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Time Series R Example

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> n = 35

> t = 1:n

> y1 = c(294,260,265,260,331,314,288,331,417,426,355,353,310,278,302,260,307,275,266,300,287,302,298,323,291,258,287,266,288,313,355,326,367,373,380)

> y2 = c(268,225,266,230,268,252,287,287,363,371,325,279,275,196,248,193,241,248,253,294,282,280,284,269,266,267,268,258,272,269,290,326,307,339,349)

> x = matrix(c(rep(1,n),1:n),n,2)

> y1

 [1] 294 260 265 260 331 314 288 331 417 426 355 353 310 278 302 260 307

[18] 275 266 300 287 302 298 323 291 258 287 266 288 313 355 326 367 373

[35] 380

> y2

 [1] 268 225 266 230 268 252 287 287 363 371 325 279 275 196 248 193 241

[18] 248 253 294 282 280 284 269 266 267 268 258 272 269 290 326 307 339

[35] 349

> solve(t(x)%*%x)

             [,1]         [,2]

[1,]  0.119327731 -0.005042017

[2,] -0.005042017  0.000280112

> beta = solve(t(x)%*%x)%*%(t(x)%*%y1)

> beta

            [,1]

[1,] 300.1949580

[2,]   0.6336134

> beta2 = solve(t(x)%*%x)%*%(t(x)%*%y2)

> beta2

           [,1]

[1,] 258.183193

[2,]   1.045378

> u = solve(t(x)%*%x)

> u

             [,1]         [,2]

[1,]  0.119327731 -0.005042017

[2,] -0.005042017  0.000280112

> e = y1-x%*%beta

> s = sqrt(sum(e^2)/(n-2))

> s

[1] 44.07472

> e2 = y2-x%*%beta2

> s2 = sqrt(sum(e2^2)/(n-2))

> s2

[1] 39.51243

> d1 = sum((e[1:34]-e[2:35])^2)/sum(e^2)

> d2 = sum((e2[1:34]-e2[2:35])^2)/sum(e2^2)

> d1;d2

[1] 0.6408324

[1] 0.7310235

> d2

[1] 0.7310235

> sd = c(s*sqrt(u[1,1]),s*sqrt(u[2,2]))

> sd2 = c(s2*sqrt(u[1,1]),s2*sqrt(u[2,2]))

> sd;sd2

[1] 15.2251029  0.7376586

[1] 13.6491115  0.6613016

> sd2

[1] 13.6491115  0.6613016

> rsqr1 = 1-sum(e^2)/sum

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