries for three-period-ahead forecasts, reporting PRIOR GUESS, POSTERIOR DISTRIBUTION, IN-SAMPLE RESULTS):
    - Example rows (as presented):
      - 0.77 4 0.075 0.014 0.04 1.4 0.048 0.003 0.027 0.017 0.023
      - 0.79 4 0.067 0.011 0.03 0.5 0.042 0.003 0.021 0.015 0.020
      - 0.79 6 0.006 0.003 0.03 1.1 0.006 0.007 0.018 0.016 0.021
      - 0.80 2 0.019 0.003 0.03 0.2 0.015 0.005 0.019 0.015 0.020
      - 0.80 2 0.075 0.008 0.05 0.6 0.048 0.005 0.032 0.015 0.019
- Dynamic regressors and climate-related dynamics
  - Dynamic regressors specification:
    - Time-varying coefficient: 훽i,t+1 = 훽i,t + 휖t, with 휖t ∼ 푁(0, 휎i2 variance_xi).
    - Dynamic regressors are always incorporated (not selected via spike-and-slab).
  - Motivation: relationships (e.g., rainfall–growth) can change due to sectoral transformation or changing climate patterns (floods/droughts).
  - Tanzania rainfall evidence:
    - Trends show changes in annual mean precipitation and increases in number of floods (figures presented).
  - Empirical results with rainfall as dynamic regressor:
    - Re-estimated over test window 2021Q1–2024Q4.
    - In-sample performance gain concentrated in early sample period.
    - Estimated dynamic rainfall coefficient:
      - Negative in earlier periods (rainfall as disruptive shock during flooding episodes).
      - Turns positive beginning 2016 (rainfall supporting agricultural output under normal conditions).
      - From 2017 onward the relationship weakens and becomes intermittently negative (structural transformation and increasing rainfall volatility).
  - Figures and diagnostics:
    - One-period-ahead prediction comparisons for baseline vs dynamic regressors (results summarized across top specifications).
    - Cumulative absolute one-period-ahead forecast errors and dynamic coefficient time series illustrated.

### VI. Conclusion — practical takeaways and recommendations
- Main conclusions
  - BSTS framework is a useful tool for nowcasting in data-constrained environments: flexible treatment of trends and seasonality, inclusion of high-frequency indicators, and capacity for dynamic regressors.
  - Application to Tanzania produced reliable forecasts that outperformed simple benchmarks (RMSE 0.46 vs AR(1) 0.8; DM p-values 0.009 and 0.002).
  - Model yields additional diagnostic outputs (predictive distributions, component decompositions, inclusion probabilities) that are valuable for operational monitoring and policy interpretation.
- Practical recommendations for operational use
  - Regular re-estimation on a limited set of calibrated specifications as new high-frequency releases arrive.
  - Use the posterior mean as a central nowcast and monitor widening forecast bands and tail risks.
  - Track stability in posterior inclusion probabilities and shifts in indicator importance as early signals of evolving macro relationships.
  - Perform robustness checks and sensitivity analysis focused on trend flexibility and variable selection priors.
  - Begin with broad prior grids and refine based on model performance and data-specific sensitivity; calibrate trend standard deviations roughly to 2 to 5 percent of the series’ standard deviation for Tanzania-like settings, but adjust for higher intrinsic volatility.
- Limitations and avenues for future work
  - Computational scaling limits as predictor set grows; spike-and-slab sparsity may under-select in short samples.
  - Forecast sensitivity to prior assumptions warrants careful calibration and economic judgment.
  - Future extensions: time-varying volatility, alternative shrinkage priors, while preserving operational simplicity for surveillance and policymaking.

*Source: IMF working paper (content unit: wpiea2026049-source-pdf — Sections II–VI, Annex).*

