https://datascienceschool.net/view-notebook/9cbbfed6d6f34f02a2cdaa422706be91/ ================================================================================ * Code ARMA(p,q) model = Characteristics of AR(p) model + Characteristics of MA(q) model ================================================================================ $$$Y_t = -\phi_1 Y_{t-1} -\phi_2 Y_{t-2} -\cdots -\phi_p Y_{t-p} + \epsilon_t + \theta_1 \epsilon_{t-1} +\theta_2 \epsilon_{t-2} \cdots +\theta_q \epsilon_{t-q}$$$ * Code previous_values_of_myself print(len(previous_values_of_myself)) # p previous_white_noises print(len(previous_white_noises)) # q current_val=ARMA_model(previous_values_of_myself,previous_white_noises) ================================================================================ * Code cond1=Condition for ARMA(p,q) to be stationarity status cond2=Condition for AR(p) to be stationarity status cond1==cond2 # True thetas=Get_coefficient_theta_from_MA(q) res=does_thetas_affect_stationarity_status_on_ARMA(p,q) print(res) # False ================================================================================ * ARMA(p,q) model $$$Y_t = -\phi_1 Y_{t-1} -\phi_2 Y_{t-2} -\cdots -\phi_p Y_{t-p} + \epsilon_t + \theta_1 \epsilon_{t-1} +\theta_2 \epsilon_{t-2} \cdots +\theta_q \epsilon_{t-q}$$$ * ARMA(p,q) model in linear probabilistic process $$$Y_t = \epsilon_t + \psi_1 \epsilon_{t-1} + \psi_2 \epsilon_{t-2} + \cdots$$$ * $$$\psi$$$ are like $$$\psi_1 = \theta_1 -\phi_1 \\ \psi_2 = \theta_2 - \phi_2 -\phi_1 \psi_1 \\ \vdots \\ \psi_j = \theta_j -\phi_p\psi_{j-p} -\phi_2 \psi_{p-1} + \cdots -\phi_1 \psi_{j-1}$$$ * Autocorrelation coefficient of ARMA(p,q) model $$$\rho_k = -\phi_1 \rho_{k-1} - \cdots - \phi_p\rho_{k-p}$$$ ================================================================================ By using above equations, you can find ARMA model wrt given Autocorrelation coefficient function ================================================================================ ================================================================================ * Code linear_probabilistic_process=convert(AR(p)_model) AR_model_in_infinite_dimension=convert(MA(q)_model) ================================================================================ * Code if AR_model_in_infinite_dimension satisties stationarity_status_condition: print("original MA(q) model is invertibile") else: print("original MA(q) model is not invertibile") ================================================================================ ret=number of MA model which has "given autocorrelation coefficient function" print(ret) # Multiples ret=number of MA model which satisfies "invertibile" print(ret) # 1