Actividad 4: Parte 1

Simulated Stock Price

Instalar paquetes y llamar librerias

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

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

#install.packages("ggplot2")
library(ggplot2)

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

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

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

Step 01) Data Collection

getSymbols('AAPL', src = 'yahoo', 
           from = "2004-01-01", to = "2024-01-03")

## [1] "AAPL"

apple <- data.frame(
  AAPL,
  date = as.Date(rownames(data.frame(AAPL)))
)

summary(apple)

##    AAPL.Open          AAPL.High           AAPL.Low          AAPL.Close     
##  Min.   :  0.3825   Min.   :  0.3884   Min.   :  0.3782   Min.   :  0.380  
##  1st Qu.:  5.8538   1st Qu.:  5.9504   1st Qu.:  5.7532   1st Qu.:  5.854  
##  Median : 21.4473   Median : 21.6714   Median : 21.2441   Median : 21.527  
##  Mean   : 42.9220   Mean   : 43.3884   Mean   : 42.4735   Mean   : 42.951  
##  3rd Qu.: 47.9694   3rd Qu.: 48.5425   3rd Qu.: 47.7531   3rd Qu.: 48.126  
##  Max.   :198.0200   Max.   :199.6200   Max.   :197.0000   Max.   :198.110  
##   AAPL.Volume        AAPL.Adjusted           date           
##  Min.   :2.405e+07   Min.   :  0.3202   Min.   :2004-01-02  
##  1st Qu.:1.122e+08   1st Qu.:  4.9329   1st Qu.:2008-12-31  
##  Median :2.739e+08   Median : 18.2892   Median :2014-01-01  
##  Mean   :4.071e+08   Mean   : 41.1501   Mean   :2013-12-31  
##  3rd Qu.:5.760e+08   3rd Qu.: 45.8199   3rd Qu.:2019-01-01  
##  Max.   :3.373e+09   Max.   :196.9277   Max.   :2024-01-02

str(apple)

## 'data.frame':    5034 obs. of  7 variables:
##  $ AAPL.Open    : num  0.385 0.382 0.397 0.395 0.408 ...
##  $ AAPL.High    : num  0.388 0.4 0.4 0.408 0.424 ...
##  $ AAPL.Low     : num  0.378 0.382 0.388 0.392 0.404 ...
##  $ AAPL.Close   : num  0.38 0.396 0.394 0.403 0.417 ...
##  $ AAPL.Volume  : num  1.45e+08 3.95e+08 5.09e+08 5.87e+08 4.60e+08 ...
##  $ AAPL.Adjusted: num  0.32 0.334 0.332 0.34 0.351 ...
##  $ date         : Date, format: "2004-01-02" "2004-01-05" ...

head(apple)

##            AAPL.Open AAPL.High AAPL.Low AAPL.Close AAPL.Volume AAPL.Adjusted
## 2004-01-02  0.384821  0.388393 0.378214   0.380000   144642400     0.3201959
## 2004-01-05  0.382500  0.399821 0.382500   0.395893   395018400     0.3335877
## 2004-01-06  0.397321  0.400357 0.387679   0.394464   509348000     0.3323835
## 2004-01-07  0.394643  0.407679 0.391607   0.403393   586874400     0.3399073
## 2004-01-08  0.407857  0.423750 0.404464   0.417143   460303200     0.3514933
## 2004-01-09  0.414821  0.430893 0.406964   0.410714   427459200     0.3460762
##                  date
## 2004-01-02 2004-01-02
## 2004-01-05 2004-01-05
## 2004-01-06 2004-01-06
## 2004-01-07 2004-01-07
## 2004-01-08 2004-01-08
## 2004-01-09 2004-01-09

tail(apple)

##            AAPL.Open AAPL.High AAPL.Low AAPL.Close AAPL.Volume AAPL.Adjusted
## 2023-12-22    195.18    195.41   192.97     193.60    37122800      192.4446
## 2023-12-26    193.61    193.89   192.83     193.05    28919300      191.8979
## 2023-12-27    192.49    193.50   191.09     193.15    48087700      191.9973
## 2023-12-28    194.14    194.66   193.17     193.58    34049900      192.4247
## 2023-12-29    193.90    194.40   191.73     192.53    42628800      191.3810
## 2024-01-02    187.15    188.44   183.89     185.64    82488700      184.5321
##                  date
## 2023-12-22 2023-12-22
## 2023-12-26 2023-12-26
## 2023-12-27 2023-12-27
## 2023-12-28 2023-12-28
## 2023-12-29 2023-12-29
## 2024-01-02 2024-01-02

Step 02) Simulate Stock Prices

mean_price <- mean(apple$AAPL.Close, na.rm = TRUE)
#sd_price <- log(sd(apple$AAPL.Close, na.rm = TRUE))

# Generate simulated stock prices using normal distribution
set.seed(123) 
simulated_prices <- rnorm(n = nrow(apple), mean = mean_price, sd = 10)

# Create a new dataframe with simulated stock prices
simulated_stock <- apple %>%
  mutate(Simulated.Close = simulated_prices)

