According to Appendix 3, AR (1) Model Coefficients:ar1 intercept0.2969 -0.0003s.e. 0.0576 0.0018sigma^2 estimated as 0.0004528: log likelihood = 675.81, aic = -1345.62ϕ0 = -0.0003*(1-0.2969)2 Details are in Apendix 3 and Apendix 5= -0.00002109AR (1) Model Form:rt = ϕ0 + ϕ1rt-1 + at , σa2rt = -0.00002109 + 0.2969rt-1+at , 0.0004528

AR(1) is equivalent to MA(1) when the autoregressive parameter is equal to 1.Group of answer choicesTrueFalse

In a pure auto-regressive process, AR(p), the value of p can be identified usingSelect one:a. Auto-correlation functionb. Ljung−Box testc. Partial auto-correlation functiond. Auto-correlation and partial auto-correlation function

Tras ajustar un modelo ARIMA a la serie mensual Consumo de Gasolina de Automóviles (1959/1 - 2019/12):um1 <- um(Y, bc = T, i = list(1, c(1,12)), ma = list(1, c(1, 12)))um1                 Estimate      Std. Errortheta1  0.6376817  0.02663501theta2  0.7297452  0.02342502se ha realizado el siguiente tratamiento de anomalíastfm1 <- outliers(um1, c = 4, type = c("AO", "LS", "TC"))tfm1                        Estimate     Std. ErrorTC52.01   0.21873384  0.03000070AO56.11   0.19688134  0.03057669AO73.12   0.20732954  0.03105188LS74.03  -0.09807832  0.02579049theta1      0.55657060  0.02628365theta2      0.70874936  0.02435791Comparando las estimaciones de los parámetros MA de ambos modelos, junto con los respectivos errores estándar, se comprueba que, al nivel de significación del 5%,...Pregunta 1Respuestaa.las anomalías son influyentes porque cambian significativamente la estimación del  parámetro MA estacional.b.las anomalías son influyentes porque cambian significativamente la estimación del  parámetro MA regular.c.las anomalías no son influyentes porque no cambian significativamente las estimaciones de los parámetros MA.d.las anomalías son influyentes porque cambian significativamente las estimaciones de los parámetros MA.

One of the sources of error in the RMSFE in the AR(1) model is: a. due to measuring variables in logarithms. b. the model only looks at the previous period's value of Y when the entire history should be taken into account. c. the error in estimating the intercept and slope coefficients. d. that the value of the explanatory variable is not known with certainty when making a forecast.

Consider two time series, {𝑥𝑡}𝑡=1𝑇 and {𝑦𝑡}𝑡=1𝑇, one generated using AR(1) and the other using MA(1), as follows:𝑥𝑡=𝛼+𝛽𝑥𝑡−1+𝜀𝑡, and𝑦𝑡=𝜇+𝜀𝑡+𝜃𝜀𝑡−1.Suppose 𝛽=𝜃=0.5.Based on the provided information, we can claim that:Group of answer choicesNone of the presented answers are correct.The first order autocorrelation of the series following the presented AR model is larger than the first order autocorreation of the series following the presented MA model.The autocorrelation functions of the two models are identical for lags greater than one.The second order autocorrelation of the series following the presented AR model is equal to zeroThe two step-ahead forecast of the series following the presented AR model is equal to the unconditional mean of the series.