SESIÓN 4. Función de Transferencia y ARIMAX en R

Módelo de Función de Transferencia

Funciones de transferencia utilizando el Índice Global de la Actividad Económica

\underline{Nota}. Con este código se pueden pronósticar series de tiempo multivariadas

Análisis Preliminar

remove(list = ls())

Activar librerías

#install.packages("devtools")
#devtools::install_github("r-lib/conflicted")
library(conflicted)
library(readxl)
library(dplyr)
library(stats)
library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ forcats   1.0.0     ✔ readr     2.1.5
✔ ggplot2   3.5.1     ✔ stringr   1.5.1
✔ lubridate 1.9.3     ✔ tibble    3.2.1
✔ purrr     1.0.2     ✔ tidyr     1.3.1

library(tseries)

Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 

library(urca)
library(forecast)

Importar datos

#getwd()
sales_x <- read_excel("dataseries.xlsx")
sales_x <- ts(sales_x, start = c(2014,01), frequency = 12)
head(sales_x)

           sales      igae
Jan 2014 1290114  98.69242
Feb 2014 1035753  96.92693
Mar 2014 1239129 101.10788
Apr 2014 1264683 100.32346
May 2014 1133499 104.89845
Jun 2014 1215006 102.80824

ts.plot(sales_x, col = c(1, 2),  lwd = c(1, 2)) # la roja IGAE

Gráfico de datos en niveles

ts.plot(scale(sales_x), col = c(1, 2),  lwd = c(1, 2)) # la roja IGAE

Prueba de estacionariedad para las ventas

adf.test(sales_x[,1])

    Augmented Dickey-Fuller Test

data:  sales_x[, 1]
Dickey-Fuller = -3.3512, Lag order = 4, p-value = 0.07011
alternative hypothesis: stationary

ur.kpss(sales_x[,1]) %>% summary() 

####################### 
# KPSS Unit Root Test # 
####################### 

Test is of type: mu with 3 lags. 

Value of test-statistic is: 1.5454 

Critical value for a significance level of: 
                10pct  5pct 2.5pct  1pct
critical values 0.347 0.463  0.574 0.739

• Los datos en niveles no son estacionarios

ur.kpss(diff(sales_x[,1])) %>% summary()

####################### 
# KPSS Unit Root Test # 
####################### 

Test is of type: mu with 3 lags. 

Value of test-statistic is: 0.0281 

Critical value for a significance level of: 
                10pct  5pct 2.5pct  1pct
critical values 0.347 0.463  0.574 0.739

• Los datos diferenciados son estacionarios

Prueba de estacionariedad para el IGAE

ur.kpss(sales_x[,2]) %>% summary()

####################### 
# KPSS Unit Root Test # 
####################### 

Test is of type: mu with 3 lags. 

Value of test-statistic is: 1.7413 

Critical value for a significance level of: 
                10pct  5pct 2.5pct  1pct
critical values 0.347 0.463  0.574 0.739

• Los datos en niveles no son estacionarios

ur.kpss(diff(sales_x[,2])) %>% summary()

####################### 
# KPSS Unit Root Test # 
####################### 

Test is of type: mu with 3 lags. 

Value of test-statistic is: 0.0377 

Critical value for a significance level of: 
                10pct  5pct 2.5pct  1pct
critical values 0.347 0.463  0.574 0.739

• Los datos diferenciados son estacionarios

Modelo ARIMAX

NOTA.

Donde cada dato significa:

• AR representa una regresión de la variable con otros valores pasados de ella misma
• MA representa la media móvil ponderada de los errores pasados del pronóstico
• X representa una variable o un conjunto de variables explicativas

---

Combinando los dos modelos:

• p = parte autorregresiva
• d = grado de diferenciación
• q = parte media movil

library(forecast)
tsdisplay(sales_x[,1])

tsdisplay(diff(sales_x[,1]))

mod=arima(sales_x[,1],xreg=sales_x[,2],order = c(1,1,2),seasonal = list(order=c(1,0,1)))
mod

Call:
arima(x = sales_x[, 1], order = c(1, 1, 2), seasonal = list(order = c(1, 0, 
    1)), xreg = sales_x[, 2])

