Adamek, R., Smeekes, S., and Wilms, I. (2023). Lasso inference for high-dimensional time series. Journal of Econometrics, 235(2), 1114â1143.
Babii, A., Ghysels, E., and Striaukas, J. (2022). Machine learning time series regressions with an application to nowcasting.
Belloni, A., Chen, D., Chernozhukov, V., and Hansen, C. (2012). Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica, 80(6), 2369â2429.
Benati, L. (2015). The long-run Phillips curve: A structural VAR investigation. Journal of Monetary Economics, 76, 15â28.
- Bickel, P. J., Ritov, Y., and Tsybakov, A. B. (2009). Simultaneous analysis of Lasso and Dantzig selector. The Annals of Statistics, 37(4), 1705â1732.
Paper not yet in RePEc: Add citation now
- Bykhovskaya, A. and Gorin, V. (2022). Cointegration in large VARs. The Annals of Statistics, 50(3), 1593â1617.
Paper not yet in RePEc: Add citation now
Cai, Z. and Wang, Y. (2014). Testing predictive regression models with nonstationary regressors. Journal of Econometrics, 178, 4â14.
Cai, Z., Chen, H., and Liao, X. (2023). A new robust inference for predictive quantile regression. Journal of Econometrics, 234(1), 227â250.
Campbell, J. Y. and Yogo, M. (2006). Efficient tests of stock return predictability. Journal of Financial Economics, 81(1), 27â60.
Caner, M. and Kock, A. B. (2018). Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso. Journal of Econometrics, 203(1), 143â168.
Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., and Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1âC68.
Chernozhukov, V., Escanciano, J. C., Ichimura, H., Newey, W. K., and Robins, J. M. (2022a). Locally robust semiparametric estimation. Econometrica, 90(4), 1501â1535.
Chernozhukov, V., Newey, W. K., and Singh, R. (2022b). Automatic debiased machine learning of causal and structural effects. Econometrica, 90(3), 967â1027.
- Davydov, Y. A. (1968). Convergence of distributions generated by stationary stochastic processes. Theory of Probability & Its Applications, 13(4), 691â696.
Paper not yet in RePEc: Add citation now
Demetrescu, M., Georgiev, I., Rodrigues, P. M., and Taylor, A. R. (2023). Extensions to IVX methods of inference for return predictability. Journal of Econometrics, 237(2), 105271.
Deshpande, Y., Javanmard, A., and Mehrabi, M. (2023). Online debiasing for adaptively collected high-dimensional data with applications to time series analysis. Journal of the American Statistical Association, 118(542), 1126â1139.
Dimand, R. W. and Geanakoplos, J. (2005). Celebrating Irving Fisher: The legacy of a great economist. The American Journal of Economics and Sociology, 64(1), 3âvi.
Dominguez, K. M., Fair, R. C., and Shapiro, M. D. (1988). Forecasting the depression: Harvard versus Yale. The American Economic Review, (pp. 595â612).
- Engemann, K. (2020). What is the Phillips curve (and why has it flattened)? Federal Reserve Bank of St. Louis, January, 14.
Paper not yet in RePEc: Add citation now
Fan, Q., Guo, Z., Mei, Z., and Zhang, C.-H. (2023). Uniform inference for nonlinear endogenous treatment effects with high-dimensional covariates. arXiv preprint arXiv:2310.08063.
Fan, R. and Lee, J. H. (2019). Predictive quantile regressions under persistence and conditional heteroskedasticity. Journal of Econometrics, 213(1), 261â280.
- Fisher, I. (1925). Our unstable dollar and the so-called business cycle. Journal of the American Statistical Association, 20(150), 179â202.
Paper not yet in RePEc: Add citation now
- Fisher, I. (1926). A statistical relation between unemployment and price changes. International Labour Review, 13, 785â792.
Paper not yet in RePEc: Add citation now
- Fisher, I. (1973). I discovered the Phillips curve: âA statistical relation between unemployment and price changesâ. Journal of Political Economy, 81(2, Part 1), 496â502.
