Escoger. Select the correct option. —Bueno, ya conociste a mis padres. ¿Ellos te hablaron de ____?—Hablamos de muchas cosas, pero de ____ no me dijeron nada.  

Escoger. Select the correct option.   Por fin [1] por qué Marlene rompió con David. ¡Está enamorada de José Luis! Ana Milena [2] llamarte ayer, pero no contestaste el teléfono. Santiago nunca me dijo cómo [3] a su novia, pero sé que fue muy romántico. Mañana me gradúo de la universidad. [4] terminar los estudios. Martín se jubiló el año pasado. [5] trabajar más. Durante la boda, Daniela no prestó atención. [6] sacar fotos.

¿Lógico o ilógico? Indicate whether the statement below is lógico (true) or ilógico (false).   Busqué por horas, pero no encontré la casa de David. No quise visitarlo.  

¿Lógico o ilógico? Indicate whether the statement below is lógico (true) or ilógico (false).   Mis padres se conocieron en Japón; por eso celebran sus aniversarios en Tokio.  

Which of the following is true for the autocovariance function of a stationary time series? Choose all correct answers.

Which of the following expressions is correct? 

Causality of an ARMA process implies that the process is also invertible.

For a stationary time series, the autocovariance function γ(h)\gamma(h) satisfies the property that γ(h)\gamma(h) depends on both the lag hh and the actual time points tt and ss.

Which of the following approaches can be used to select the order of an ARMA model? Choose all correct answers.  

ARIMA Modeling and Forecasting 2a. Split the data in Training and Testing sets. Leave the last 8 observations for testing, the rest will be your training set. You will apply the same trend-seasonality model from Question 1d on the Training set and forecast the corresponding data for the testing set. Calculate the MAPE and interpret it. How does it compare to the MAPE in 1(d)? Why is it different? Hints:  – Keep in mind that modeling factors may require extra steps on the data preparation.  – You can use predict, or predict.gam for your predictions.  2b. Fit an ARMA model using the residuals from the model in Question 2a. Find the order of the ARMA model using a max order 6 for p and q, and 1 for d.  Use AICc as the criterion for the order selection. What are the selected orders? Use the forecast from the model you find and add them to the forecast values in 2a. Comment on what would be the logic of this procedure? 2c. Fit an SARIMA model to the training dataset using ARIMA orders (10,1,8) and seasonal orders (1,0,1). Comment on the model goodness of fit. 2d. Use the model from Question 2c to forecast the next eight time points (testing dataset) using the **8 lags ahead approach**. Overlay the observed versus predicted values for both series, including 95% confidence intervals. Calculate the MAPE of the prediction and comment on the prediction performance of the model. What approach would you use for this data? Why?