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on Econometric Time Series |
| By: | Manabu Asai (Faculty of Economics Soka University, Japan.); Shelton Peiris (School of Mathematics and Statistics University of Sydney, Australia.); Michael McAleer (Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute Erasmus School of Economics Erasmus University Rotterdam, The Netherlands and Department of Quantitative Economics Complutense University of Madrid, Spain And Institute of Advanced Sciences Yokohama National University, Japan.) |
| Abstract: | In recent years fractionally differenced processes have received a great deal of attention due to their exibility in nancial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum. Forestimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the rst step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the nite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against theRSV-GGLM model. We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory. |
| Keywords: | Stochastic Volatility; Realized Volatility Measure; Long Memory; Gegenbauer Polynomial; Seasonality; Whittle Likelihood. |
| JEL: | C18 C21 C58 |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:ucm:doicae:1726&r=ets |
| By: | Goodwin, Thomas (Tasmanian School of Business & Economics, University of Tasmania); Tian, Jing (Tasmanian School of Business & Economics, University of Tasmania) |
| Abstract: | We propose a state space modeling framework to evaluate a set of forecasts that target the same variable but are updated along the forecast horizon. The approach decomposes forecast errors into three distinct horizon-specific processes, namely, bias, rational error and implicit error, and attributes forecast revisions to corrections for these forecast errors. We derive the conditions under which forecasts that contain error that is irrelevant to the target can still present the second moment bounds of rational forecasts. By evaluating multi-horizon daily maximum temperature forecasts for Melbourne, Australia, we demonstrate how this modeling framework analyzes the dynamics of the forecast revision structure across horizons. Understanding forecast revisions is critical for weather forecast users to determine the optimal timing for their planning decision. |
| Keywords: | Rational forecasts, implicit forecasts, forecast revision structure, weather forecasts |
| JEL: | C32 C53 |
| Date: | 2017 |
| URL: | http://d.repec.org/n?u=RePEc:tas:wpaper:23745&r=ets |
| By: | Mika Meitz; Pentti Saikkonen |
| Abstract: | Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also attracted recent interest. This paper considers testing for regime switching when the regime switching probabilities are time-varying and depend on observed data (`observation-dependent regime switching'). Specifically, we consider the likelihood ratio test for observation-dependent regime switching in mixture autoregressive models. The testing problem is highly nonstandard, involving unidentified nuisance parameters under the null, parameters on the boundary, singular information matrices, and higher-order approximations of the log-likelihood. We derive the asymptotic null distribution of the likelihood ratio test statistic in a general mixture autoregressive setting using high-level conditions that allow for various forms of dependence of the regime switching probabilities on past observations, and we illustrate the theory using two particular mixture autoregressive models. The likelihood ratio test has a nonstandard asymptotic distribution that can easily be simulated, and Monte Carlo studies show the test to have satisfactory finite sample size and power properties. |
| Date: | 2017–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1711.03959&r=ets |
| By: | Buncic, Daniel (Financial Stability Department, Central Bank of Sweden) |
| Abstract: | Exponential smooth transition autoregressive (ESTAR) models are widely used in the international finance literature, particularly for the modelling of real exchange rates. We show that the exponential function is ill-suited as a regime weighting function because of two undesirable properties. Firstly, it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter , which governs the shape of the function, is ‘small’. This leads to an identification problem with respect to the transition function parameter and the slope vector, as both enter as a product into the conditional mean of the model. Secondly, the exponential regime weighting function can behave like an indicator function (or dummy variable) for very large values of the transition function parameter . This has the effect of ‘spuriously overfitting’ a small number of observations around the location parameter µ. We show that both of these effects lead to estimation problems in ESTAR models. We illustrate this by means of an empirical replication of a widely cited study, as well as a simulation exercise. |
| Keywords: | Exponential STAR; non-linear time series models; identification and estimation issues; exponential weighting function; real exchange rates; simulation analysis. |
| JEL: | C13 C15 C50 F30 F44 |
| Date: | 2017–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:rbnkwp:0344&r=ets |
| By: | AMBA OYON, Claude Marius; Mbratana, Taoufiki |