Paper not yet in RePEc: Add citation now
- Fu, W. and Knight, K. (2000). Asymptotics for Lasso-type estimators. The Annals of Statistics, 28(5), 1356â1378.
Paper not yet in RePEc: Add citation now
Giannone, D., Lenza, M., and Primiceri, G. E. (2021). Economic predictions with big data: The illusion of sparsity.
Gold, D., Lederer, J., and Tao, J. (2020). Inference for high-dimensional instrumental variables regression. Journal of Econometrics, 217(1), 79â111.
Granger, C. W. and Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2(2), 111â120.
Jansson, M. and Moreira, M. J. (2006). Optimal inference in regression models with nearly integrated regressors. Econometrica, 74(3), 681â714.
- Javanmard, A. and Montanari, A. (2014). Confidence intervals and hypothesis testing for high-dimensional regression.
Paper not yet in RePEc: Add citation now
Koo, B., Anderson, H. M., Seo, M. H., and Yao, W. (2020). High-dimensional predictive regression in the presence of cointegration. Journal of Econometrics, 219(2), 456â477.
Kostakis, A., Magdalinos, T., and Stamatogiannis, M. P. (2015). Robust econometric inference for stock return predictability.
- Kostakis, A., Magdalinos, T., and Stamatogiannis, M. P. (2018). Taking stock of long-horizon predictability tests: Are factor returns predictable? Available at SSRN 3284149.
Paper not yet in RePEc: Add citation now
Lee, J. H. (2016). Predictive quantile regression with persistent covariates: IVX-QR approach. Journal of Econometrics, 192(1), 105â118.
- Lee, J. H., Shi, Z., and Gao, Z. (2022). On LASSO for predictive regression. Journal of Econometrics, 229(2), 322â349.
Paper not yet in RePEc: Add citation now
- Lin, Z. and Lu, C. (1997). Limit theory for mixing dependent random variables, volume 378. Springer Science & Business Media.
Paper not yet in RePEc: Add citation now
- Liu, X., Long, W., Peng, L., and Yang, B. (2023). A unified inference for predictive quantile regression. Journal of the American Statistical Association, (pp. 1â15).
Paper not yet in RePEc: Add citation now
Liu, X., Yang, B., Cai, Z., and Peng, L. (2019). A unified test for predictability of asset returns regardless of properties of predicting variables. Journal of Econometrics, 208(1), 141â159.
Magdalinos, T. and Phillips, P. C. (2009). Limit theory for cointegrated systems with moderately integrated and moderately explosive regressors. Econometric Theory, 25(2), 482â526.
- Mankiw, N. G. (2024). Six beliefs I have about inflation: Remarks prepared for nber conference on âinflation in the covid era and beyondâ. Journal of Monetary Economics, (pp. 103631).
Paper not yet in RePEc: Add citation now
McCracken, M. W. and Ng, S. (2016). FRED-MD: A monthly database for macroeconomic research. Journal of Business & Economic Statistics, 34(4), 574â589.
Medeiros, M. C., Vasconcelos, G. F., Veiga, AÌ., and Zilberman, E. (2021). Forecasting inflation in a data-rich environment: the benefits of machine learning methods. Journal of Business & Economic Statistics, 39(1), 98â119.
Mei, Z. and Shi, Z. (2024). On LASSO for high dimensional predictive regression. Journal of Econometrics, 242(2), 105809.
- Mei, Z., Phillips, P. C., and Shi, Z. (2024). The boosted hodrick-prescott filter is more general than you might think. Journal of Applied Econometrics.
Paper not yet in RePEc: Add citation now
Onatski, A. and Wang, C. (2018). Alternative asymptotics for cointegration tests in large VARs. Econometrica, 86(4), 1465â1478.
Phillips, A. W. (1958). The relation between unemployment and the rate of change of money wage rates in the united kingdom, 1861-1957. Economica, 25(100), 283â299.
Phillips, P. C. (2015). Halbert White Jr. memorial JFEC lecture: Pitfalls and possibilities in predictive regression. Journal of Financial Econometrics, 13(3), 521â555.
