Assignment #5: Time Series Analysis Simple Moving Average A _ 2(most recent k data vaiues') _ i=rk+13'i _ 31th + + yt_1 + 3': J't+1 k k k where Hl = forecast of the time series for period t + 1 yt = actuai value of time series in period t k = number of periods of time series data used to generate the forecase ii=1IYt 57r+1| Mean Absolute Error (MAE) = 11 Question la) Forecast the future demand for bag of apple based on the historical data given below using each forecast method. Actual Demand 4-week moving average (53\". 1) Absolute Forecast Error (4- 01:) week} \"It": ' 53:\" I} Question lb) what is the forecast the future demand for bag of' apple based on the historical data given above for week 15 and week 20 using above forecast method using 4weeks smoothing average? Week 15 =" Week 20 =" Question 1c) Forecast the future demand for bag of apple based on the historical data given below using each forecast method. Actual Demand 7-week moving average (5?\" 1) Absolute Forecast Error (1'- U:) week} \"J": ' n I} 6 23 5.99 6.55 6.78 6.12 5.88 5.34 5.5? 5.98 5.20 l 1 5.1 s 12 13 6.89 r4 9' E E I m 6.78 98 at a II 3 M 7.32 HHIIIIIIIIIIIIIIIIIIII b) q; 7.20 Question 1d) what is the forecast the future demand for bag of apple based on the historical data given above for week 15 and week 20 using forecast method using 7 weeks smoothing average? Week 15 -='7 Week 20 ='7 Question 1e) Comparing MAEs of 4week and 7weeks moving average. which forecasting model is the best? Exponential Smoothing 57r+i = \"yr + (1 My} where Put = forecast of the time series for period t + 1 y; = actuai mine of time series in period t yr = forecast o f the time series f or period t a = smoothing constant (0 S a S 1) Question 11) Forecast the future demand for bag of apple based on the historical data given below using each forecast method. Exponential smoothing forecast Absolute Forecast Error (Yr) Wm} using a = 0-2 {IYr foul) -_ - -_ -_ -_ - -_ n_ - n n_ -- -_ n_ -_ n- -_ n l-n Question lg) what is the forecast the future demand for bag of apple based on the historical data given above for week 15 and week 20 using forecast method using exponential smoothing. Week 15 = Week 20 ="' Question 1h) Comparing MAEs of 4week moving average, 7week moving average and exponential smoothing {a = 0.2), which forecasting model is the best? Question 2) The monthly demand for units manufactured by Tesla Company has been as follows in 2022: Year Month Units January 500 February 470 March 510 April 495 May $10 June 450 2022 July 410 August 475 September 505 October 490 November $25 December 550 January 510 February 570 March 530 April 513 May 560 2023 June 590 July 520 August 576 September October November December a. Use the three-month moving average method to forecast the number of units for next year-2023 September to December. b. Calculate the mean absolute error (MAE) of the three-month moving average method for September to December of 2023. c. Use the exponential smoothing methods to forecast the number of units for September to December 2023. Assume the initial forecast for February 2022 was 470 units. Use smoothing constant alpha (a) = 0.4. d. Calculate the mean absolute error (MAE) of the exponential smoothing method for September to December 2023. e. Compare the MAEs for both forecasting methods. Which one should be used for future demand forecasting