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on Econometric Time Series |
| By: | Bo Zhang; Jiti Gao; Guangming Pan; Yanrong Yang |
| Abstract: | Cross-sectional structures and temporal tendency are important features of highdimensional time series. Based on eigen-analysis on sample covariance matrices, we propose a novel approach to identifying four popular structures of high-dimensional time series, which are grouped in terms of factor structures and stationarity. The proposed three-step method includes: (1) the ratio statistic of empirical eigenvalues; (2) a projected Augmented Dickey-Fuller Test; (3) a new unit-root test based on the largest empirical eigenvalues. We develop asymptotic properties for these three statistics to ensure the feasibility for the whole procedure. Finite sample performances are illustrated via various simulations. Our results are further applied to analyze U.S. mortality data, U.S. house prices and income, and U.S. sectoral employment, all of which possess cross-sectional dependence as well as non-stationary temporal dependence. It is worth mentioning that we also contribute to statistical justification for the benchmark paper by Lee and Carter (1992) in mortality forecasting. |
| Keywords: | factor model, non-stationarity, sample covariance matrix, stationarity |
| JEL: | C18 C32 C55 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2023-22&r=ets |
| By: | Hong, Y.; Linton, O. B.; McCabe, B.; Sun, J.; Wang, S. |
| Abstract: | A popular self-normalization (SN) approach in time series analysis uses the variance of a partial sum as a self-normalizer. This is known to be sensitive to irregularities such as persistent autocorrelation, heteroskedasticity, unit roots and outliers. We propose a novel SN approach based on the adjusted-range of a partial sum, which is robust to these aforementioned irregularities. We develop an adjusted-range based Kolmogorov-Smirnov type test for structural breaks for both univariate and multivariate time series, and consider testing parameter constancy in a time series regression setting. Our approach can rectify the well-known power decrease issue associated with existing self-normalized KS tests without having to use backward and forward summations as in Shao and Zhang (2010), and can alleviate the “better size but less power†phenomenon when the existing SN approaches (Shao, 2010; Zhang et al., 2011; Wang and Shao, 2022) are used. Moreover, our proposed tests can cater for more general alternatives. Monte Carlo simulations and empirical studies demonstrate the merits of our approach. |
| Keywords: | Change-Point Testing, CUSUM Process, Parameter Constancy, Studentization |
| JEL: | C12 C19 |
| Date: | 2023–11–06 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:2367&r=ets |
| By: | Guglielmo Maria Caporale; Luis Alberiko Gil-Alana |
| Abstract: | This paper introduces a new modelling approach that incorporates nonlinear, exponential deterministic terms into a fractional integration model. The proposed model is based on a specific version of Robinson’s (1994) tests and is more general that standard time series models, which only allow for linear trends. Montecarlo simulations show that it performs well in finite sample. Three empirical examples confirm that the suggested specification captures the properties of the data adequately. |
| Keywords: | exponential time trends, fractional integration, Montecarlo simulations |
| JEL: | C22 C15 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_10774&r=ets |
| By: | Chaya Weerasinghe; Ruben Loaiza-Maya; Gael M. Martin; David T. Frazier |
| Abstract: | Approximate Bayesian Computation (ABC) has gained popularity as a method for conducting inference and forecasting in complex models, most notably those which are intractable in some sense. In this paper we use ABC to produce probabilistic forecasts in state space models (SSMs). Whilst ABC-based forecasting in correctly-specified SSMs has been studied, the misspecified case has not been investigated, and it is that case which we emphasize. We invoke recent principles of ‘focused’ Bayesian prediction, whereby Bayesian updates are driven by a scoring rule that rewards predictive accuracy; the aim being to produce predictives that perform well in that rule, despite misspecification. Two methods are investigated for producing the focused predictions. In a simulation setting, `coherent' predictions are in evidence for both methods: the predictive constructed via the use of a particular scoring rule predicts best according to that rule. Importantly, both focused methods typically produce more accurate forecasts than an exact, but misspecified, predictive. An empirical application to a truly intractable SSM completes the paper. |
| Keywords: | Approximate Bayesian computation, auxiliary model, loss-based prediction, focused Bayesian prediction, proper scoring rules, stochastic volatility model |
| JEL: | C11 C53 C58 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2023-12&r=ets |
| By: | Reinhard Ellwanger, Stephen Snudden, Lenin Arango-Castillo (Wilfrid Laurier University) |
| Abstract: | Economists often need to forecast temporally aggregated data, such as monthly or quarterly averages. However, when the underlying data is persistent, constructing forecasts with aggregated data is inefficient. We propose a new forecasting method, Period-End-Point Sampling (PEPS), which uses end-of-period data to create point-in-time forecasts for aggregated data. We show that PEPS forecasts rival the accuracy of bottom-up forecasts and substantially outperform forecasts constructed with averaged data. Importantly, the PEPS method allows models to maintain the lower frequency of the forecast target. Real-time forecast applications to monthly nominal 10-year bond yields and the real prices of gasoline and copper find that disaggregated forecasts can outperform the end-of-month no-change forecasts. |
| Keywords: | Forecasting and Prediction Methods, Interest Rates, Commodity Prices |
| JEL: | C1 C53 E47 F37 Q47 |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:wlu:lcerpa:bm0142&r=ets |
| By: | Alexandre Bonnet R. Costa; Pedro Cavalcanti G. Ferreira; Wagner Piazza Gaglianone; Osmani Teixeira C. Guillén; João Victor Issler; Artur Brasil Fialho Rodrigues |
| Abstract: | The objective of this paper is to propose an approach for dating recessions in real time (or slightly a posteriori) that is suitable to a big data environment. Our proposal is to mix the canonical correlation approach of Issler and Vahid (2006) with the big data approach defended by Stock and Watson (2014). We incorporate the good elements of each approach into one. This involves solving both the problem of missing data and high dimensionality in big databases, besides defining a decision rule on how to choose the best forecasting model in real time. Our empirical results show it is possible to track the state of the U.S. and European economies using the models developed here, as long as appropriate techniques to reduce the dimensionality of the databases are implemented - canonical correlations coupled with principal component analysis. Depending on the cutoffs chosen, the models predict recessions in real time with an accuracy of 98% and 80%, respectively, for the U.S. and the Euro Area. |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:bcb:wpaper:587&r=ets |