labels = [r"$\varepsilon_t = y_{t}-\hat{\alpha}-\hat{\beta}x_{t}$"] samples = numpy.array([εt]) comparison_plot(title, samples, labels, plot_name) # %% arima.adf_report(εt) # %% title = f"ECM Simulation, " + r"$\phi=$" + f"{numpy.array2string(arima_params['φ'], precision=2, separator=',')}, " + r"$\lambda=$" + f"{format(ecm_params['λ'], '2.2f')}, " + r"$\beta=$" + f"{format(ecm_params['β'], '2.2f')}, " + r"$\gamma=$" + f"{format(ecm_params['γ'], '2.2f')}, " + r"$\sigma=$" + f"{format(ecm_params['σ'], '2.2f')}" plot_name = f"cointegration_ecm_simulation_acf_pacf{image_postfix}" max_lag = 15 ylim = [-0.5, 1.1] arima.acf_pcf_plot(title, εt, ylim, max_lag, plot_name) # %% model_fit = arima.arma_estimate_parameters(εt, (1, 0)) print(model_fit.summary()) # %% arima_params = {"φ": numpy.array([0.5]), "δ": numpy.array([]), "d": 1} ecm_params = {"δ": 0.0, "γ": 0.5, "λ": -1.0, "α": 0.0, "β": 0.5, "σ": 1.0} n = 1000 image_postfix = f"_φ_{format(arima_params['φ'][0], '1.1f')}_β_{format(ecm_params['β'], '1.1f')}_λ_{format(ecm_params['λ'], '1.1f')}_γ_{format(ecm_params['γ'], '1.1f')}_σ_{format(ecm_params['σ'], '1.1f')}" xt, yt = ecm_sample_generate(arima_params, ecm_params, n)
arima.adf_report(darima1) # %% model_fit = arima.arma_estimate_parameters(darima1, (1, 0)) print(model_fit.summary()) # %% title = r"ARIMA(1,1,0) $\Delta x_t$ ACF-PACF Comparison: " + r"$\phi=$"+f"{numpy.array2string(φ1, precision=2, separator=',')}, " + r"$\delta=$"+f"{numpy.array2string(δ1, precision=2, separator=',')}" plot_name = "aima_estimation_1_1_0_pacf_acf_Δx_comparison" max_lag = 15 ylim = [-0.1, 1.1] arima.acf_pcf_plot(title, darima1, ylim, max_lag, plot_name) # %% title = "ARIMA(1,1,0) Residual Distribution Comparison with Normal(0, 1)" plot_name = "aima_estimation_1_1_0_residual_distribution" pdf_samples(title, normal_pdf(0.0, 1.0), model_fit.resid, plot_name, xrange=None, ylimit=None) # %% φ2 = numpy.array([0.8]) δ2 = numpy.array([]) d = 2 n = 10000 arima1 = arima_generate_sample(φ2, δ2, d, n)