Actividad 2

Ejemplo en clase : Poblacion

Instalar paquetes y llamar librerias

#install.packages("forecast")
library(forecast)

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

#install.packages("tidyverse")
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.0.4

## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Instalar base de datos

#file.choose()
poblacion <- read_csv("/Users/juanmauangers/Downloads/population.csv")

## Rows: 6020 Columns: 3
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): state
## dbl (2): year, population
## 
## 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.

Entender la base de datos

summary(poblacion)

##     state                year        population      
##  Length:6020        Min.   :1900   Min.   :   43000  
##  Class :character   1st Qu.:1930   1st Qu.:  901483  
##  Mode  :character   Median :1960   Median : 2359000  
##                     Mean   :1960   Mean   : 3726003  
##                     3rd Qu.:1990   3rd Qu.: 4541883  
##                     Max.   :2019   Max.   :39512223

str(poblacion)

## spc_tbl_ [6,020 × 3] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ state     : chr [1:6020] "AK" "AK" "AK" "AK" ...
##  $ year      : num [1:6020] 1950 1951 1952 1953 1954 ...
##  $ population: num [1:6020] 135000 158000 189000 205000 215000 222000 224000 231000 224000 224000 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   state = col_character(),
##   ..   year = col_double(),
##   ..   population = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>

head(poblacion)

## # A tibble: 6 × 3
##   state  year population
##   <chr> <dbl>      <dbl>
## 1 AK     1950     135000
## 2 AK     1951     158000
## 3 AK     1952     189000
## 4 AK     1953     205000
## 5 AK     1954     215000
## 6 AK     1955     222000

Serie de Tiempo en Texas

poblacion_texas <- poblacion %>% filter(state=="TX")
ggplot(poblacion_texas, aes(x=year, y=population)) +
  geom_line() +
  labs(title = "Poblacion de Texas", x ="Año", 
       y = "Poblacion")

ts_texas <- ts(poblacion_texas$population, start=1900, frequency = 1) # Serie de Tiempo Anual
# ts_texas <- ts(poblacion_texas$population, start=1900, frequency = 4) # Serie de Tiempo Trimestral
# ts_texas <- ts(poblacion_texas$population, start=1900, frequency = 12) # Serie de Tiempo mensual
arima_texas <- auto.arima(ts_texas)
summary(arima_texas)

## Series: ts_texas 
## ARIMA(0,2,2) 
## 
## Coefficients:
##           ma1      ma2
##       -0.5950  -0.1798
## s.e.   0.0913   0.0951
## 
## sigma^2 = 1.031e+10:  log likelihood = -1527.14
## AIC=3060.28   AICc=3060.5   BIC=3068.6
## 
## Training set error measures:
##                    ME     RMSE      MAE       MPE      MAPE      MASE
## Training set 12147.62 99818.31 59257.39 0.1046163 0.5686743 0.2672197
##                     ACF1
## Training set -0.02136734

pronostico_texas <- forecast(arima_texas, level = 95, h = 10)
pronostico_texas

##      Point Forecast    Lo 95    Hi 95
## 2020       29398472 29199487 29597457
## 2021       29806827 29463665 30149990
## 2022       30215183 29742956 30687410
## 2023       30623538 30024100 31222977
## 2024       31031894 30303359 31760429
## 2025       31440249 30579246 32301253
## 2026       31848605 30851090 32846119
## 2027       32256960 31118581 33395339
## 2028       32665316 31381587 33949044
## 2029       33073671 31640070 34507272

plot(pronostico_texas, main = "Poblacion en Texas")

Ejercicio en Clase Lunes 17: Mapa

Instalar paquetes y llamar librerias

#install.packages("forecast")
library(forecast)
#install.packages("tidyverse")
library(tidyverse)
#install.packages("maps")
library(maps)

## 
## Attaching package: 'maps'

## The following object is masked from 'package:purrr':
## 
##     map

Instalar Base de Datos

#file.choose()
poblacion <- read_csv("/Users/juanmauangers/Downloads/population.csv")

## Rows: 6020 Columns: 3
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): state
## dbl (2): year, population
## 
## 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.

