Matrix Differential Calculus with Applications in Statistics and Econometrics

The autoregressive model for cointegrated variables is analyzed with respect to the role of the constant and linear terms. Various models for 1(1) variables defined by restrictions on the deterministic terms are discussed, and it is shown that statistical inference can be performed by reduced rank regression. The asymptotic distributions of the test statistics and estimators are found. A similar analysis is given for models for 1(2) variables with a constant term.

The role of the constant and linear terms in cointegration analysis of nonstationary variables : Cointegrated systems. I

Causal relationships in econometrics are typically based on the concept of predictability and are established by testing Granger causality. Such relationships are susceptible to change, especially during times of financial turbulence, making the real‐time detection of instability an important practical issue. This article develops a test for detecting changes in causal relationships based on a recursive evolving window, which is analogous to a procedure used in recent work on financial bubble detection. The limiting distribution of the test takes a simple form under the null hypothesis and is easy to implement in conditions of homoskedasticity and conditional heteroskedasticity of an unknown form. Bootstrap methods are used to control family‐wise size in implementation. Simulation experiments compare the efficacy of the proposed test with two other commonly used tests, the forward recursive and the rolling window tests. The results indicate that the recursive evolving approach offers the best finite sample performance, followed by the rolling window algorithm. The testing strategies are illustrated in an empirical application that explores the causal relationship between the slope of the yield curve and real economic activity in the United States over the period 1980–2015.

/pdf/change-detection-and-the-causal-impact-of-the-yield-curve-4hamaaz70u.pdf

Change Detection and the Causal Impact of the Yield Curve

http://www.uni-konstanz.de/FuF/wiwi/workingpaperseries/WP_13_Brueggemann-Jentsch-Trenkler_2014.pdf

Inference in VARs with Conditional Heteroskedasticity of Unknown Form

Time series analyses are statistical methods used to assess trends in repeated measurements taken at regular intervals and their associations with other trends or events, taking account of the temporal structure of such data. Addiction research often involves assessing associations between trends in target variables (e.g. population cigarette smoking prevalence) and predictor variables (e.g. average price of a cigarette), known as a multiple time series design, or interventions or events (e.g. introduction of an indoor smoking ban), known as an interrupted time series design. There are many analytical tools available, each with its own strengths and limitations. This paper provides addiction researchers with an overview of many of the methods available (GLM, GLMM, GLS, GAMM, ARIMA, ARIMAX, VAR, SVAR, VECM) and guidance on when and how they should be used, sample size det ermination, reporting and interpretation. The aim is to provide increased clarity for researchers proposing to undertake these analyses concerning what is likely to be acceptable for publication in journals such as Addiction. Given the large number of choices that need to be made when setting up time series models, the guidance emphasizes the importance of pre-registering hypotheses and analysis plans before the analyses are undertaken.

/pdf/understanding-and-using-time-series-analyses-in-addiction-3eqnwon17z.pdf

Understanding and using time series analyses in addiction research

 We study the asymptotic behaviour of the least squares estimator, of the residual autocorrelations and of the Ljung–Box (or Box–Pierce) portmanteau test statistic for multiple autoregressive time series models with nonindependent innovations Under mild assumptions, it is shown that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chi-squared random variables When the innovations exhibit conditional heteroscedasticity or other forms of dependence, this asymptotic distribution can be quite different from that of models with independent and identically distributed innovations Consequently, the usual chi-squared distribution does not provide an adequate approximation to the distribution of the Box–Pierce goodness-of-fit portmanteau test in the presence of nonindependent innovations Hence we propose a method to adjust the critical values of the portmanteau tests Monte carlo experiments illustrate the finite sample performance of the modified portmanteau test

/pdf/multivariate-portmanteau-test-for-autoregressive-models-with-3bnq4ytw5v.pdf

Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors

Adaptive estimation of vector autoregressive models with time-varying variance: Application to testing linear causality in mean

Corrected portmanteau tests for VAR models with time-varying variance

This article considers the volatility modeling for autoregressive univariate time series. A benchmark approach is the stationary autoregressive conditional heteroscedasticity (ARCH) model of Engle. Motivated by real data evidence, processes with nonconstant unconditional variance and ARCH effects have been recently introduced. We take into account this type of nonstationarity in variance and propose simple testing procedures for ARCH effects. Adaptive McLeod and Li’s portmanteau and ARCH-LM tests for checking the presence of such second-order dynamics are provided. The standard versions of these tests, commonly used by practitioners, suppose constant unconditional variance. The failure of these standard tests with time-varying unconditional variance is highlighted. The theoretical results are illustrated by means of simulated and real data. Supplementary materials for this article are available online.

Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance

The volatility modeling for autoregressive univariate time series is considered. A benchmark approach is the stationary ARCH model of Engle (1982). Motivated by real data evidence, processes with non constant unconditional variance and ARCH effects have been recently introduced. We take into account such possible non stationarity and propose simple testing procedures for ARCH effects. Adaptive McLeod and Li's portmanteau and ARCH-LM tests for checking for second order dynamics are provided. The standard versions of these tests, commonly used by practitioners, suppose constant unconditional variance. We prove the failure of these standard tests with time-varying unconditional variance. The theoretical results are illustrated by mean of simulated and real data.

Hamdi Raïssi

Papers

Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors

Adaptive estimation of vector autoregressive models with time-varying variance: Application to testing linear causality in mean

Corrected portmanteau tests for VAR models with time-varying variance

Testing Second-Order Dynamics for Autoregressive Processes in Presence of Time-Varying Variance

Testing second order dynamics for autoregressive processes in presence of time-varying variance