ts927

1 sarima error

https://kh555069.shinyapps.io/tsshiny1/

sarima.for(x[1:(1274+110)],n.ahead = 1,2,0,5,3,1,4,7)

Error in optim(init[mask], armafn, method = optim.method, hessian = TRUE, : non-finite finite-difference value [2] In addition: Warning message: In log(s2) : NaNs produced

沒符合 stationary 導致 MLE 發散

ggtsdisplay(x,points = F, main = "")

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2 exponential smoothing with regressor

2.1 mdoels

• the change in the regressor : \(~\Delta_{z_1,t}=z_{1,t}-z_{1,t-1}~\) , where \(~z_{1,t}~\) is regressor.

• \(b_{1,t-1}\) is a growth for a unit change in the regressor \(~z_{1,t}\), \(b_{1,t-1}\) is NOT the time trend.

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2.1.1 ESWR(A,N,N,1,0)

additive error, none trend, none seasonality, with a time varying parameter of the regressor

\[ \left\{ \begin{array}\\ y_t=l_{t-1}+b_{1,t-1}\Delta_{z_1,t}+\varepsilon_t\\ l_t=l_{t-1}+b_{1,t-1}\Delta_{z_1,t}+\alpha\varepsilon_t\\ b_{1,t}=b_{1,t-1}+\beta_1\varepsilon_t /\Delta_{z_1,t}\\ \end{array} \right. \]

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2.1.2 ESWR(A,N,N,0,1)

additive error, none trend, none seasonality, with a time invariant regressor

\[ \left\{ \begin{array}\\ y_t=l_{t-1}+b_{1,t-1}\Delta_{z_1,t}+\varepsilon_t\\ l_t=l_{t-1}+b_{1,t-1}\Delta_{z_1,t}+\alpha\varepsilon_t\\ b_{1,t}=b_{1,t-1}\\ \end{array} \right . \]

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2.1.3 ESWR(A,N,A,1,0)

additive error, none trend, additive seasonality, with a time varying parameter of the regressor

\[ \left\{ \begin{array}\\ y_t=l_{t-1}+b_{1,t-1}\Delta_{z_1,t}+\varepsilon_t \\ l_t=l_{t-1}+b_{1,t-1}\Delta_{z_1,t}+\alpha\varepsilon_t \\ s_t=s_{t-m}+\gamma\varepsilon_t \\ b_{1,t}=b_{1,t-1}+\beta_1\varepsilon_t /\Delta_{z_1,t} \\ \end{array} \right . \]

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