Entender la Base de Datos

summary(poblacion)

##     state                year        population      
##  Length:6020        Min.   :1900   Min.   :   43000  
##  Class :character   1st Qu.:1930   1st Qu.:  901483  
##  Mode  :character   Median :1960   Median : 2359000  
##                     Mean   :1960   Mean   : 3726003  
##                     3rd Qu.:1990   3rd Qu.: 4541883  
##                     Max.   :2019   Max.   :39512223

str(poblacion)

## spc_tbl_ [6,020 × 3] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ state     : chr [1:6020] "AK" "AK" "AK" "AK" ...
##  $ year      : num [1:6020] 1950 1951 1952 1953 1954 ...
##  $ population: num [1:6020] 135000 158000 189000 205000 215000 222000 224000 231000 224000 224000 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   state = col_character(),
##   ..   year = col_double(),
##   ..   population = col_double()
##   .. )
##  - attr(*, "problems")=<externalptr>

head(poblacion)

## # A tibble: 6 × 3
##   state  year population
##   <chr> <dbl>      <dbl>
## 1 AK     1950     135000
## 2 AK     1951     158000
## 3 AK     1952     189000
## 4 AK     1953     205000
## 5 AK     1954     215000
## 6 AK     1955     222000

Serie de Tiempo en Texas

poblacion_texas <- poblacion %>% filter(state=="TX")
ggplot(poblacion_texas, aes(x=year, y=population)) +
  geom_line() +
  labs(title = "Poblacion de Texas", x ="Año", 
       y = "Poblacion")

ts_texas <- ts(poblacion_texas$population, start=1900, frequency = 1) # Serie de Tiempo Anual
# ts_texas <- ts(poblacion_texas$population, start=1900, frequency = 4) # Serie de Tiempo Trimestral
# ts_texas <- ts(poblacion_texas$population, start=1900, frequency = 12) # Serie de Tiempo mensual
arima_texas <- auto.arima(ts_texas)
summary(arima_texas)

## Series: ts_texas 
## ARIMA(0,2,2) 
## 
## Coefficients:
##           ma1      ma2
##       -0.5950  -0.1798
## s.e.   0.0913   0.0951
## 
## sigma^2 = 1.031e+10:  log likelihood = -1527.14
## AIC=3060.28   AICc=3060.5   BIC=3068.6
## 
## Training set error measures:
##                    ME     RMSE      MAE       MPE      MAPE      MASE
## Training set 12147.62 99818.31 59257.39 0.1046163 0.5686743 0.2672197
##                     ACF1
## Training set -0.02136734

pronostico_texas <- forecast(arima_texas, level = 95, h = 10)
pronostico_texas

##      Point Forecast    Lo 95    Hi 95
## 2020       29398472 29199487 29597457
## 2021       29806827 29463665 30149990
## 2022       30215183 29742956 30687410
## 2023       30623538 30024100 31222977
## 2024       31031894 30303359 31760429
## 2025       31440249 30579246 32301253
## 2026       31848605 30851090 32846119
## 2027       32256960 31118581 33395339
## 2028       32665316 31381587 33949044
## 2029       33073671 31640070 34507272

plot(pronostico_texas, main = "Poblacion en Texas")

Crear un Mapa

# Crear un mapa de EUA por decada, con un gradiente verde-rojo de la poblacion por estado, desde 1950 hasta 2050
map(database = "state")
map(database = "state", regions = "Texas", col = "red", fill = TRUE, add = TRUE)
map(database = "state", regions = "New York", col = "green", fill = TRUE, add = TRUE)

Generar Pronostico por Cada Estado

# Suponiendo que en 'poblacion' tienes columnas:
# state (abreviatura, ej. "TX"), year (año), population (valor)
poblacion_extended <- poblacion %>%
  group_by(state) %>%
  arrange(year) %>%
  # Para cada estado, creamos un df con valores observados + pronóstico
  do({
    df <- .
    # Años mínimos y máximos en tus datos
    min_year <- min(df$year)
    max_year <- max(df$year)
    