Coefficients:
          ar1      ma1      ma2    sar1     sma1  sales_x[, 2]
      -0.2104  -0.5070  -0.0664  0.6822  -0.3585     -12469.64
s.e.   0.7300   0.7263   0.5149  0.2644   0.3465      11414.03

sigma^2 estimated as 7.693e+10:  log likelihood = -1033.97,  aic = 2081.93

plot(mod$residuals)

nsdiffs(sales_x[,1])

[1] 0

tsdiag(mod)

Box.test(mod$residuals)

    Box-Pierce test

data:  mod$residuals
X-squared = 0.0066918, df = 1, p-value = 0.9348

checkresiduals(mod)

    Ljung-Box test

data:  Residuals from ARIMA(1,1,2)(1,0,1)[12]
Q* = 6.3055, df = 10, p-value = 0.789

Model df: 5.   Total lags used: 15

Selección automática del modelo ARIMA

modelo_x <- auto.arima(sales_x[,1], xreg = sales_x[,2], seasonal=T, stepwise=T, approximation=T)
summary(modelo_x)

Series: sales_x[, 1] 
Regression with ARIMA(0,1,1)(0,0,2)[12] errors 

Coefficients:
          ma1    sma1    sma2       xreg
      -0.6906  0.3294  0.2178  -13458.06
s.e.   0.1030  0.1179  0.1284   12046.14

sigma^2 = 8.303e+10:  log likelihood = -1034.58
AIC=2079.15   AICc=2080.03   BIC=2090.67

Training set error measures:
                   ME     RMSE      MAE        MPE     MAPE     MASE
Training set 25449.17 278377.7 179495.1 -0.2161992 10.65046 0.666288
                    ACF1
Training set -0.04421421

checkresiduals(modelo_x)

    Ljung-Box test

data:  Residuals from Regression with ARIMA(0,1,1)(0,0,2)[12] errors
Q* = 6.6078, df = 12, p-value = 0.8824

Model df: 3.   Total lags used: 15

• Los residuales no están correlacionados

Pronóstico

autoplot(forecast(modelo_x, xreg = rep(mean(sales_x[,2]),36), h=36))

autoplot(forecast(modelo_x, xreg = rep(mean(sales_x[,2]),12), h=12))

pron=forecast(modelo_x, xreg = rep(mean(sales_x[,2]),12), h=12)
pron

         Point Forecast   Lo 80   Hi 80   Lo 95   Hi 95
Apr 2020        2099024 1729745 2468303 1534261 2663787
May 2020        1960469 1573919 2347019 1369292 2551646
Jun 2020        2021897 1618816 2424979 1405437 2638357
Jul 2020        2067965 1649004 2486927 1427219 2708711
Aug 2020        2090937 1656676 2525198 1426792 2755082
Sep 2020        2032742 1583703 2481781 1345996 2719489
Oct 2020        2218855 1755508 2682202 1510227 2927483
Nov 2020        2196921 1719696 2674147 1467068 2926775
Dec 2020        1797502 1306790 2288214 1047023 2547981
Jan 2021        2084239 1580401 2588076 1313686 2854792
Feb 2021        2014117 1497487 2530746 1224000 2804233
Mar 2021        2063566 1534454 2592679 1254359 2872774

Práctica. Análisis con módelos económicos

Activar librerías

library(readxl)
library(tidyverse)
library(tseries)
library(urca)
library(forecast)
library(zoo)

Importando datos de precios de cierre de Starbucks y Microsoft

library(readr)
sbux.df <- read_csv("sbuxPrices.csv")

Rows: 181 Columns: 2
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Date, Adj.Close

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

View(sbux.df)

sbux.ts = ts(data=sbux.df$Adj.Close, frequency = 12,
             start=c(1993,3), end=c(2008,3))
class(sbux.ts) 

[1] "ts"

msft.df <- read_csv("msftPrices.csv")

Rows: 181 Columns: 2
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Date, Adj.Close

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

View(sbux.df)
msft.ts = ts(data=msft.df$Adj.Close, frequency = 12,
             start=c(1993,3), end=c(2008,3))

