This paper investigates the issue of determining dimensions row and column factor spaces in matrix-valued data. Exploiting eigen-gap spectrum sample second moment matrices data, we propose a family randomised tests to check whether one-way or two-way structure exists not. Our do not require any arbitrary thresholding on eigenvalues, can be applied with (virtually) no restrictions relative rate ...

The main purpose of this paper is to discern the dynamic causal relationships (in the Granger (temporal) sense) among sales, advertising and prices in the context of the Portuguese car market. The present research (based on multiple cointegration tests preceded by various unit root or non-stationarity tests) is one of the first attempts at putting the salesmarketing mix analysis within a multiv...

We examine the succinctness of one-way, rotating, sweeping, and two-way deterministic finite automata (1dfas, rdfas, sdfas, 2dfas) and their nondeterministic and randomized counterparts. Here, a sdfa is a 2dfa whose head can change direction only on the endmarkers and a rdfa is a sdfa whose head is reset to the left end of the input every time the right end-marker is read. We study the size com...