UNIVERSIDAD CUAUHTÉMOC PLANTEL AGUASCALIENTES

EDUCACIÓN A DISTANCIA

Maestría en Ciencia de los Datos y

Procesamiento de Datos Masivos

(Big-Data)

Segundo Cuatrimestre

Sergio Andrés Fonseca Chitiva

MODELOS ESTADÍSTICOS DINÁMICOS

Nombre del profesor

Jonás Velasco Alvares

Fecha de entrega

Noviembre 01 2015

“EXCELENTES PROFESIONISTAS, MEJORES SERES HUMANOS”

Descripción de la Actividad(es): El alumno deberá realizar el ejercicio 1 y 7 del capítulo 3 dentro del MATERIAL II 1. Para realizar los ejercicios, los datos se encuentran en el recurso DATOS III 2. Enviar en un archivo PDF el desarrollo de los ejercicios. Desarrollo de la actividad(es): 3.6 Exercises 1. a) Describe the association and calculate the ccf between x and y for k equal to 1, 10, and 100. > w <- 1:100 > x <- w + k * rnorm(100) > y <- w + k * rnorm(100) > ccf(x, y)

Nombre de la Unidad. Ejercicio de la unidad 3

Objetivo de la Unidad. Realizar los ejercicios indicados para este capitulo.

Respecto a x,y están relacionadas de una forma lineal puesto que respeto al tiempo esta sustrayendo el t, donde la variable de correlación disminuye a medida que aumenta la variable k b) Describe the association between x and y, and calculate the ccf. > Time <- 1:370 > x <- sin(2 * pi * Time / 37) > y <- sin(2 * pi * (Time + 4) / 37)

Investigate the effect of adding independent random variation to x and y.

Las variables x y ondas sinusoidales Y tanto seguir de período de 37 veces unidades, con x la zaga y por 4 unidades de tiempo. La relación entre las variables se pueden ver usando plot (x, y) que muestra x,y tienen una relación no lineal dispersa sobre una elíptica camino. 7. Continue the following exploratory time series analysis using the global temperature series from §1.4.5.

a) Produce a time plot of the data. Plot the aggregated annual mean series and a boxplot that summarises the observed values for each season, and comment on the plots. www <- "C:/global.dat" Global <- scan(www) Global.ts <- ts(Global, st = c(1856, 1), end = c(2005, 12),fr = 12) plot(Global.ts) plot(aggregate(Global.ts)) boxplot(Global.ts ~ cycle(Global.ts))

www <- "C:/global.dat"

b) Decompose the series into the components trend, seasonal effect, and residuals, and plot the decomposed series. Produce a plot of the trend with a superimposed seasonal effect. plot(decompose(Global.ts)) Global.decom <- decompose(Global.ts, type = "mult") plot(Global.decom) Trend <- Global.decom$trend Seasonal <- Global.decom$seasonal ts.plot(cbind(Trend, Trend * Seasonal), lty = 1:2)

b) Plot the correlogram of the residuals from question 7b. Comment on the plot, explaining any ‘significant’ correlations at significant lags. acf(Global.ts, xlab = 'lag (months)', main="")

c) Fit an appropriate Holt-Winters model to the monthly data. Explain why you chose that particular Holt-Winters model, and give the parameter estimates. www <- "C:/global.dat" Global.dat <- read.table(www, header = T); attach(Global.dat) Global.ts <- ts(Global, st = c(1856, 1), end = c(2005, 12),fr = 12) plot(Global.ts, xlab = "Time / months", ylab = "Complaints")

> Comp.hw1 <- HoltWinters(Global.ts, beta = 0, gamma = 0) ; Comp.hw1 Holt-Winters exponential smoothing with trend and additive seasonal component.

Call: HoltWinters(x = Global.ts, beta = 0, gamma = 0) Smoothing parameters: alpha: 0.2739402 beta : 0 gamma: 0 Coefficients: [,1] a 0.455717898 b -0.011593386 s1 0.005628472 s2 0.301878472 s3 -0.067454861 s4 -0.217163194 s5 -0.141163194 s6 0.117961806 s7 0.146878472 s8 0.147295139 s9 -0.016538194 s10 -0.046079861 s11 -0.270329861 s12 0.039086806

>

d) Using the fitted model, forecast values for the years 2005–2010. Add these forecasts to a time plot of the original series. Under what circumstances would these forecasts be valid? What comments of caution would you make to an economist or politician who wanted to use these forecasts to make statements about the potential impact of global warming on the world economy?

> sweetw.hw ; sweetw.hw$coef ; sweetw.hw$SSE Holt-Winters exponential smoothing with trend and multiplicative seasonal component. Call: HoltWinters(x = sweetw.ts, seasonal = "mult") Smoothing parameters: alpha: 0.1318678 beta : 0.01806184 gamma: 0.2098766 Coefficients: [,1] a -0.454634140 b -0.004121177 s1 0.905377892 s2 0.604204844 s3 0.920640265 s4 0.992255863 s5 0.938399013 s6 0.529044547 s7 0.536223475 s8 0.492175735 s9 0.836452811 s10 0.846716956 s11 1.389375941 s12 0.876335635 a b s1 s2 s3 s4 -0.454634140 -0.004121177 0.905377892 0.604204844 0.920640265 0.992255863 s5 s6 s7 s8 s9 s10 0.938399013 0.529044547 0.536223475 0.492175735 0.836452811 0.846716956 s11 s12 1.389375941 0.876335635 [1] 5.064764

>

www <- "C:/global.dat" Global.dat <- read.table(www, header = T); attach(Global.dat) sweetw.ts <- ts(global, start = c(2005,1), end = c(2010, 12),freq = 12) plot(sweetw.ts, xlab= "Time (months)", ylab = "sales (1000 litres)") sweetw.hw <- HoltWinters (sweetw.ts, seasonal = "mult") sweetw.hw ; sweetw.hw$coef ; sweetw.hw$SSE

sqrt(sweetw.hw$SSE/length(Global)) sd(Global) plot (sweetw.hw$fitted) plot (sweetw.hw)