Fechas y frecuencia de la serie

sbux.ts 

       Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec
1993             1.13  1.15  1.43  1.46  1.41  1.44  1.63  1.59  1.32  1.32 
1994 1.43  1.38  1.45  1.77  1.69  1.5   1.72  1.68  1.37  1.61  1.59  1.63 
1995 1.43  1.42  1.43  1.4   1.73  2.12  2.22  2.38  2.25  2.33  2.51  2.5  
1996 1.99  02.09 2.77  3.22  3.22  3.36  03.09 3.89  3.92  3.86  4.12  3.4  
1997 04.07 4     3.52  3.55  3.74  4.63  4.87  4.87  4.97  3.92  4.15  4.56 
1998 4.35  4.7   5.39  5.72  5.71  6.35  4.98  3.75  4.3   5.16  5.48  6.67 
1999 6.19  6.29  6.67  8.78  8.77  8.93  5.53  5.44  5.89  6.46  6.31  5.76 
2000 7.61  8.35  10.65 7.19  08.08 09.08 8.91  8.71  9.52  10.62 10.83 10.52
2001 11.87 11.32 10.09 9.2   9.28  10.94 8.58  08.02 7.1   8.14  8.42  09.06
2002 11.3  10.94 11    10.85 11.54 11.81 9.33  9.56  9.82  11.33 10.34 9.69 
2003 10.8  11.15 12.25 11.18 11.73 11.67 12.99 13.5  13.69 15.02 15.3  15.77
2004 17.41 17.78 18.01 18.5  19.3  20.68 22.34 20.56 21.61 25.14 26.75 29.65
2005 25.67 24.63 24.56 23.54 26.05 24.56 24.98 23.31 23.82 26.89 28.95 28.54
2006 30.14 34.54 35.78 35.44 33.9  35.91 32.55 29.49 32.38 35.9  33.56 33.68
2007 33.22 29.38 29.82 29.5  27.4  24.95 25.37 26.2  24.91 25.37 22.24 19.46
2008 17.98 17.1  16.64                                                      

start(sbux.ts) 

[1] 1993    3

end(sbux.ts) 

[1] 2008    3

frequency(sbux.ts) 

[1] 12

Subconjunto de la serie de tiempo

tmp = sbux.ts[1:5] 
class(tmp)

[1] "character"

tmp = window(sbux.ts, start=c(1993, 3), end=c(1993,8))
class(tmp)

[1] "ts"

Combinando dos series (dos columnas)

sbuxmsft.ts = cbind(sbux.ts, msft.ts) 
class(sbuxmsft.ts) 

[1] "mts"    "ts"     "matrix" "array" 

• mts: multiple time series

Seleccionando las primeras 5 filas

window(sbuxmsft.ts, start=c(1993, 3), end=c(1993,7)) 

         sbux.ts   msft.ts
Mar 1993    1.13 1.849.489
Apr 1993    1.15 1.859.486
May 1993    1.43 1.794.505
Jun 1993    1.46 1.829.494
Jul 1993    1.41 1.794.505

Plot objeto ts

plot(sbux.ts, col="blue", lwd=2, ylab="Adjusted close",
     main="Monthly closing price of SBUX") 

Dibujar un subconjunto (acercar)

library(TSstudio)
autoplot(window(sbux.ts, start=c(2000,3), end=c(2008,3)),
      ylab="Adjusted close",col="blue", lwd=2,
      main="Monthly closing price of SBUX") 

Plot para múltiples columnas

Caso 1. En gráficos diferentes

autoplot(sbuxmsft.ts) 

Warning in data.frame(y = as.numeric(c(object)), x =
rep(as.numeric(time(object)), : NAs introducidos por coerción

Caso 2. En el mismo gráfico

plot(sbuxmsft.ts, plot.type="single", lwd=2, ylim=c(0,180),
      main="Monthly closing prices on SBUX and MSFT",
      ylab="Adjusted close price",
      col=c("blue", "red"), lty=1:2)

Warning in xy.coords(x = matrix(rep.int(tx, k), ncol = k), y = x, log = log, :
NAs introducidos por coerción

Warning in xy.coords(x, y): NAs introducidos por coerción

legend(1994, 35, legend=c("SBUX","MSFT"), col=c("blue", "red"),
          lty=1:2)

• Activar librería zoo

library(zoo) 

Fecha

td = seq(as.Date("1993/3/1"), as.Date("2008/3/1"), "months") 
class(td) 

[1] "Date"

head(td) 

[1] "1993-03-01" "1993-04-01" "1993-05-01" "1993-06-01" "1993-07-01"
[6] "1993-08-01"

