Joe Messina ISA 225 April 18, 2021 1. Which of the following is relatively easier to estimate in time series modeling? A) Cyclical B) Seasonality C) Trend D) No difference between Seasonality and Cyclical 2. Which of the following is an example of time series problem? 1. Estimating number of hotel rooms booking in next 6 months. 2. Estimating the total sales in next 3 years of an insurance company. 3. Estimating the number of calls for the next one week. A) Only 3 B) 1 and 2 C) 2 and 3 D) 1 and 3 E) 1,2 and 3 3. Smoothing parameter α close to 1 gives more weight or influence to recent observations over the forecast. A) TRUE B) FALSE 4. The following is a plot of monthly housing sales from 1973-1996. a) Is the above plot a time series? If yes, describe the time series with components. If no, explain why? Yes, the plot above is a time series that has an irregular component, which is neither systematic nor predictable. There’s a strong relationship, but neither a positive nor negative trend. There is also no consistent repeating variation.5. The demand (in thousands) of a particular item in a factory has varied as follows. Year 2016 2017 2018 2019 2020 2021 Production 120 123 124 128 127 131 a. Based on the above time series (table), make a forecast of the demand of this factory in 2022 using simple moving average method with lag of three. Year 2016 2017 2018 2019 2020 2021 Predicted production value (L=3) X X X 122.34 125 126.34 The predicted demand for the production value of this factory in 2022 is 128.67 with L=3. b. Based on the above time series (table), make a forecast of the demand of this factory in 2022 using exponential smoothing method with α=0.65. Year 2016 2017 2018 2019 2020 2021 Predicted production value (a=0.65) X 120 121.95 123.28 126.35 126.77 The predicted demand for the production value of this factory in 2022 is 129.52 with a=0.65. c. Calculate the MAPE for both methods described in a) and b). Which method provide a more reliable forecast?MAPE Forecast #1 (Simple moving average method)= 3.19 MAPE Forecast #2 (Exponential smoothing method)= 2.3 Therefore, the Exponential smoothing method provides a more reliable forecast. 6. Based on the following time series, please suggest which method should we use to make better forecasting? Smoothing method or Regression-based method? Why? We should use the smoothing method since the variation in the data is large. 7. Below we see a plot of the closing price of the DJIA with exponentially smoothed method using α = 0.70 and α = 0.15. Please identify which line is performed with the parameter α = 0.15, why? The yellow line is performed with the parameter a=0.15. We know this because when a is closer to zero, remote data is dampened out more slowly, producing forecasts that are more stable and smoother. The yellow line is clearly smoother than the blue line, which is more volatile and sporadic.8. The following is the regression output after the natural log transformation of the response variable sales. a) Please write down the regression equation based on the output. ln(y)= 0.07x – 139.92 y= e^0.07x – 139.92 b) From the plot, we can clearly see the seasonal component. How would you add this component into the regression? Describe in details. Consider the seasonal component as a categorical variable with 4 categories: Q1, Q2, Q3, and Q4. Then, create 3 dummy variables c) After adding the seasonal component into the regression, write down the general format of the model. Is it an additive model or a multiplicative model? Y-hat= T * S Y-hat= e^b0+b1x1 * e^b2x2 + b3x3 + b4x4 This is a multiplicative model since we are modeling the logarithm of the response