    # Creamos la serie de tiempo anual
    ts_pop <- ts(df$population, start = min_year, frequency = 1)
    
    # Determinamos cuántos años faltan para llegar a 2050
    horizon <- 2050 - max_year
    
    # Si el dataset llega hasta antes de 2050, hacemos forecast
    if(horizon > 0){
      fit <- auto.arima(ts_pop)
      fc <- forecast(fit, h = horizon)
      
      # Data frame con los datos pronosticados
      years_forecast <- (max_year + 1):2050
      df_forecast <- data.frame(
        state      = unique(df$state),
        year       = years_forecast,
        population = as.numeric(fc$mean)
      )
      
      # Unimos histórico + forecast
      df_all <- bind_rows(
        # Histórico (columnas relevantes)
        df %>% select(state, year, population),
        # Futuro
        df_forecast
      )
    } else {
      # Si ya tenemos datos hasta 2050 o más, no pronosticamos
      df_all <- df
    }
    
    df_all
  }) %>%
  ungroup()

Convertir abreviaturas de estado (p.ej., “TX”) a nombres completos

df_state_names <- data.frame(
  state_abb  = state.abb,
  state_name = tolower(state.name),
  stringsAsFactors = FALSE
)

poblacion_full <- poblacion_extended %>%
  left_join(df_state_names, by = c("state" = "state_abb"))

Unir la geometría de los estados con los datos de población

# 4.1) Obtenemos las coordenadas de polígonos con 'map_data("state")'
states_map <- map_data("state")

# 4.2) Hacemos left_join para heredar la columna 'population' (por estado y año)
map_data_joined <- states_map %>%
  left_join(poblacion_full, by = c("region" = "state_name"))

Filtrar décadas entre 1950 y 2050

map_data_decadas <- map_data_joined %>%
  mutate(year = as.numeric(year)) %>%
  filter(year >= 1950, year <= 2050, year %% 10 == 0)

Graficar con ggplot2 (rojo = población baja, verde = población alta)Filtrar décadas entre 1950 y 2050

ggplot(map_data_decadas, aes(x = long, 
                             y = lat, 
                             group = group, 
                             fill = population)) +
  geom_polygon(color = "black", size = 0.1) +
  # Gradiente de rojo a verde 
  scale_fill_gradient(low = "red", high = "green", 
                      na.value = "grey90") +
  facet_wrap(~ year) +
  coord_fixed(1.3) +
  labs(title = "Población de EUA por Estado (1950 - 2050, por década)",
       fill = "Población estimada") +
  theme_void() +
  theme(legend.position = "right",
        strip.text = element_text(face = "bold"))

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Actividad 2. Leche saborizante hersheys

## Instalar paquetes y llamar librerias

#install.packages("forecast")
library(forecast)
#install.packages("tidyverse")
library(tidyverse)
#install.packages("ggplot2")
library(ggplot2)
#install.packages("readxl")
library(readxl)

Instalar base de datos

#file.choose()
ventas <- read_excel("/Users/juanmauangers/Downloads/Ventas_Históricas_Lechitas.xlsx")
head(ventas)

## # A tibble: 6 × 1
##   Ventas
##    <dbl>
## 1 25521.
## 2 23740.
## 3 26254.
## 4 25868.
## 5 27073.
## 6 27150.

1. AutoARIMA

ts_ventas <- ts(ventas$Ventas, start=c(2017,1), frequency = 12) # Serie de Tiempo mensual
autoplot(ts_ventas) + labs(title = "Ventas de leche saborizada Hershey's", x="tiempo", y="ventas (en miles de dolares)")

arima_ventas <- auto.arima(ts_ventas)
summary(arima_ventas)