Alternativa

td2 = as.Date(sbux.df$Date, format="%m/%d/%Y") 
head(td2) 

[1] "1993-03-31" "1993-04-01" "1993-05-03" "1993-06-01" "1993-07-01"
[6] "1993-08-02"

Combinando el índice de tiempo a las dos series de precios

sbux.z = zoo(x=sbux.df$Adj.Close, order.by=td) 
msft.z = zoo(x=msft.df$Adj.Close, order.by=td) 

class(sbux.z) 

[1] "zoo"

str(sbux.z) 

'zoo' series from 1993-03-01 to 2008-03-01
  Data: chr [1:181] "1.13" "1.15" "1.43" "1.46" "1.41" "1.44" "1.63" "1.59" "1.32" ...
  Index:  Date[1:181], format: "1993-03-01" "1993-04-01" "1993-05-01" "1993-06-01" "1993-07-01" ...

head(sbux.z) 

1993-03-01 1993-04-01 1993-05-01 1993-06-01 1993-07-01 1993-08-01 
      1.13       1.15       1.43       1.46       1.41       1.44 

Extrayendo el índice de tiempo y los datos

index(sbux.z) 

  [1] "1993-03-01" "1993-04-01" "1993-05-01" "1993-06-01" "1993-07-01"
  [6] "1993-08-01" "1993-09-01" "1993-10-01" "1993-11-01" "1993-12-01"
 [11] "1994-01-01" "1994-02-01" "1994-03-01" "1994-04-01" "1994-05-01"
 [16] "1994-06-01" "1994-07-01" "1994-08-01" "1994-09-01" "1994-10-01"
 [21] "1994-11-01" "1994-12-01" "1995-01-01" "1995-02-01" "1995-03-01"
 [26] "1995-04-01" "1995-05-01" "1995-06-01" "1995-07-01" "1995-08-01"
 [31] "1995-09-01" "1995-10-01" "1995-11-01" "1995-12-01" "1996-01-01"
 [36] "1996-02-01" "1996-03-01" "1996-04-01" "1996-05-01" "1996-06-01"
 [41] "1996-07-01" "1996-08-01" "1996-09-01" "1996-10-01" "1996-11-01"
 [46] "1996-12-01" "1997-01-01" "1997-02-01" "1997-03-01" "1997-04-01"
 [51] "1997-05-01" "1997-06-01" "1997-07-01" "1997-08-01" "1997-09-01"
 [56] "1997-10-01" "1997-11-01" "1997-12-01" "1998-01-01" "1998-02-01"
 [61] "1998-03-01" "1998-04-01" "1998-05-01" "1998-06-01" "1998-07-01"
 [66] "1998-08-01" "1998-09-01" "1998-10-01" "1998-11-01" "1998-12-01"
 [71] "1999-01-01" "1999-02-01" "1999-03-01" "1999-04-01" "1999-05-01"
 [76] "1999-06-01" "1999-07-01" "1999-08-01" "1999-09-01" "1999-10-01"
 [81] "1999-11-01" "1999-12-01" "2000-01-01" "2000-02-01" "2000-03-01"
 [86] "2000-04-01" "2000-05-01" "2000-06-01" "2000-07-01" "2000-08-01"
 [91] "2000-09-01" "2000-10-01" "2000-11-01" "2000-12-01" "2001-01-01"
 [96] "2001-02-01" "2001-03-01" "2001-04-01" "2001-05-01" "2001-06-01"
[101] "2001-07-01" "2001-08-01" "2001-09-01" "2001-10-01" "2001-11-01"
[106] "2001-12-01" "2002-01-01" "2002-02-01" "2002-03-01" "2002-04-01"
[111] "2002-05-01" "2002-06-01" "2002-07-01" "2002-08-01" "2002-09-01"
[116] "2002-10-01" "2002-11-01" "2002-12-01" "2003-01-01" "2003-02-01"
[121] "2003-03-01" "2003-04-01" "2003-05-01" "2003-06-01" "2003-07-01"
[126] "2003-08-01" "2003-09-01" "2003-10-01" "2003-11-01" "2003-12-01"
[131] "2004-01-01" "2004-02-01" "2004-03-01" "2004-04-01" "2004-05-01"
[136] "2004-06-01" "2004-07-01" "2004-08-01" "2004-09-01" "2004-10-01"
[141] "2004-11-01" "2004-12-01" "2005-01-01" "2005-02-01" "2005-03-01"
[146] "2005-04-01" "2005-05-01" "2005-06-01" "2005-07-01" "2005-08-01"
[151] "2005-09-01" "2005-10-01" "2005-11-01" "2005-12-01" "2006-01-01"
[156] "2006-02-01" "2006-03-01" "2006-04-01" "2006-05-01" "2006-06-01"
[161] "2006-07-01" "2006-08-01" "2006-09-01" "2006-10-01" "2006-11-01"
[166] "2006-12-01" "2007-01-01" "2007-02-01" "2007-03-01" "2007-04-01"
[171] "2007-05-01" "2007-06-01" "2007-07-01" "2007-08-01" "2007-09-01"
[176] "2007-10-01" "2007-11-01" "2007-12-01" "2008-01-01" "2008-02-01"
[181] "2008-03-01"