| Abstract: | This paper develops estimators for simultaneous equations with spatial autoregressive or spatial moving average error components. We derive a limited information estimator and a full information estimator. We give the generalized method of moments to get each coefficient of the spatial dependence of each equation in spatial autoregressive case as well as spatial moving average case. The results of our Monte Carlo suggest that our estimators are consistent. When we estimate the coefficient of spatial dependence it seems better to use instrumental variables estimator that takes into account simultaneity. We also apply these set of estimators on real data. |
| Keywords: | Panel data, SAR process, SMA process, Simultaneous equations, Spatial error components |
| JEL: | C13 C33 |
| Date: | 2017–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:82395&r=ets |
| By: | Søren Johansen (Department of Economics, University of Copenhagen and CREATES); Morten Ørregaard Nielsen (Department of Economics, University of Copenhagen Queen?s University and CREATES) |
| Abstract: | We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and show that the test statistic for the ususal CVAR model is asymptotically chi-squared distributed. Because the usual CVAR model lies on the boundary of the parameter space for the fractional CVAR in Johansen and Nielsen (2012a), the analysis requires the study of the fractional CVAR model on a slightly larger parameter space so that the CVAR model lies in the interior. This in turn implies some further analysis of the asymptotic properties of the fractional CVAR model. |
| Keywords: | Cointegration, fractional integration, likelihood inference, vector autoregressive model. |
| JEL: | C32 |
| Date: | 2017–10–31 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1723&r=ets |
| By: | Manabu Asai (Faculty of Economics, Soka University, Japan); Michael McAleer (Department of Quantitative Finance, National Tsing Hua University, Taiwan; Discipline of Business Analytics, University of Sydney Business School, Australia; Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, The Netherlands); Shelton Peiris (School of Mathematics and Statistics University of Sydney, Australia) |
| Abstract: | In recent years fractionally differenced processes have received a great deal of attention due to their flexibility in fi nancial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum. For estimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the fi rst step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against the RSV-GGLM model. We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory. |
| Keywords: | Stochastic Volatility; Realized Volatility Measure; Long Memory; Gegenbauer Polynomial; Seasonality; Whittle Likelihood |
| JEL: | C18 C21 C58 |
| Date: | 2017–11–03 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20170105&r=ets |
| By: | Svetunkov, Ivan; Boylan, John Edward |
| Abstract: | Intermittent demand forecasting is an important supply chain task, which is commonly done using methods based on exponential smoothing. These methods however do not have underlying statistical models, which limits their generalisation. In this paper we propose a general state-space model that takes intermittence of data into account, extending the taxonomy of exponential smoothing models. We show that this model has a connection with conventional non-intermittent state space models and underlies Croston’s and Teunter-Syntetos-Babai (TSB) forecasting methods. We discuss properties of the proposed models and show how a selection can be made between them in the proposed framework. We then conduct experiments on simulated data and on two real life datasets, demonstrating advantages of the proposed approach. |
| Keywords: | Intermittent demand, supply chain, forecasting, state-space models |
| JEL: | C53 |
| Date: | 2017–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:82487&r=ets |
| By: | Wang, Xiaohu (The Chinese University of Hong Kong); Yu, Jun (School of Economics, Singapore Management University) |
| Abstract: | This paper develops the asymptotic theory of the ordinary least squares estimator of the autoregressive (AR) coefficient in various AR models, when data is generated from trend-stationary models in different forms. It is shown that, depending on how the autoregression is specified, the commonly used right-tailed unit root tests may tend to reject the null hypothesis of unit root in favor of the explosive alternative. A new procedure to implement the right-tailed unit root tests is proposed. It is shown that when the data generating process is trend-stationary, the test statistics based on the proposed procedure cannot find evidence of explosiveness. Whereas, when the data generating process is mildly explosive, the unit root tests find evidence of explosiveness. Hence, the proposed procedure enables robust bubble testing under deterministic trends. Empirical implementation of the proposed procedure using data from the stock and the real estate markets in the US reveals some interesting findings. While our proposed procedure flags the same number of bubbles episodes in the stock data as the method developed in Phillips, Shi and Yu (2015a, PSY), the estimated termination dates by the proposed procedure match better with the data. For real estate data, all negative bubble episodes flagged by PSY are no longer regarded as bubbles by the proposed procedure. |
| Keywords: | Autoregressive regressions; right-tailed unit root test; explosive and mildly explosive processes; deterministic trends; coefficient-based statistic; t-statistic. |
| JEL: | C12 C22 G01 |
| Date: | 2017–09–22 |
| URL: | http://d.repec.org/n?u=RePEc:ris:smuesw:2017_014&r=ets |