Discovering Graphical Granger Causality Using the Truncating Lasso Penalty

Components of biological systems interact with each other in order to carry out vital cell functions. Such information can be used to improve estimation and inference, and to obtain better insights into the underlying cellular mechanisms. Discovering regulatory interactions among genes is therefore an important problem in systems biology. Whole-genome expression data over time provides an opportunity to determine how the expression levels of genes are affected by changes in transcription levels of other genes, and can therefore be used to discover regulatory interactions among genes. In this paper, we propose a novel penalization method, called truncating lasso, for estimation of causal relationships from time-course gene expression data. The proposed penalty can correctly determine the order of the underlying time series, and improves the performance of the lasso-type estimators. Moreover, the resulting estimate provides information on the time lag between activation of transcription factors and their effects on regulated genes. We provide an efficient algorithm for estimation of model parameters, and show that the proposed method can consistently discover causal relationships in the large $p$, small $n$ setting. The performance of the proposed model is evaluated favorably in simulated, as well as real, data examples. The proposed truncating lasso method is implemented in the R-package grangerTlasso and is available at http://www.stat.lsa.umich.edu/~shojaie.Comment: 12 pages, 4 figures, 1 tabl

Casual Compressive Sensing for Gene Network Inference

We propose a novel framework for studying causal inference of gene interactions using a combination of compressive sensing and Granger causality techniques. The gist of the approach is to discover sparse linear dependencies between time series of gene expressions via a Granger-type elimination method. The method is tested on the Gardner dataset for the SOS network in E. coli, for which both known and unknown causal relationships are discovered

Application of Auto-Regressive Distributed Lag Model (ARDL) Bound Test on Selected Macroeconomic Variables

This study examined the application of Auto-regressive distributed lag model (ARDL) bound test on some selected macroeconomic variables spanning from 1981-2017 obtained from the statistical Bulletin of Central Bank of Nigeria (CBN). The data were analyzed using the E-views 9.0 software. F-statistic of 5.9167 was found to be higher than the critical value of 3.79 in the Lower Bound I(0) and 4.85 in the Upper bound I(1)  at the 5 % level, thus null hypothesis was rejected. ARDL (1, 2, 0) was found to be the best fit model for showing a long-run and short-run relationship between Gross Domestic Product (GDP), Exchange rate, and Interest rate. There is a long-run relationship among GDP, Exchange rate, and Interest rate which means that the variables under study are co-integrated. Also, a unidirectional relationship running from exchange rate to GDP exist. The study recommends the use of supportive fiscal and monetary policies that will tighten the local currency market and provide a set of incentives aimed at removing anti-export bias barriers so as to promote exports and boost GDP, particularly non-oil exports and discourage import of consumer goods to stabilize the exchange rate. Keywords: ARDL Bound test; Gross Domestic Product; Exchange rate; Macroeconomic Variables; Interest rate.JEL Codes: E06; O2; O

A Direct Estimation of High Dimensional Stationary Vector Autoregressions

The vector autoregressive (VAR) model is a powerful tool in modeling complex time series and has been exploited in many fields. However, fitting high dimensional VAR model poses some unique challenges: On one hand, the dimensionality, caused by modeling a large number of time series and higher order autoregressive processes, is usually much higher than the time series length; On the other hand, the temporal dependence structure in the VAR model gives rise to extra theoretical challenges. In high dimensions, one popular approach is to assume the transition matrix is sparse and fit the VAR model using the "least squares" method with a lasso-type penalty. In this manuscript, we propose an alternative way in estimating the VAR model. The main idea is, via exploiting the temporal dependence structure, to formulate the estimating problem into a linear program. There is instant advantage for the proposed approach over the lasso-type estimators: The estimation equation can be decomposed into multiple sub-equations and accordingly can be efficiently solved in a parallel fashion. In addition, our method brings new theoretical insights into the VAR model analysis. So far the theoretical results developed in high dimensions (e.g., Song and Bickel (2011) and Kock and Callot (2012)) mainly pose assumptions on the design matrix of the formulated regression problems. Such conditions are indirect about the transition matrices and not transparent. In contrast, our results show that the operator norm of the transition matrices plays an important role in estimation accuracy. We provide explicit rates of convergence for both estimation and prediction. In addition, we provide thorough experiments on both synthetic and real-world equity data to show that there are empirical advantages of our method over the lasso-type estimators in both parameter estimation and forecasting.Comment: 36 pages, 3 figur