### References

### References

### Nowcasting and Mixed-Frequency Methods
- Akbal, O., Choi, S., Narita, F., and Yao, J. 2023. “Panel nowcasting for countries whose quarterly GDPs are unavailable.” IMF Working Paper, 23/158.
- Armesto, M. T., Engemann, K., and Owyang, M., 2010. “Forecasting with mixed frequencies.” Review, 92, issue Nov, p. 521-536.
- Banbura, M., Giannone, D., and Reichlin, L., 2011. Nowcasting. Oxford Handbook on Economic Forecasting.
- Clements, M. P., and Galvão, A. B., 2008. “Macroeconomic Forecasting with Mixed-Frequency Data: Forecasting Output Growth in the United States.” Journal of Business & Economic Statistics, 26(4), 546–554. http://www.jstor.org/stable/27639011
- Giannone, D., Reichlin, L., and Small, D., 2008. "Nowcasting: The real-time informational content of macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 55(4), pages 665-676, May.
- Giannone, D., Agrippino, S. M., & Modugno, M., 2013. Nowcasting China Real GDP. CIRANO.
- Mariano, R. and Murasawa, Y., 2010. A Coincident Index, Common Factors, and Monthly Real GDP*, Oxford Bulletin of Economics and Statistics, 72, issue 1, p. 27-46.
- Pérez, F., 2018. "Nowcasting Peruvian GDP using Leading Indicators and Bayesian Variable Selection," Working Papers 2018-010, Banco Central de Reserva del Perú.

### Bayesian Structural Time Series, Variable Selection, and Machine Learning Approaches
- Scott, S. L. and Varian, H. R. 2014. Predicting the present with Bayesian structural time series. International Journal of Mathematical Modelling and Numerical Optimisation 5, 4–23.
- Scott, S. L. and Varian, H. R. 2015. Bayesian variable selection for nowcasting economic time series. In A. Goldfarb, S. Greenstein, and C. Tucker, eds., Economics of Digitization, 119 –136. NBER Press, London.
- Qiu, J., Jammalamadaka, S. R., and Ning, N. 2018. Multivariate Bayesian Structural Time Series Model. Journal of Machine Learning Research 19 (2018) 1-33.
- Kohns, D., and Bhattacharjee, A., 2023. "Nowcasting growth using Google Trends data: A Bayesian Structural Time Series model," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1384-1412.
- Bok, B., Caratelli, D., Giannone, D., Sbordone, A. M., Tambalotti, A. 2018. “Macroeconomic Nowcasting and Forecasting with Big Data.” Annual Review Economics. 10:615-643.
- D'Agostino, A. and Gambetti, L. and Giannone, D., 2010. “Macroeconomic Forecasting and Structural Change.” ECB Working Paper No. 1167.
- Diebold, F. and Mariano, R., 1995. “Comparing Predictive Accuracy” Journal of Business & Economic Statistics, July 1995, Vol. 13, No. 3.
- Scott, S. L., 2024. bsts: Bayesian Structural Time Series. R package version 0.9.10, <https://CRAN.R-project.org/package=bsts>.
- Qiu, J., Jammalamadaka, S. R., and Ning, N. 2018. Multivariate Bayesian Structural Time Series Model. Journal of Machine Learning Research 19 (2018) 1-33.
- Woloszko, N., 2020. "Tracking activity in real time with Google Trends", OECD Economics Department Working Papers, No. 1634, OECD Publishing, Paris, https://doi.org/10.1787/6b9c7518-en.
- Kohns, D., and Bhattacharjee, A., 2023. "Nowcasting growth using Google Trends data: A Bayesian Structural Time Series model," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1384-1412.

### Data Sources, Remote Sensing, and Climate Portals
- Didan, K., 2021. MODIS/Terra Vegetation Indices 16-Day L3 Global 500m SIN Grid V061. distributed by NASA EOSDIS Land Processes Distributed Active Archive Center, https://doi.org/10.5067/MODIS/MOD13A1.061. Date Accessed 2024-12-01.
- World Bank, Climate Change Knowledge Portal, 2024. URL: https://climateknowledgeportal.worldbank.org/. Date Accessed: 2024-12-01.

### IMF, Regional, and National Reports Cited
- Bear, A., Guerreiro, V., and Silungwe, A., 2022. “2020 Global Stocktaking of National Accounts Statistics: Availability for Policy and Surveillance” IMF Working Paper No. 22/29.
- Barhoumi, K., Choi, S., Iyer, T., Li, J., Ouattara, F., Tiffin, A., and Yao, J., 2022. “Overcoming Data Sparsity: A Machine Learning Approach to Track the Real-Time Impact of COVID-19 in Sub-Saharan Africa.” IMF Working Paper, 22/88.
- International Monetary Fund. 2024. Regional Economic Outlook: Sub-Saharan Africa— A Tepid and Pricey Recovery. Washington, DC, April.

*Nowcasting Growth Using the Bayesian Structural Time Series Model: Application to Tanzania — Working Paper No. WP/2026/049*

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_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026049-source-pdf.pdf_