THE CONNECTEDNESS BETWEEN THE SENTIMENT INDEX AND STOCK RETURN VOLATILITY UNDER COVID-19: A TIME-VARYING PARAMETER VECTOR AUTOREGRESSION APPROACH

We analyze the connectedness between the sentiment index and the return and volatility of the crude oil, stock and gold markets by employing the time-varying parameter vector autoregression model vis-à-vis the coronavirus disease (COVID-19) epidemic. Our sentiment index is constructed via text mining technology. We also employ a network to visualize and better understand the structure of the connectedness. The results confirm that the sentiment index is the net pairwise directional connectedness receiver, while the infectious disease equity market volatility tracker is the transmitter. Furthermore, the impact of the COVID-19 pandemic on the total connectedness of volatility is unprecedented.

Time Series Methods and Repeated Sample Surveys

<p>When applied to a sequence of repeated surveys, the traditional sample survey estimators of means or totals for one time period only, fail to take advantage of any time series structure. Such structure may result from correlation between successive responses for resampled individuals, or from time series properties in the parameters of interest. Historically, the initial published papers on time series improvement of repeated sample survey estimates allowed only the first possibility, treating the sum over the population of the individual responses as fixed; individual responses were seen as having stochastic properties only with respect to the sampling scheme. The alternative and later development allowed that both individual responses and their sum have stochastic properties with respect to a superpopulation from which the population of individual responses are drawn. Superpopulations allowed the application of mainstream time series techniques, including signal extraction and stochastic least squares, to repeated sample survey data. These developments in their historical perspective are the topic of Chapter 1. Superpopulation models may also be applied to sample surveys from a single time period, and superpopulation and design properties of the one period linear non-homogeneous sample survey estimator form the topic of Chapter 2; this estimator is sufficiently general to subsume almost all single period non-informative sample survey estimators, and Chapter 2 allows systematisation of a wide range of previously disparate results. This linear estimator may also be extended beyond one time period to include the known estimators for repeated surveys, and this topic, together with a consideration of the effects of data agqregation on non-stochastic and stochastic least squares, is the subject of Chapter 3. Given the central role of the general linear model, and the time series nature of repeated surveys, projection and parameter updating formulae for linear models should form an integral part of repeated survey analysis. The correlation of sample survey errors however, invalidates the formulae appropriate to the known iid error case, and Chapters 4 and 5 develop the general formulae to allow correlated error structure. Chapter 4 considers parameter vectors of fixed length, as for example, for polynomial models, and provides formulae for estimating the length of the parameter vector, and for calculating independent recursive residuals and cusums when further data are added to the model. Chapter 5 considers updating and projection formulae in a wider context, and allows that the parameter vector may be stochastic or non-stochastic and that its length may increase with additional data; it consequently provides a general extension of the Kalman filter to the case of coloured noise over time. The paucity of suitable data has limited data analysis to that contained in Chapter 6, where a simulation study and an analysis of medical data gauge the efficacy of polynomial models in time with multiple observations per time point and autocorrelated errors. The formulae of Chapter 4 allow testing for the constancy of the regression relationships over time. The appendix details SAS computer programs for fitting the polynomial models of Chapter 6.</p>

Time Series Methods and Repeated Sample Surveys

<p>When applied to a sequence of repeated surveys, the traditional sample survey estimators of means or totals for one time period only, fail to take advantage of any time series structure. Such structure may result from correlation between successive responses for resampled individuals, or from time series properties in the parameters of interest. Historically, the initial published papers on time series improvement of repeated sample survey estimates allowed only the first possibility, treating the sum over the population of the individual responses as fixed; individual responses were seen as having stochastic properties only with respect to the sampling scheme. The alternative and later development allowed that both individual responses and their sum have stochastic properties with respect to a superpopulation from which the population of individual responses are drawn. Superpopulations allowed the application of mainstream time series techniques, including signal extraction and stochastic least squares, to repeated sample survey data. These developments in their historical perspective are the topic of Chapter 1. Superpopulation models may also be applied to sample surveys from a single time period, and superpopulation and design properties of the one period linear non-homogeneous sample survey estimator form the topic of Chapter 2; this estimator is sufficiently general to subsume almost all single period non-informative sample survey estimators, and Chapter 2 allows systematisation of a wide range of previously disparate results. This linear estimator may also be extended beyond one time period to include the known estimators for repeated surveys, and this topic, together with a consideration of the effects of data agqregation on non-stochastic and stochastic least squares, is the subject of Chapter 3. Given the central role of the general linear model, and the time series nature of repeated surveys, projection and parameter updating formulae for linear models should form an integral part of repeated survey analysis. The correlation of sample survey errors however, invalidates the formulae appropriate to the known iid error case, and Chapters 4 and 5 develop the general formulae to allow correlated error structure. Chapter 4 considers parameter vectors of fixed length, as for example, for polynomial models, and provides formulae for estimating the length of the parameter vector, and for calculating independent recursive residuals and cusums when further data are added to the model. Chapter 5 considers updating and projection formulae in a wider context, and allows that the parameter vector may be stochastic or non-stochastic and that its length may increase with additional data; it consequently provides a general extension of the Kalman filter to the case of coloured noise over time. The paucity of suitable data has limited data analysis to that contained in Chapter 6, where a simulation study and an analysis of medical data gauge the efficacy of polynomial models in time with multiple observations per time point and autocorrelated errors. The formulae of Chapter 4 allow testing for the constancy of the regression relationships over time. The appendix details SAS computer programs for fitting the polynomial models of Chapter 6.</p>

