Recent Theoretical Results for Time Series Models with GARCH Errors

2002 ◽  
Vol 16 (3) ◽  
pp. 245-269 ◽  
Author(s):  
W. K. Li ◽  
Shiqing Ling ◽  
Michael McAleer
2018 ◽  
Vol 38 (2) ◽  
pp. 317-357
Author(s):  
Maciej Kawecki ◽  
Roman Różański ◽  
Grzegorz Chłapiński ◽  
Marcin Hławka ◽  
Krzysztof Jamróz ◽  
...  

In the paper, the construction of unconditional bootstrap prediction intervals and regions for some class of second order stationary multivariate linear time series models is considered. Our approach uses the sieve bootstrap procedure introduced by Kreiss 1992 and Bühlmann 1997. Basic theoretical results concerning consistency of the bootstrap replications and the bootstrap prediction regions are proved. We present a simulation study comparing the proposed bootstrap methods with the Box–Jenkins approach.


2020 ◽  
Vol 19 ◽  

Some methods for estimating VARMA models, and Multivariate Time Series Models in general, rely on the use of a Hankel matrix. Some authors suggest taking a larger dimension than theoretically necessary for this matrix. If the data sample is populous enough and the Hankel matrix dimension is unnecessarily large, this may result in an unnecessary number of computations, as well as in worse numerical and statistical results. We provide some theoretical results to know which is the Hankel matrix with the lowest dimension that is theoretically necessary and illustrate, with several simulated VARMA models, that using a dimension of the Hankel matrix greater than the theoretical minimal dimension proposed as valid does not necessarily lead to improved estimates. Although we use two algorithms, our main contributions are independent of the estimation method considered. We note that our paper does not include any comparisons between different algorithms for estimating VARMA models, as this is not our aim.


Marketing ZFP ◽  
2010 ◽  
Vol 32 (JRM 1) ◽  
pp. 24-29
Author(s):  
Marnik G. Dekimpe ◽  
Dominique M. Hanssens

2020 ◽  
Vol 5 (1) ◽  
pp. 374
Author(s):  
Pauline Jin Wee Mah ◽  
Nur Nadhirah Nanyan

The main purpose of this study is to compare the performances of univariate and bivariate models on four time series variables of the crude palm oil industry in Peninsular Malaysia. The monthly data for the four variables, which are the crude palm oil production, price, import and export, were obtained from Malaysian Palm Oil Board (MPOB) and Malaysian Palm Oil Council (MPOC). In the first part of this study, univariate time series models, namely, the autoregressive integrated moving average (ARIMA), fractionally integrated autoregressive moving average (ARFIMA) and autoregressive autoregressive (ARAR) algorithm were used for modelling and forecasting purposes. Subsequently, the dependence between any two of the four variables were checked using the residuals’ sample cross correlation functions before modelling the bivariate time series. In order to model the bivariate time series and make prediction, the transfer function models were used. The forecast accuracy criteria used to evaluate the performances of the models were the mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). The results of the univariate time series showed that the best model for predicting the production was ARIMA  while the ARAR algorithm were the best forecast models for predicting both the import and export of crude palm oil. However, ARIMA  appeared to be the best forecast model for price based on the MAE and MAPE values while ARFIMA  emerged the best model based on the RMSE value.  When considering bivariate time series models, the production was dependent on import while the export was dependent on either price or import. The results showed that the bivariate models had better performance compared to the univariate models for production and export of crude palm oil based on the forecast accuracy criteria used.


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