Phillips, P. C. and Lee, J. H. (2013). Predictive regression under various degrees of persistence and robust long-horizon regression. Journal of Econometrics, 177(2), 250â264.
Phillips, P. C. and Lee, J. H. (2016). Robust econometric inference with mixed integrated and mildly explosive regressors. Journal of Econometrics, 192(2), 433â450.
Phillips, P. C. and Magdalinos, T. (2007). Limit theory for moderate deviations from a unit root. Journal of Econometrics, 136(1), 115â130.
- Phillips, P. C. and Magdalinos, T. (2009). Econometric inference in the vicinity of unity. Singapore Management University, CoFie Working Paper, 7.
Paper not yet in RePEc: Add citation now
Phillips, P. C. and Shi, Z. (2021). Boosting: Why you can use the HP filter. International Economic Review, 62(2), 521â570.
Shi, Z. (2016). Estimation of sparse structural parameters with many endogenous variables. Econometric Reviews, 35(8-10), 1582â1608.
Smeekes, S. and Wijler, E. (2018). Macroeconomic forecasting using penalized regression methods. International Journal of Forecasting, 34(3), 408â430.
Smeekes, S. and Wijler, E. (2021). An automated approach towards sparse single-equation cointegration modelling. Journal of Econometrics, 221(1), 247â276.
Stambaugh, R. F. (1999). Predictive regressions. Journal of Financial Economics, 54(3), 375â421.
- Step 2. Verifying (A.2). We use the strong Gaussian approximation from Lin and Lu (1997)âs Theorem 9.3.1. Specifically, define g(x) = exp(x). By the sub-exponential tail imposed by Assumption 1, the sub-exponential norm of εk,t, denoted as â¥Îµk,tâ¥g in Lin and Lu (1997), is uniformly bounded by an absolute constant. It then suffices to verify the following two conditions required in the aforementioned theorem: (i) Vk,t ⥠ct for some absolute constant c. (ii) Pâ d=1 α(d)1/4 log(1/α(d)) < â, where the parameter δ in Lin and Lu (1997, Theorem 9.3.1) is taken as 2.
Paper not yet in RePEc: Add citation now
- Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B: Statistical Methodology, 58(1), 267â288.
Paper not yet in RePEc: Add citation now
Tu, Y. and Xie, X. (2023). Penetrating sporadic return predictability. Journal of Econometrics, 237(1), 105509.
- van de Geer, S., BuÌhlmann, P., Ritov, Y., and Dezeure, R. (2014). On asymptotically optimal confidence regions and tests for high-dimensional models. The Annals of Statistics, 42(3), 1166â1202.
Paper not yet in RePEc: Add citation now
Xu, K.-L. (2020). Testing for multiple-horizon predictability: Direct regression based versus implication based. The Review of Financial Studies, 33(9), 4403â4443.
Yang, B., Liu, X., Peng, L., and Cai, Z. (2021). Unified tests for a dynamic predictive regression. Journal of Business & Economic Statistics, 39(3), 684â699.
Yang, B., Long, W., Peng, L., and Cai, Z. (2020). Testing the predictability of us housing price index returns based on an IVX-AR model. Journal of the American Statistical Association, 115(532), 1598â1619.
Zhang, C.-H. and Zhang, S. S. (2014). Confidence intervals for low dimensional parameters in high dimensional linear models. Journal of the Royal Statistical Society Series B: Statistical Methodology, 76(1), 217â242.
Zhang, R., Robinson, P., and Yao, Q. (2019). Identifying cointegration by eigenanalysis. Journal of the American Statistical Association, 114(526), 916â927.
Zhang, X. and Cheng, G. (2017). Simultaneous inference for high-dimensional linear models. Journal of the American Statistical Association, 112(518), 757â768.
Zhu, F., Cai, Z., and Peng, L. (2014). Predictive regressions for macroeconomic data. The Annals of Applied Statistics, 8(1), 577 â 594.