Actividad 2

Ejercicio en clase: Población

#Librerías
library(forecast)

## Registered S3 method overwritten by 'quantmod':
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library(tidyverse)

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## ✔ forcats   1.0.0     ✔ stringr   1.5.1
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## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.0.4

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library(ggplot2)
library(maps)

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

library(readxl)

#Base de datos
poblacion <- read_csv("/Users/lishdz/Desktop/8vo/periodo 1/modulo 1 - r/population.csv", show_col_types = FALSE)

Entender la base de datos

summary(poblacion) #min= 1900 max = 2019

##     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 de Texas

poblacion_texas <- poblacion %>% filter(state == "TX")

ggplot(poblacion_texas, aes(x=year, y=population)) +
  geom_line() + 
  labs(title = "Población de Texas", x = "Año", y = "Población")

ts_texas <- ts(poblacion_texas$population, start = 1900, frequency = 1)

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) #h = num predicciones
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 = "Población en Texas")

Ejercicio en clase: Lunes 17

Crear un maps

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)

# dataframe para resultados
forecast_results <- list()

# lista de los estados
states <- unique(poblacion$state)

for (state in states) {
  
  # Filtrar por estado
  poblacion_state <- poblacion %>%
    filter(state == !!state) %>%
    arrange(year)
  
  # debugging
  #print(paste("Processing:", state))
  #print(poblacion_state)
  
  # timeseries
  ts_state <- ts(poblacion_state$population, start = min(poblacion_state$year), frequency = 1)
  
  if (length(ts_state) > 2) {
    
    # modelo arima
    arima_state <- auto.arima(ts_state)
    
    # Forecast para el siguiente año
    forecast_state <- forecast(arima_state, h = 1)
    
    next_year <- max(poblacion_state$year) + 1
    forecast_value <- as.numeric(forecast_state$mean)
    #print(forecast_value)
    
    forecast_results[[state]] <- data.frame(state = state, year = next_year, population = forecast_value)
  }
}

# Juntar predicciones
forecast_results_df <- bind_rows(forecast_results)

# Juntar datos originales y predicción
poblacion <- bind_rows(poblacion, forecast_results_df)

datos_decadas <- poblacion %>% filter(year %in% c("1950", "1960", "1970", "1980", "1990", "2000", "2010", "2020"))

state_conversion <- data.frame(
  Abbreviation = state.abb,
  State = state.name
)

datos_decadas <- datos_decadas %>% left_join(state_conversion, by = c("state" = "Abbreviation")) %>%
  select(-state)

library(sf)       
library(maps)   
library(mapdata)
library(scales)

us_states <- map_data("state") %>%
  rename(State = region) %>%
  mutate(State = str_to_title(State))

map_data_merged <- left_join(us_states, datos_decadas, by = c("State"))

ggplot(map_data_merged, aes(long, lat, group = group, fill = population)) +
  geom_polygon(color = "white") +
  scale_fill_viridis_c(option = "turbo", na.value = "gray80", 
                       labels = label_comma()) +  
  theme_minimal() +
  labs(title = "Distribución de la población - predicción 2020", 
       fill = "Población") +
  coord_fixed(1.3) +
  facet_wrap(~ year)

ACTIVIDAD 2: Leches de Hershey

#Importar la base de datos
ventas <- read_xlsx("/Users/lishdz/Desktop/8vo/periodo 1/modulo 1 - r/Ventas_Históricas_Lechitas.xlsx")

Modelo 1. Auto ARIMA

ts_ventas <- ts(ventas$Ventas, start= c(2017, 1), frequency = 12)
autoplot(ts_ventas) + labs(title= "Ventas de Leche Saborizada Hershey's", x="Tiempo", y="Miles de dólares")

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= "Pronóstico de ventas de Leche Saborizada Hershey's 2020", x="Tiempo", y="Miles de dólares")

# Modelo de regresión 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_a <- data.frame(mes=37:48)
prediccion_regresion <- predict(regresion_ventas, siguiente_a)
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="Pronóstico de ventas de Leche Saborizada Hershey's 2020", xlab="Tiempo", ylab="Miles de dólares")
abline(regresion_ventas, col="blue")
points(siguiente_a$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

Conclusiones

El mejor modelo que se adapta a la serie es el SARIMA con un MAPE de 0.71%, comparado con la Regresión Lineal que es de 2.01%.

Para el siguiente año, la proyección de ventas es la siguiente:

Mes y Año	Escenario Esperado	Escenario Pesimista	Escenario Optimista
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

ventas_por_anio <- read.csv("/Users/lishdz/Desktop/8vo/periodo 1/modulo 1 - r/ventas_por_anio.csv")

ggplot(ventas_por_anio, aes(x=mes, y= ventas, col=as.factor(anio), group=anio)) + 
  geom_line() +
  labs(title = "Ventas de Leche Saborizada Hershey's por Año", x="Mes", y="Miles de dólares")

Nuestra recomendación realizar campañas publicitarias para incitar el consumo del producto en el primer semestre del año.