Code for Chapter 7 (Model Estimation):

• Verifications/Duplication of Figures or Results from the Text
  • chap_7_dup_table_7_2.R (duplicates some of the numbers in this table)
    
  • chap_7_dup_table_7_4_N_5.R (duplicates some of the numbers in this table)
    
  • chap_7_dup_fig_7_2.R (duplicates the minimum found from the plot)
    
  • chap_7_dup_table_7_7.R (duplicates the numbers in this table)
    
  • chap_7_dup_table_7_9.R (duplicates the numbers in this table)
    
  • chap_7_dup_table_7_11.R (duplicates the numbers in this table)
    
• Codes for fitting ARIMA models:
  • IMA_minimization.R (brute force minimization of S(lambda_-1,lambda₀,lambda₁))
    
  • Evaluating the conditional sum of squares of [a_t] for various models
    • cond_sum_of_squares_ARMA_01.R (evaluates S_*(theta) for a MA(1) model)
      
  • Evaluating the unconditional sum of squares of [a_t] for various models
    • uncond_sum_of_squares_ARMA_01.R (evaluates S(theta) for a MA(1) model)
      
    • uncond_sum_of_squares_ARMA_02.R (evaluates S(lambda₀,lambda₁) for a MA(2) model)
      
    • uncond_sum_of_squares_ARMA_03.R (evaluates S(lambda_-1,lambda₀,lambda₁) for a MA(3) model)
      
    • uncond_sum_of_squares_ARMA_10.R (evaluates S(phi₁) for a AR(1) model)
      
    • uncond_sum_of_squares_ARMA_20.R (evaluates S(phi₁,phi₂) for a AR(2) model)
      
    • uncond_sum_of_squares_ARMA_30.R (evaluates S(phi₁,phi₂,phi₃) for a AR(3) model)
      
    • uncond_sum_of_squares_ARMA_11.R (evaluates S(theta) for a AR(1) MA(1) model)
      
  • Numerically evaluate the parameter derivatives of [a_t] for various models
    • numerically_evaluate_xt_ARMA_01.R (evaluates the derivative of S with respect to theta for a MA(1))
      
    • numerically_evaluate_xt_ARMA_02.R (evaluates the derivative of S with respect to thetas for a MA(2))
      
  • Newtons method to find MA(q) parameters
    • newton_fit_ARMA_01.R (estimate parameters of a MA(1) model)
      
    • newton_fit_ARMA_02.R (estimate parameters of a MA(2) model)
      
    • theta_to_lambda_ARMA_02.R (translates between thetas and lambda for a MA(2) model)
      
    • lambda_to_theta_ARMA_02.R (translates between lambda and thetas for a MA(2) model)
      
    • theta_to_lambda_ARMA_03.R (translates between thetas and lambda for a MA(3) model)
      
    • lambda_to_theta_ARMA_03.R (translates between lambda and thetas for a MA(3) model)
      
• Problem Solutions
  • chap_7_prob_1_N_2.R (some computations for this problems)