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on Econometric Time Series |
| By: | Anna Bykhovskaya; Vadim Gorin |
| Abstract: | The paper studies non-stationary high-dimensional vector autoregressions of order $k$, VAR($k$). Additional deterministic terms such as trend or seasonality are allowed. The number of time periods, $T$, and number of coordinates, $N$, are assumed to be large and of the same order. Under such regime the first-order asymptotics of the Johansen likelihood ratio (LR), Pillai-Barlett, and Hotelling-Lawley tests for cointegration is derived: Test statistics converge to non-random integrals. For more refined analysis, the paper proposes and analyzes a modification of the Johansen test. The new test for the absence of cointegration converges to the partial sum of the Airy$_1$ point process. Supporting Monte Carlo simulations indicate that the same behavior persists universally in many situations beyond our theorems. The paper presents an empirical implementation of the approach to the analysis of stocks in S$\&$P$100$ and of cryptocurrencies. The latter example has strong presence of multiple cointegrating relationships, while the former is consistent with the null of no cointegration. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.07150&r= |
| By: | Bu, R.; Li, D.; Linton, O.; Wang, H. |
| Abstract: | In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For the highfrequency data contaminated by the microstructure noise, we introduce a localised pre-averaging estimation method in the high-dimensional setting which first pre-whitens data via a kernel filter and then uses the estimation tool developed in the noise-free scenario, and further derive the uniform convergence rates for the developed spot volatility matrix estimator. In addition, we also combine the kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector, and establish the relevant uniform consistency result. Numerical studies are provided to examine performance of the proposed estimation methods in finite samples. |
| Keywords: | Brownian semi-martingale, Kernel smoothing, Microstructure noise, Sparsity, Spot volatility matrix, Uniform consistency |
| JEL: | C10 C14 C22 |
| Date: | 2022–03–16 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camjip:2208&r= |
| By: | Hauber, Philipp |
| Abstract: | Factor models feature prominently in the macroeconomic nowcasting literature, yet no clear consensus has emerged regarding the question of how many and which variables to select in such applications. Examples of both large-scale models, estimated with data sets consisting of over 100 time series as well as small-scale models based on only a few, pre-selected variables can be found in the literature. To adress the issue of variable selection in factor models, in this paper we employ sparse priors on the loadings matrix. These priors concentrate more mass at zero than those conventionally used in the literature while retaining fat tails to capture signals. As a result, variable selection and estimation can be performed simultaneously in a Bayesian framework. Using large data sets consisting of over 100 variables, we evaluate the performance of sparse factor models in real-time for US and German GDP point and density nowcasts. We find that sparse priors lead to relatively small gains in nowcast accuracy compared to a benchmark Normal prior. Moreover, different types of sparse priors discussed in the literature yield very similar results. Our findings are compatible with the hypothesis that large macroeconomic data sets typically used in now- or forecasting applications are not sparse but dense. |
| Keywords: | factor models,sparsity,nowcasting,variable selection |
| JEL: | C11 C53 C55 E37 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:esprep:251551&r= |
| By: | Hafner, Christian (Université catholique de Louvain, LIDAM/ISBA, Belgium); Linton, Oliver (obl20@cam.ac.uk); Wang, Linqi (Université catholique de Louvain, LIDAM/LFIN, Belgium) |
| Abstract: | We introduce a new class of semiparametric dynamic autoregressive models forthe Amihud illiquidity measure, which captures both the long-run trend in the illiquidity series with a nonparametric component and the short-run dynamics with an autoregressive component. We develop a GMM estimator based on conditional moment restrictions and an efficient semiparametric ML estimator based on an iid assumption. We derive large sample properties for both estimators. We further develop a methodology to detect the occurrence of permanent and transitory breaks in the illiquidity process. Finally, we demonstrate the model performance and its empirical relevance on two applications. First, we study the impact of stock splits on the illiquidity dynamics of the five largest US technology company stocks. Second, we investigate how the different components of the illiquidity process obtained from our model relate to the stock market risk premium using data on the S&P 500 stock market index. |
| Keywords: | Nonparametric ; Semiparametric ; Splits ; Structural Change |
| JEL: | C12 C14 |
| Date: | 2022–02–23 |
| URL: | http://d.repec.org/n?u=RePEc:ajf:louvlf:2022002&r= |
| By: | Alexander Chudik; M. Hashem Pesaran; Ron P. Smith |
| Abstract: | The idea that certain economic variables are roughly constant in the long run is an old one. Kaldor described them as stylized facts, whereas Klein and Kosobud labelled them great ratios. While such ratios are widely adopted in theoretical models in economics as conditions for balanced growth, arbitrage or solvency, the empirical literature has tended to find little evidence for them. We argue that this outcome could be due to episodic failure of cointegration, possible two-way causality between the variables in the ratios and cross-country error dependence due to latent factors. We propose a new system pooled mean group estimator (SPMG) to deal with these features. Using this new panel estimator and a dataset spanning almost one and a half centuries and 17 countries, we find support for five out of the seven great ratios that we consider. Extensive Monte Carlo experiments also show that the SPMG estimator with bootstrapped confidence intervals stands out as the only estimator with satisfactory small sample properties. |
| Keywords: | great ratios; arbitrage conditions; heterogeneous panels; episodic cointegration; two-way long-run causality; error cross-sectional dependence |
| JEL: | B4 C18 C33 C5 |
| Date: | 2022–03–18 |
| URL: | http://d.repec.org/n?u=RePEc:fip:feddgw:93887&r= |