# View first few rows
head(simulated_stock)

##            AAPL.Open AAPL.High AAPL.Low AAPL.Close AAPL.Volume AAPL.Adjusted
## 2004-01-02  0.384821  0.388393 0.378214   0.380000   144642400     0.3201959
## 2004-01-05  0.382500  0.399821 0.382500   0.395893   395018400     0.3335877
## 2004-01-06  0.397321  0.400357 0.387679   0.394464   509348000     0.3323835
## 2004-01-07  0.394643  0.407679 0.391607   0.403393   586874400     0.3399073
## 2004-01-08  0.407857  0.423750 0.404464   0.417143   460303200     0.3514933
## 2004-01-09  0.414821  0.430893 0.406964   0.410714   427459200     0.3460762
##                  date Simulated.Close
## 2004-01-02 2004-01-02        37.34610
## 2004-01-05 2004-01-05        40.64908
## 2004-01-06 2004-01-06        58.53794
## 2004-01-07 2004-01-07        43.65594
## 2004-01-08 2004-01-08        44.24374
## 2004-01-09 2004-01-09        60.10151

simulated_stock$date <- as.Date(simulated_stock$date)


real_prices <- simulated_stock$AAPL.Close
simulated_prices <- simulated_stock$Simulated.Close

# Remove NA values (if any)
valid_indices <- complete.cases(real_prices, simulated_prices)
real_prices <- real_prices[valid_indices]
simulated_prices <- simulated_prices[valid_indices]

Step 03) Calculate Error Metrics and Interpret the results

# Mean Absolute Error (MAE)
mae_value <- mae(real_prices, simulated_prices)

# Mean Squared Error (MSE)
mse_value <- mse(real_prices, simulated_prices)

# Root Mean Squared Error (RMSE)
rmse_value <- rmse(real_prices, simulated_prices)

# R-squared (R²)
r_squared <- cor(real_prices, simulated_prices)^2

# Mean Absolute Percentage Error (MAPE)
mape_value <- mean(abs((real_prices - simulated_prices) / real_prices)) * 100

# Print results
cat("Mean Absolute Error (MAE):", mae_value, "\n")

## Mean Absolute Error (MAE): 41.33864

cat("Mean Squared Error (MSE):", mse_value, "\n")

## Mean Squared Error (MSE): 2944.238

cat("Root Mean Squared Error (RMSE):", rmse_value, "\n")

## Root Mean Squared Error (RMSE): 54.26083

cat("R-squared Score (R²):", r_squared, "\n")

## R-squared Score (R²): 0.0002366267

cat("Mean Absolute Percentage Error (MAPE):", mape_value, "%\n")

## Mean Absolute Percentage Error (MAPE): 782.793 %

# Calculate errors
errors <- simulated_prices - real_prices  # Difference between simulated and real prices
abs_errors <- abs(errors)                 # Absolute errors
squared_errors <- errors^2                # Squared errors
percentage_errors <- abs_errors / real_prices * 100  # Percentage errors

# Add errors to the dataset
simulated_stock$Error <- NA
simulated_stock$Absolute_Error <- NA
simulated_stock$Squared_Error <- NA
simulated_stock$Percentage_Error <- NA

# Store errors in dataset
simulated_stock$Error[valid_indices] <- errors
simulated_stock$Absolute_Error[valid_indices] <- abs_errors
simulated_stock$Squared_Error[valid_indices] <- squared_errors
simulated_stock$Percentage_Error[valid_indices] <- percentage_errors

ggplot(simulated_stock, aes(x = date, y = Error, fill = Error > 0)) +
  geom_col() +  # Creates a bar plot
  geom_hline(yintercept = 0, linetype = "dashed", color = "black") +
  scale_fill_manual(values = c("red", "blue"), labels = c("Underestimated", "Overestimated")) +
  labs(title = "Stock Price Simulation Errors Over Time",
       x = "Date", 
       y = "Error (Simulated - Real)", 
       fill = "Error Type") +
  theme_minimal()

Interpret the results

How close was the simulated data to real stock prices?
The simulated stock prices compared to the real stock prices using the mean and normal distribution resulted in simultaed prices that were considerably off to the real stock prices. This was due to the fact that the simultaed stock prices were only using the mean and a standard deviation to simulated the real stock prices. Due to the simplicity of the simulation and the fact that this is a time series dataset the stock prices aren’t considered accurate.

What does the R² value indicate?
The R² that was calculated for the real and the simulated stock prices is 0.0002366267. This indicates that the simulated prices have almost no real appliaction to explain the real stock prices.

How high is the MAPE percentage?
The MAPE percentage of the simulated and real stock prices simulation is 782.793 %. This means that the simulated stock prices deviate from the real stock prices on average nearly 8 times. This indicates that the simulation is very inaccurate at compared to the real prices.

Step 04) Visualize the Results

# Plot real vs. simulated stock prices
ggplot(simulated_stock, aes(x = date)) + geom_line(aes(y = AAPL.Close, color = "Real Prices"), size = 1) +
geom_line(aes(y = Simulated.Close, color = "Simulated Prices"), size = 1, linetype = "dashed") +
labs(title = "Real vs Simulated Apple Stock Prices (2005-2024)",
       x = "Date", 
       y = "Stock Price (USD)",
       color = "Legend") +
  scale_color_manual(values = c("Real Prices" = "blue", "Simulated Prices" = "red")) +
  theme_minimal()

## 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.

# Plot real vs. simulated stock prices