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Engineering Statistics Handbook Episode 8 Part 14

Tham khảo tài liệu 'engineering statistics handbook episode 8 part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | with ỉ alí 1 at I 1 a2L Estimation of parameters and covariance matrix difficult The estimation of the matrix parameters and covariance matrix is complicated and very difficult without computer software. The estimation of the Moving Average matrices is especially an ordeal. If we opt to ignore the MA component s we are left with the ARV model given by ộl L-L 2 1-2 Ộịì L-ịì al where xt is a vector of observations X t x2t xnt at time t at is a vector of white noise a t a2t . ant at time t 6.4.5. Multivariate Time Series Models Diagonal The diagonal terms of each Phi matrix are the scalar estimates for each series terms of in this case Phi matrix 111 2 11 for the input series X 01 22 -2 22 for the output series Y. Transfer The lower off-diagonal elements represent the influence of the input on the mechanism output. This is called the transfer mechanism or transfer-function model as discussed by Box and Jenkins in Chapter 11. The Ộ terms here correspond to their ẵ terms. The upper off-diagonal terms represent the influence of the output on the input. Feedback This is called feedback . The presence of feedback can also be seen as a high value for a coefficient in the correlation matrix of the residuals. A true transfer model exists when there is no feedback. This can be seen by expressing the matrix form into scalar form 01.1 02.11 Í2 1 J2Ĩ í-1 2 12Í í-2 alí yt 0L221 Í-I - - 2 22Ỉfí-2 ộl L t-L H 2 1 í-2 H 2Í Delay Finally delay or dead time can be measured by studying the lower off-diagonal elements again. If for example 0121 is non-significant the delay is 1 time period. NIST SEMATECH HOME tools a AIDS search BACK NEXT http www.itl.nist.gov div898 handbook pmc section4 pmc45.htm 3 of 3 5 1 2006 10 35 31 AM 6.4.5.I. Example of Multivariate Time Series Analysis ENGINEERING STATISTICS HANDBOOK hW TOOLS 4 aids Isẽarch back Nixf 6. Process or Product Monitoring and Control 6.4. Introduction to Time Series Analysis 6.4.5. Multivariate Time Series Models 6.4.5.I. Example of .