Fe-Mn-Si-based shape memory alloys are the most favorable for largescale applications owing to low cost, good workability, good machinability, and good weldability. However, polycrystalline Fe-Mn-Si-based shape memory alloys have low recovery strains of only 2-3% after solution treatment, although monocrystalline ones reach a large recovery strain of %9%. This review gives an overview of the improvement of recovery strains for polycrystalline Fe-Mn-Si-based shape memory alloys. It is proposed that two fundamental aspects, that is, composition design and microstructure design, shall be satisfied for obtaining large recovery strains of above 6%. Alloying compositions determining the ceiling of recovery strains shall follow three guidelines: (i) Si content is 5-6 wt%; (ii) 20 wt% Mn 32 wt%; (iii) addition of elements strongly strengthening austenite matrix. Microstructure design includes coarsening austenitic grains and reducing twin boundaries as far as possible together with introducing a high density of stacking faults and second phases of strengthening austenite.
This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standardized residuals. We then study two portmanteau statistics, called Q1(M) and Q2(M), for model checking. A residual-based bootstrap method is provided and demonstrated as an effective way to approximate the diagnostic checking statistics. Simulations are used to compare the performance of the proposed statistics with other methods available in the literature. In addition, we also investigate the effect of GARCH shocks on checking a fitted VARMA model. Empirical sizes and powers of the proposed statistics are investigated and the results suggest a procedure of using jointly Q1(M) and Q2(M) in diagnostic checking. The bivariate time series of FTSE 100 and DAX index returns is used to illustrate the performance of the proposed portmanteau statistics. The results show that it is important to consider the cross-product series of standardized residuals and GARCH effects in model checking
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