Aggregate by User-Defined Function and Regression in R
Overview of the Problem
In this article, we will delve into a common challenge faced by data analysts and statisticians: aggregating data using user-defined functions while also incorporating regression analysis. Specifically, we’ll focus on a Stack Overflow question that presents an interesting scenario where the goal is to calculate beta and co-skewness (using regression) per year for a large dataset.
Background
To tackle this problem, it’s essential to understand some fundamental concepts in R and statistics:
- XTS: A package used for time series analysis. XTS allows you to manipulate and analyze time series data efficiently.
- Aggregate function: Used to perform operations on a group of observations or data points within the dataset. In this case, we want to calculate beta (a measure of market risk) and co-skewness per year.
- Regression analysis: A statistical technique used to establish relationships between variables. We’ll use regression to estimate beta and co-skewness for each year.
Data Preparation
First, let’s create a sample dataset in R using the xts package:
# Set seed for reproducibility
set.seed(123)
# Create a time series with 7 variables (6 technical indicators + 1 risk-free rate)
testsample <- xts(matrix(runif(140, -1, 1), ncol=7),
order.by = seq.Date(as.Date("2008-12-24"), by = "day", length.out = 20))
# Set column names
colnames(testsample) <- c(paste0("x", seq(from=1, to=6), ""), "RF")
This code generates a sample dataset with 7 columns representing different technical indicators and the risk-free rate.
Beta Calculation
Next, we want to calculate beta using a user-defined function. However, R’s aggregate function requires the input data to be in a specific format:
# Format years as integers for correct aggregation
yrs <- format(index(testsample), format = "%y")
# Define CAPM beta calculation function
CAPM.beta <- function(Ra, Rb) {
return((Ra - Rb) / Ra)
}
# Calculate beta using aggregate function
Beta <- aggregate(testsample ~ yrs, testsample,
function(x) CAPM.beta(Ra = x, Rb = testsample[index(x), "RF"]),
drop = FALSE, na.action = na.pass)
Here, we define a CAPM_beta function to calculate the beta based on market returns (Ra) and risk-free rate returns (Rb). The aggregate function applies this calculation to each year’s data.
However, this approach throws an error because R expects time series objects to be in a specific format. To resolve this issue, we need to convert our dataset into a suitable format:
# Reshape time series data for correct aggregation
Beta <- aggregate(testsample ~ yrs, by = list(testsample),
function(x) {
# Calculate CAPM beta
Ra <- x[, "x1"]
Rb <- x[, "RF"]
# Apply CAPM_beta function to each row (i.e., each time point)
lapply(Ra, function(ra) CAPM_beta(Ra = ra, Rb = Rb))
}
)
This revised approach leverages the by argument in aggregate, which allows us to aggregate data by a specified list. We reshape our dataset using x[, "RF"] for risk-free rate returns.
However, the above code still doesn’t produce the desired output because it calculates CAPM beta only once per row instead of aggregating all years’ returns and then calculating the average beta. To fix this issue:
# Reshape time series data for correct aggregation
Beta <- aggregate(testsample ~ yrs, by = list(testsample),
function(x) {
# Calculate sum of CAPM beta values across all time points per row (i.e., each year)
Ra <- x[, "x1"]
Rb <- x[, "RF"]
# Apply CAPM_beta function to each time point within a year
lapply(Ra, function(ra) {
CAPM.beta(Ra = ra, Rb = mean(x[index(x, ., "RF") == index(Rb, "RF"), "RF"])
})
}
)
Here, we use mean to calculate the average risk-free rate return for each year and then apply the CAPM beta function.
Co-Skewness Calculation
Next, let’s address the co-skewness calculation:
# Calculate co-skewness using linear regression
COSKEW <- lapply(1:(ncol(testsample) - 1),
function(x) {
# Define linear regression model for column x[x] ~ RF + I(RF^2)
lm_model <- lm(x[, x] ~ RF + I(RF^2), data = testsample)
# Extract coefficient of skewness
coef(lm_model)[3]
}
)
This code uses linear regression to model the relationship between each technical indicator (x[x]) and risk-free rate returns (RF).
However, this approach doesn’t aggregate co-skewness per year. To fix this issue:
# Calculate co-skewness using linear regression
COSKEW <- aggregate(testsample ~ yrs, by = list(testsample),
function(x) {
# Define linear regression model for each column x[x] ~ RF + I(RF^2)
lm_models <- lapply(1:(ncol(x[, "x"])),
function(i) {
lm_model <- lm(x[i, "x" . [i]] ~ RF + I(RF^2), data = testsample)
# Extract coefficient of skewness
coef(lm_model)[3]
})
# Aggregate co-skewness per year
sapply(1:(length(lm_models)), function(i) mean(lm_models[i]))
}
)
Here, we apply linear regression to each technical indicator column (x[x]) using I(RF^2) for quadratic effects. We then aggregate the co-skewness per year by taking the average of all calculated values.
Conclusion
In this article, we explored a common challenge in R: aggregating data using user-defined functions while also incorporating regression analysis. We presented an example where the goal was to calculate beta and co-skewness per year for a large dataset.
We discussed several approaches to address this challenge, including reshaping time series data, using aggregate with by, applying linear regression models, and aggregating results.
By following these steps and understanding the underlying concepts in R and statistics, you can tackle similar challenges in your own data analysis projects.
Last modified on 2024-06-10