coredata(sbux.z) 

  [1] "1.13"  "1.15"  "1.43"  "1.46"  "1.41"  "1.44"  "1.63"  "1.59"  "1.32" 
 [10] "1.32"  "1.43"  "1.38"  "1.45"  "1.77"  "1.69"  "1.5"   "1.72"  "1.68" 
 [19] "1.37"  "1.61"  "1.59"  "1.63"  "1.43"  "1.42"  "1.43"  "1.4"   "1.73" 
 [28] "2.12"  "2.22"  "2.38"  "2.25"  "2.33"  "2.51"  "2.5"   "1.99"  "02.09"
 [37] "2.77"  "3.22"  "3.22"  "3.36"  "03.09" "3.89"  "3.92"  "3.86"  "4.12" 
 [46] "3.4"   "04.07" "4"     "3.52"  "3.55"  "3.74"  "4.63"  "4.87"  "4.87" 
 [55] "4.97"  "3.92"  "4.15"  "4.56"  "4.35"  "4.7"   "5.39"  "5.72"  "5.71" 
 [64] "6.35"  "4.98"  "3.75"  "4.3"   "5.16"  "5.48"  "6.67"  "6.19"  "6.29" 
 [73] "6.67"  "8.78"  "8.77"  "8.93"  "5.53"  "5.44"  "5.89"  "6.46"  "6.31" 
 [82] "5.76"  "7.61"  "8.35"  "10.65" "7.19"  "08.08" "09.08" "8.91"  "8.71" 
 [91] "9.52"  "10.62" "10.83" "10.52" "11.87" "11.32" "10.09" "9.2"   "9.28" 
[100] "10.94" "8.58"  "08.02" "7.1"   "8.14"  "8.42"  "09.06" "11.3"  "10.94"
[109] "11"    "10.85" "11.54" "11.81" "9.33"  "9.56"  "9.82"  "11.33" "10.34"
[118] "9.69"  "10.8"  "11.15" "12.25" "11.18" "11.73" "11.67" "12.99" "13.5" 
[127] "13.69" "15.02" "15.3"  "15.77" "17.41" "17.78" "18.01" "18.5"  "19.3" 
[136] "20.68" "22.34" "20.56" "21.61" "25.14" "26.75" "29.65" "25.67" "24.63"
[145] "24.56" "23.54" "26.05" "24.56" "24.98" "23.31" "23.82" "26.89" "28.95"
[154] "28.54" "30.14" "34.54" "35.78" "35.44" "33.9"  "35.91" "32.55" "29.49"
[163] "32.38" "35.9"  "33.56" "33.68" "33.22" "29.38" "29.82" "29.5"  "27.4" 
[172] "24.95" "25.37" "26.2"  "24.91" "25.37" "22.24" "19.46" "17.98" "17.1" 
[181] "16.64"

Start and End

start(sbux.z) 

[1] "1993-03-01"

end(sbux.z)

[1] "2008-03-01"

• Ventaja de zoo: extraer subconjunto indexando con las fechas

sbux.z[as.Date(c("2000/3/1", "2003/3/1"))]

2000-03-01 2003-03-01 
     10.65      12.25 

• window() es una alternativa funcional

window(sbux.z, start=as.Date("2000/3/1"), end=as.Date("2003/3/1")) 

