Installation of the Libraries

Libraries

If making the financial analysis of the stock exchange data, the following packages are needed:

  1. quantmod
  2. PerformanceAnalytics
  3. tidyquant
#install.packages("PerformanceAnalytics", repos = "http://cran.us.r-project.org")
#install.packages("dplyr", repos = "http://cran.us.r-project.org")
#install.packages("tidyquant", repos = "http://cran.us.r-project.org")
#install.packages("quantmod", repos = "http://cAs iran.us.r-project.org")
#install.packages("tseries", repos = "http://cran.us.r-project.org")
#install.packages("tidyverse", repos = "http://cran.us.r-project.org")

library(PerformanceAnalytics)  #useful package !!!
## Loading required package: xts
## Loading required package: zoo
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library(quantmod)              # useful package
## Loading required package: TTR
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library(tidyquant)             # useful
## Loading required package: lubridate
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library(randtests)  # for runs test

# other libraries

library(ggplot2)
library(dplyr)
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## ######################### Warning from 'xts' package ##########################
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## # source() into this session won't work correctly.                            #
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## # Use stats::lag() to make sure you're not using dplyr::lag(), or you can add #
## # conflictRules('dplyr', exclude = 'lag') to your .Rprofile to stop           #
## # dplyr from breaking base R's lag() function.                                #
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library(tseries)
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## Attaching package: 'tseries'
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library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ purrr   1.0.2     ✔ tibble  3.2.1
## ✔ readr   2.1.5     ✔ tidyr   1.3.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(plotly)
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library(hrbrthemes)
library(xts)
library(knitr)
library(kableExtra)
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library(car)
## Loading required package: carData
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library(mathjaxr)
library(zoo)
rm(list=ls())

Data download

If downloading the stock-exchange data, we use the quantmod package command “getSymbols”. COmmand “Ad” enables extraction of just Adjusted closing prices of the day.

# Load the required package
library(quantmod)

# Set dates for data retrieval
start_date <- "2010-01-01"
end_date <- "2022-12-31"
symbol <-"F"

# Download the data for Ford (ticker symbol: F)
getSymbols(symbol, src = "yahoo", from = start_date, to = end_date, auto.assign = TRUE)
## [1] "F"
# Extract the adjusted close prices
adot.close <- Ad(getSymbols(symbol, src = "yahoo", from = start_date, to = end_date, auto.assign = FALSE))
title <- paste(symbol) 
plot(adot.close, col="red", main=title)

valtozas <- diff(adot.close)
median_valtozas <- median(valtozas, na.rm = TRUE)  # Compute median excluding NA
valtozas[is.na(valtozas)] <- median_valtozas # replacing missing returns by their estimates by median




acf(valtozas,main="Autocorrelations of Price differences")

The above given Autocorrelation function is a function, which assigns each lag a correlation between actual return and a lagged return by a specified number of periods (varying from 1 to 30 ). If the correlations would be within the band between two blue dotted lines, we could accept the hypothesis that price movements of the F are not information weakly efficient. On the other side, lags 7 and 15 seem to be statistically significant (at 5 percent significance level). Remember, it can by just demonstration of the Type 1 Error !!! There are just 2 cases of 30 - that is why we are prone to reject the alternative hypothesis. We do not have any information to reject \(H_0\), prices can be considered as weakly efficient.

To test the weak form of the efficiency, we can use Runs test. We are using the diferenced time series as in the previous example. Therafter, we substitute

# Load the required package
library(randtests)

# Perform the Runs Test
#runs_test_result <- runs.test(as.vector(valtozas))

# Print the result
#print(runs_test_result)

\(H_0: \quad \text{Price movements reflect a weak form of the efficiency}\) \(H_1: \quad \text{Price movements deny the weak form of the efficiency}\)

In our case p-value is high, we reject the alternative, we deny the alternative hypothesis of absenting the weak form of the efficiency.

Semi-strong form of the efficiency

All public (but not inside) information is calculated into a stock’s current price. Neither fundamental nor technical analysis can be used to achieve superior gains.

Test Event Studies: These studies examine the stock price reaction to new public information, such as earnings announcements, to determine how quickly and accurately prices adjust.

Strong form of the efficiency

Both the public and inside information is calculated into a stock current price.