Simulation of Autocorrelation in Linear Regression Model

autocorrelation_simulation.R

# Function to conduct simulation
generate_beta = function(ti, rho, repetition) {
  # Vector intercept and slope
  vector_intercept_auto = rep(x = 0, len = repetition)
  vector_slope_auto = rep(x = 0, len = repetition)
  vector_intercept_non = rep(x = 0, len = repetition)
  vector_slope_non = rep(x = 0, len = repetition)
  
  j = 1
  while (j < (repetition + 1)) {
    t = 1:ti
    number_data = length(t)
    error_t = rnorm(n = number_data, mean = 0, sd = 1)
    # Create an empty vector for the Vt
    vector_vt = rep(x = 0, len = number_data)
    # Generate the vector Vt
    vector_vt[1] = rho * rnorm(n = 1, mean = 0, sd = 1) + error_t[1]
    for (i in 2:number_data) {
      vector_vt[i] = rho * vector_vt[i-1] + error_t[i]
    }
    # Generate vector Ut
    scalar_v = mean(vector_vt)
    vector_ut = vector_vt - scalar_v
    # Generate vector Yt and Zt
    vector_yt = 1 + 0.8 * t + vector_ut
    vector_zt = 1 + 0.8 * t + error_t
    
    # Regression with autocorrelation
    model_autocorrelation = lm(formula = vector_yt ~ t)
    vector_intercept_auto[j] = as.numeric(model_autocorrelation$coefficients[1])
    vector_slope_auto[j] = as.numeric(model_autocorrelation$coefficients[2])
    
    # Regression without autocorrelation
    model_nonautocorrelation = lm(formula = vector_zt ~ t)
    vector_intercept_non[j] = as.numeric(model_nonautocorrelation$coefficients[1])
    vector_slope_non[j] = as.numeric(model_nonautocorrelation$coefficients[2])
    
    # Index
    j = j + 1
  }
  
  # Save the intercept and slope to the dataframe
  beta_coefficient = data.frame(rho,
                                vector_intercept_non,
                                vector_slope_non,
                                vector_intercept_auto,
                                vector_slope_auto)
  colnames(beta_coefficient) = c('Rho',
                                 'interceptNonAutocorrelation', 
                                 'slopeNonAutocorrelation',
                                 'interceptAutocorrelation',
                                 'slopeAutocorrelation')
  return(beta_coefficient)
}

# Generate the simulation
df = data.frame()
for (rho in seq(-1,1,0.1)) {
  beta_coef = generate_beta(ti = 30, rho = rho, repetition = 1000)
  df = rbind(df, beta_coef)
}

# Print the result
View(df)