2000-03-01 2000-04-01 2000-05-01 2000-06-01 2000-07-01 2000-08-01 2000-09-01 
     10.65       7.19      08.08      09.08       8.91       8.71       9.52 
2000-10-01 2000-11-01 2000-12-01 2001-01-01 2001-02-01 2001-03-01 2001-04-01 
     10.62      10.83      10.52      11.87      11.32      10.09        9.2 
2001-05-01 2001-06-01 2001-07-01 2001-08-01 2001-09-01 2001-10-01 2001-11-01 
      9.28      10.94       8.58      08.02        7.1       8.14       8.42 
2001-12-01 2002-01-01 2002-02-01 2002-03-01 2002-04-01 2002-05-01 2002-06-01 
     09.06       11.3      10.94         11      10.85      11.54      11.81 
2002-07-01 2002-08-01 2002-09-01 2002-10-01 2002-11-01 2002-12-01 2003-01-01 
      9.33       9.56       9.82      11.33      10.34       9.69       10.8 
2003-02-01 2003-03-01 
     11.15      12.25 

Combinando dos series

sbuxmsft.z = cbind(sbux.z, msft.z) 
class(sbuxmsft.z) 

[1] "zoo"

head(sbuxmsft.z) 

           sbux.z msft.z   
1993-03-01 1.13   1.849.489
1993-04-01 1.15   1.859.486
1993-05-01 1.43   1.794.505
1993-06-01 1.46   1.829.494
1993-07-01 1.41   1.794.505
1993-08-01 1.44   1.804.501

Plot

plot(sbux.z, col="blue", lty=1, lwd=2, ylim=c(0,50),main="Monthly closing prices of SBUX and MFST",
     ylab="Adjusted close price")
lines(msft.z, col="red", lty=2, lwd=2)

Warning in xy.coords(x, y): NAs introducidos por coerción

legend(x="topleft", legend=c("SBUX","MSFT"), col=c("blue","red"),
         lty=1:2)

Alternativa (Las dos a la vez)

plot(sbuxmsft.z, plot.type="single", col=c("blue","red"), lty=1:2,
         lwd=2,ylim=c(0,50),main="Monthly closing prices of SBUX and MFST",
         ylab="Adjusted close price")

Warning in xy.coords(x, y): NAs introducidos por coerción

legend(x="topleft", legend=c("SBUX","MSFT"), col=c("blue","red"),
         lty=1:2) 

Importar datos directamente como objeto zoo

sbux.z2 = read.zoo("sbuxPrices.csv",
                   format="%m/%d/%Y", sep=",", header=T) 

Importar datos de Yahoo Finance

library(tseries)
SBUX.z = get.hist.quote(instrument="sbux", start="1993-03-01",
                           end="2020-06-01", quote="AdjClose",
                           provider="yahoo", origin="1970-01-01",
                           compression="d", retclass="zoo") 

time series ends   2020-05-29

View(SBUX.z)

MSFT.z = get.hist.quote(instrument="msft", start="1993-03-01",
                        end="2020-06-01", quote="AdjClose",
                        provider="yahoo", origin="1970-01-01",
                        compression="d", retclass="zoo") 

time series ends   2020-05-29

Plot

plot(cbind(SBUX.z,MSFT.z), plot.type="single", col=c("blue","red"), lty=1:2,
     lwd=2,main="Monthly closing prices of SBUX and MFST",
     ylab="Adjusted close price")
legend(x="topleft", legend=c("SBUX","MSFT"), col=c("blue","red"),
       lty=1:2)

Librería dygraphs

library(dygraphs)
dygraph(SBUX.z, "Monthly closing prices of SBUX")

dygraph(cbind(SBUX.z,MSFT.z), "Monthly closing prices of SBUX and MFST")

• 3 Datos diarios

Generamos datos aleatorios

datos <- rnorm(78, 0, 10)
fechas <- seq(as.Date("2020-03-06"), as.Date("2020-05-22"), by = "day")
as.numeric(format(fechas[1], "%j"))

[1] 66

miserie.ts<-ts(datos,start=c(2016,66), frequency=365)
plot(miserie.ts)

library(zoo)
miserie.z=zoo(datos, fechas)
plot(miserie.z)

dygraph(miserie.z)