## Series: ts_ventas 
## ARIMA(1,0,0)(1,1,0)[12] with drift 
## 
## Coefficients:
##          ar1     sar1     drift
##       0.6383  -0.5517  288.8979
## s.e.  0.1551   0.2047   14.5026
## 
## sigma^2 = 202701:  log likelihood = -181.5
## AIC=371   AICc=373.11   BIC=375.72
## 
## Training set error measures:
##                    ME    RMSE    MAE        MPE      MAPE       MASE      ACF1
## Training set 25.22158 343.864 227.17 0.08059932 0.7069542 0.06491044 0.2081026

pronostico_ventas <- forecast(arima_ventas, level = 95, h = 12)
pronostico_ventas

##          Point Forecast    Lo 95    Hi 95
## Jan 2020       35498.90 34616.48 36381.32
## Feb 2020       34202.17 33155.28 35249.05
## Mar 2020       36703.01 35596.10 37809.92
## Apr 2020       36271.90 35141.44 37402.36
## May 2020       37121.98 35982.07 38261.90
## Jun 2020       37102.65 35958.90 38246.40
## Jul 2020       37151.04 36005.73 38296.34
## Aug 2020       38564.64 37418.70 39710.58
## Sep 2020       38755.22 37609.03 39901.42
## Oct 2020       39779.02 38632.72 40925.32
## Nov 2020       38741.63 37595.28 39887.97
## Dec 2020       38645.86 37499.50 39792.22

autoplot(pronostico_ventas)+labs(title = "Pronostico de ventas leche Hershey's", x="Tiempo", y= "Miles de dolares")

## 2. Modelo regresion lineal

ventas$mes <- 1:36
regresion_ventas <- lm(Ventas~mes, data = ventas)
summary(regresion_ventas)

## 
## Call:
## lm(formula = Ventas ~ mes, data = ventas)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2075.79  -326.41    33.74   458.40  1537.04 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 24894.67     275.03   90.52   <2e-16 ***
## mes           298.37      12.96   23.02   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 808 on 34 degrees of freedom
## Multiple R-squared:  0.9397, Adjusted R-squared:  0.9379 
## F-statistic: 529.8 on 1 and 34 DF,  p-value: < 2.2e-16

siguiente_anio <- data.frame(mes=37:48)
prediccion_regresion <- predict(regresion_ventas, siguiente_anio)
prediccion_regresion

##        1        2        3        4        5        6        7        8 
## 35934.49 36232.86 36531.23 36829.61 37127.98 37426.35 37724.73 38023.10 
##        9       10       11       12 
## 38321.47 38619.85 38918.22 39216.59

plot(ventas$mes,ventas$Ventas, main="Pronostico de ventas 2020 Leche Hersheys", xlab="Tiempo", ylab="Miles de dolares")
abline(regresion_ventas, col="blue")
points(siguiente_anio$mes,prediccion_regresion, col="red")

predicciones_reales <- predict(regresion_ventas, ventas)

MAPE <- mean(abs((ventas$Ventas - predicciones_reales)/ventas$Ventas))*100
MAPE

## [1] 2.011297

3. Conclusiones

El mejor modelo que se adapta a la serie es el SARIMA con un MAPE de 0.70, comparado con la regresion lineal que su MAPE es de 2.01%. Para el siguiente año la proyeccion de ventas es la siguiente:

Mes y año	Escenario Optimista	Escenario esperado	Escenario pesimista
Jan 2020	35498.90	34616.48	36381.32
Feb 2020	34202.17	33155.28	35249.05
Mar 2020	36703.01	35596.10	37809.92
Apr 2020	36271.90	35141.44	37402.36
May 2020	37121.98	35982.07	38261.90
Jun 2020	37102.65	35958.90	38246.40
Jul 2020	37151.04	36005.73	38296.34
Aug 2020	38564.64	37418.70	39710.58
Sep 2020	38755.22	37609.03	39901.42
Oct 2020	39779.02	38632.72	40925.32
Nov 2020	38741.63	37595.28	39887.97
Dec 2020	38645.86	37499.50	39792.22