On LASSO Inference for High Dimensional Predictive Regression

About one century ago, quantitative analysis and forecasting services were made available to businesses and the general public (Dominguez et al., 1988). Irving Fisher (1867-1947) spearheaded this initiative, pioneering data-driven forecasting practices grounded in theoretical foundations. His renowned theories, namely the monetary quantity theory, inflation-deflation theory, and index theory, were supported by statistical evidence. For example, Fisher (1925) was one of the earliest attempts to understand the source of business cycles in association with the price level (inflation), and Fisher (1926) was the first to report "a statistical relation between unemployment and price changes", today better known as the Phillips curve. Statistical inference is crucial for integrating economic theory and empirical data, which has become a tradition upheld by successive generations of researchers. In today's era of big data, we have unprecedented access to a vast amount of digital information about the economy. Recent advancements in statistical inference have uncovered new empirical patterns in prediction practices using datasets with temporal features. This paper aims at a plain quest: in a high dimensional linear predictive regression model when the number of potential regressors is larger than the sample size, how to conduct asymptotically valid statistical inference for a regressor of particular interest. To the best of our knowledge, no paper has solved this question before.