We study regime-specific systematic comovement between two large panels of variables that exhibit an approximate factor structure. Within each panel we identify threshold-type regimes through shifts in the factor loadings. For the resulting regimes, and with regard to the relation between any two variables in different panels, we define as “systematic” the comovement that is generated by the common components of the variables. In our setup, changes in comovement are identified by regime shifts in the loadings. After constructing measures of systematic comovement between the two panels, we propose estimators for these measures and derive their asymptotic properties. We develop inferential procedures to formally test for changes in systematic comovement between regimes. The empirical analysis of two large panels of U.S. and international equity returns shows that their systematic comovement increases when U.S. macroeconomic uncertainty is sufficiently high.

Temporal disaggregation is a method commonly used in official statistics to enable high-frequency estimates of key economic indicators, such as GDP. Traditionally, such methods have relied on only a couple of high-frequency indicator series to produce estimates. However, the prevalence of large, and increasing, volumes of administrative and alternative data-sources motivates the need for such methods to be adapted for high-dimensional settings. In this work, we propose a novel sparse temporal-disaggregation procedure and contrast this with the classical Chow-Lin method. We demonstrate the performance of our proposed method through simulation study, highlighting various ad- vantages realised. We also explore its application to disaggregation of UK gross domestic product data, demonstrating the method’s ability to operate when the number of potential indicators is greater than the number of low-frequency observations.

This paper applies neural network models to forecast inflation. The use of a particular recurrent neural network, the long-short term memory model, or LSTM, that summarizes macroeconomic information into common components is a major contribution of the paper. Results from an exercise with US data indicate that the estimated neural nets usually present better forecasting performance than standard benchmarks, especially at long horizons. The LSTM in particular is found to outperform the traditional feed-forward network at long horizons, suggesting an advantage of the recurrent model in capturing the long-term trend of inflation. This finding can be rationalized by the so called long memory of the LSTM that incorporates relatively old information in the forecast as long as accuracy is improved, while economizing in the number of estimated parameters. Interestingly, the neural nets containing macroeconomic information capture well the features of inflation during and after the Great Recession, possibly indicating a role for nonlinearities and macro information in this episode. The estimated common components used in the forecast seem able to capture the business cycle dynamics, as well as information on prices.

Cointegration between Periodically Integrated (PI) processes has been analyzed among other by Birchenhall, Bladen-Hovell, Chui, Osborn, and Smith (1989), Boswijk and Franses (1995), Franses and Paap (2004), Kleibergen and Franses (1999) and del Barrio Castro and Osborn (2008). However, so far there is not a method, published in an academic journal, that allows us to determine the cointegration rank between PI processes. This paper fills the gap, a method to determine the cointegration rank between a set PI Processes based on the idea of pseudo-demodulation is proposed in the context of Seasonal Cointegration by del Barrio Castro, Cubadda and Osborn (2020). Once a pseudo-demodulation time series is obtained the Johansen (1995) procedure could be applied to determine the cointegration rank. A Monte Carlo experiment shows that the proposed approach works satisfactorily for small samples.

The smoothness of subdiagonals of the Cholesky factor of large covariance matrices is closely related to the degree of nonstationarity of autoregressive models for time series data. Heuristically, one expects for nearly stationary covariance matrix entries in each subdiagonal of the Cholesky factor of its inverse to be approximately the same in the sense that the sum of the absolute values of successive differences is small. Statistically, such smoothness is achieved by regularizing each subdiagonal using fused-type lasso penalties. We rely on the standard Cholesky factor as the new parameter within a regularized normal likelihood setup which guarantees: (1) joint convexity of the likelihood function, (2) strict convexity of the likelihood function restricted to each subdiagonal even when n < p, and (3) positive-definiteness of the estimated covariance matrix. A block coordinate descent algorithm, where each block is a subdiagonal, is proposed, and its convergence is established under mild conditions. Lack of decoupling of the penalized likelihood function into a sum of functions involving individual subdiagonals gives rise to some computational challenges and advantages relative to two recent algorithms for sparse estimation of the Cholesky factor, which decouple row-wise. Simulation results and real data analysis show the scope and good performance of the proposed methodology.

Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimension. They are seemingly mutually exclusive. In this paper, we propose a simple lifting method that combines the merits of these two models in a supervised learning methodology that allows to efficiently explore all the information in high-dimensional datasets. The method is based on a flexible model for panel data, called factor-augmented regression model with both observable, latent common factors, as well as idiosyncratic components as high-dimensional covariate variables. This model not only includes both factor regression and sparse regression as specific models but also significantly weakens the cross-sectional dependence and hence facilitates model selection and interpretability. The methodology consists of three steps. At each step, the remaining cross-section dependence can be inferred by a novel test for covariance structure in high-dimensions. We developed asymptotic theory for the factor-augmented sparse regression model and demonstrated the validity of the multiplier bootstrap for testing high-dimensional covariance structure. This is further extended to testing high-dimensional partial covariance structures. The theory and methods are further supported by an extensive simulation study and applications to the construction of a partial covariance network of the financial returns and a prediction exercise for a large panel of macroeconomic time series from FRED-MD database.