Statistical Inference for Piecewise Affine System Identification

This short note studies the problem of piecewise affine system identification, being a special nonlinear system based on our previous contribution on it. Two different identification strategies are proposed to achieve our mission, such as centralized identification and distributed identification. More specifically, for centralized identification, the total observed input-output data are used to estimate all unknown parameter vectors simultaneously without any consideration on the classification process. But for distributed identification, after the whole observed input-output data are classified into their own right subregions, then part input-output data, belonging to the same subregion, are applied to estimate the unknown parameter vector. Whatever the centralized identification and distributed identification, the final decision is to determine the unknown parameter vector in one linear form, so the recursive least squares algorithm and its modified form with the dead zone are studied to deal with the statistical noise and bounded noise, respectively. Finally, one simulation example is used to compare the identification accuracy for our considered two identification strategies.

When is there a representer theorem?

We consider a general regularised interpolation problem for learning a parameter vector from data. The well-known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the data points. This is at the core of kernel methods in machine learning as it makes the problem computationally tractable. Most literature deals only with sufficient conditions for representer theorems in Hilbert spaces and shows that the regulariser being norm-based is sufficient for the existence of a representer theorem. We prove necessary and sufficient conditions for the existence of representer theorems in reflexive Banach spaces and show that any regulariser has to be essentially norm-based for a representer theorem to exist. Moreover, we illustrate why in a sense reflexivity is the minimal requirement on the function space. We further show that if the learning relies on the linear representer theorem, then the solution is independent of the regulariser and in fact determined by the function space alone. This in particular shows the value of generalising Hilbert space learning theory to Banach spaces.

Does Investor Sentiment Affect Clean Energy Stock? Evidence from TVP-VAR-Based Connectedness Approach

We investigated the connectedness of the returns and volatility of clean energy stock, technology stock, crude oil, natural gas, and investor sentiment based on the time-varying parameter vector autoregressive (TVP-VAR) connectedness approach. The empirical results indicate that the average total connectedness is higher in the volatility system than in the return system. The investor sentiment has a weak impact on clean energy stock. Our results show that the dynamic total connectedness across assets in the system varies with time. Furthermore, the dynamic total connectedness increases significantly during financial turmoil. Dynamic total volatility connectedness is more sensitive to financial turmoil. By comparing the connectedness estimated by the TVP-VAR model with the rolling-window VAR model, we find the dynamic total return connectedness of the TVP-VAR model is similar to the estimated results of a 200 day rolling-window VAR model.

Endogenous Time Variation in Vector Autoregressions

We introduce a new class of time-varying parameter vector autoregressions (TVP-VARs) where the identified structural innovations are allowed to influence the dynamics of the coefficients in these models. An estimation algorithm and a parametrization conducive to model comparison are also provided. We apply our framework to the US economy. Scenario analysis suggests that, once accounting for the influence of structural shocks on the autoregressive coefficients, the effects of monetary policy on economic activity are larger and more persistent than in an otherwise standard TVP-VAR. Our results also indicate that cost-push shocks play a prominent role in understanding historical changes in inflation-gap persistence.

Targeted Undersmoothing: Sensitivity Analysis for Sparse Estimators

This paper proposes a procedure for assessing sensitivity of inferential conclusions for functionals of sparse high-dimensional models following model selection. The proposed procedure is called targeted undersmoothing. Functionals considered include dense functionals that may depend on many or all elements of the highdimensional parameter vector. The sensitivity analysis is based on systematic enlargements of an initially selected model. By varying the enlargements, one can conduct sensitivity analysis about the strength of empirical conclusions to model selection mistakes. We illustrate the procedure's performance through simulation experiments and two empirical examples.