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on Econometric Time Series |
| By: | Perron, Pierre; Yamamoto, Yohei; Zhou, Jing |
| Abstract: | We provide a comprehensive treatment for the problem of testing jointly for structural changes in both the regression coeffcients and the variance of the errors in a single equation system involving stationary regressors. Our framework is quite general in that we allow for general mixing-type regressors and the assumptions on the errors are quite mild. Their distribution can be non-Normal and conditional heteroskedasticity is permitted. Extensions to the case with serially correlated errors are also treated. We provide the required tools to address the following testing problems, among others: a) testing for given numbers of changes in regression coeffcients and variance of the errors; b) testing for some unknown number of changes within some pre-specified maximum; c) testing for changes in variance (regression coeffcients) allowing for a given number of changes in the regression coeffcients (variance); d) a sequential procedure to estimate the number of changes present. These testing problems are important for practical applications as witnessed by interests in macroeconomics and finance where documenting structural changes in the variability of shocks to simple autoregressions or Vector Autoregressive Models has been a concern. |
| Keywords: | Change-point, Variance shift, Conditional heteroskedasticity, Likelihood ratio tests |
| JEL: | C22 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hiasdp:hias-e-85&r=all |
| By: | Perron, Pierre; Yamamoto, Yohei |
| Abstract: | In empirical applications based on linear regression models, structural changes often occur in both the error variance and regression coefficients possibly at different dates. A commonly applied method is to first test for changes in the coefficients (or in the error variance) and, conditional on the break dates found, test for changes in the variance (or in the coefficients). In this note, we provide evidence that such procedures have poor finite sample properties when the changes in the first step are not correctly accounted for. In doing so, we show that the test for changes in the coefficients (or in the variance) ignoring changes in the variance (or in the coefficients) induces size distortions and loss of power. Our results illustrate a need for a joint approach to test for structural changes in both the coefficients and the variance of the errors. We provide some evidence that the procedures suggested by Perron, Yamamoto and Zhou (2019) provide tests with good size and power. |
| Keywords: | structural change, variance shifts, CUSUM of squares tests, hypothesis testing, Sup-LR test |
| JEL: | C12 C38 |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2019-01&r=all |
| By: | Hauber, Philipp; Schumacher, Christian; Zhang, Jiachun |
| Abstract: | We provide a simulation smoother to a exible state-space model with lagged states and lagged dependent variables. Qian (2014) has introduced this state-space model and proposes a fast Kalman filter with time-varying state dimension in the presence of missing observations in the data. In this paper, we derive the corresponding Kalman smoother moments and propose an efficient simulation smoother, which relies on mean corrections for unconditional vectors. When applied to a factor model, the proposed simulation smoother for the states is efficient compared to other state-space models without lagged states and/or lagged dependent variables in terms of computing time. |
| Keywords: | state-space model,missing observations,Kalman filter and smoother,simulation smoothing,factor model |
| JEL: | C11 C32 C38 C63 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdps:152019&r=all |
| By: | Naimoli, Antonio; Storti, Giuseppe |
| Abstract: | We propose a novel approach to modelling and forecasting high frequency trading volumes. The new model extends the Component Multiplicative Error Model of Brownlees et al. (2011) by introducing a more flexible specification of the long-run component. This uses an additive cascade of MIDAS polynomial filters, moving at different frequencies, in order to reproduce the changing long-run level and the persistent autocorrelation structure of high frequency trading volumes. After investigating its statistical properties, the merits of the proposed approach are illustrated by means of an application to six stocks traded on the XETRA market in the German Stock Exchange. |
| Keywords: | Intra-daily trading volume, dynamic component models, long-range dependence, forecasting. |
| JEL: | C22 C53 C58 |
| Date: | 2019–05–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:93802&r=all |
| By: | Michal Bencik (National Bank of Slovakia) |
| Abstract: | The output gap derived by conventional methods is dependent on data from national accounts statistics. Consequently, the output gap is usually the subject of significant updates if hard data are revised. Reliability of output gap estimates can also be affected by properties of the applied method, for instance the end-point problem (e.g. in the commonly used HP filter). The aim of this paper is to offer a solid methodology to measure output gap using exclusively the output series and surveys that allow for a less uncertain assessment, while eliminating the endpoint problem. We present and apply a method of constructing the output gap from surveys in Slovakia. The method consists of principal component analysis and Kalman smoother applied to the first principal component. The path of the resulting output gap is fairly similar to the path of other measures of output gap, but its revisions (especially during the outbreak of the Great Financial Crisis) are smaller than those of traditional measures. |
| Keywords: | Output Gap, Survey Indicators, Principal Components, Kalman Filter |
| JEL: | E32 |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:svk:wpaper:1061&r=all |
| By: | Masaaki Fukasawa; Tetsuya Takabatake; Rebecca Westphal |
| Abstract: | Rough volatility models are continuous time stochastic volatility models where the volatility process is driven by a fractional Brownian motion with the Hurst parameter less than half, and have attracted much attention since a seminal paper titled "Volatility is rough" was posted on SSRN in 2014 claiming that they explain a scaling property of realized variance time series. From our point of view, the analysis is not satisfactory because the estimation error of the latent volatility was not taken into account; we show by simulations that it in fact results in a fake scaling property. Motivated by this preliminary finding, we construct a quasi-likelihood estimator for a fractional stochastic volatility model and apply it to realized variance time series to examine whether the volatility is really rough. Our quasi-likelihood is based on a central limit theorem for the realized volatility estimation error and a Whittle-type approximation to the auto-covariance of the log-volatility process. We prove the consistency of our estimator under high frequency asymptotics, and examine by simulations the finite sample performance of our estimator. Our empirical study suggests that the volatility is indeed rough; actually it is even rougher than considered in the literature. |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1905.04852&r=all |