Forecasting Sales and Price for Existing Single-Family Homes: A VAR Model with Error Correction

In this paper we forecast demand for existing single-family housing in the United States. We first find that sales volume (sales) and median sales price (price) have unit roots. We then find that sales and price are cointegrated. We develop a vector autoregressive (VAR) model with error correction to further examine the causality between sales and price. We find that there exists a bidirectional causality relationship between sales and price. Price affects sales significantly and sales affects price weakly. With the VAR model we then forecast sales and price for existing single-family housing during the period 1991 to 1994 by using a recursive method. We find that our predictions for sales and price fit the actual data well.

A Possible Hermitian Neutrino Mixing Ansatz

Using a recent global analysis result after the precise measurement of $\theta_ {13}$, a possible Herimtian neutrino mixing ansatz is discussed, the mixing matrix is symmetric and also symmetric with respect with the second diagonal line in the leading order. This leading order ansatz predicts $\theta_{13}=12.2^\circ$. Next, consider the hierarchy structure of the lepton mass matrix as the origin of perturbation of the mixing matrix, we find that this ansatz with perturbation can fit current data very well.Comment: 13 pages, 4 figure

On the Noether charge and the gravity duals of quantum complexity

The physical relevance of the thermodynamic volumes of AdS black holes to the gravity duals of quantum complexity was recently argued by Couch et al. In this paper, by generalizing the Wald-Iyer formalism, we derive a geometric expression for the thermodynamic volume and relate its product with the thermodynamic pressure to the non-derivative part of the gravitational action evaluated on the Wheeler-DeWitt patch. We propose that this action provides an alternative gravity dual of the quantum complexity of the boundary theory. We refer this to "complexity=action 2.0" (CA-2) duality. It is significantly different from the original "complexity=action" (CA) duality as well as the "complexity=volume 2.0" (CV-2) duality proposed by Couch et al. The latter postulates that the complexity is dual to the spacetime volume of the Wheeler-DeWitt patch. To distinguish our new conjecture from the various dualities in literature, we study a number of black holes in Einstein-Maxwell-Dilation theories. We find that for all these black holes, the CA duality generally does not respect the Lloyd bound whereas the CV-2 duality always does. For the CA-2 duality, although in many cases it is consistent with the Lloyd bound, we also find a counter example for which it violates the bound as well.Comment: minor corrections, references added,29pages,7figure