Part 1: Forecasting in Australia (40 points)(This question took place in 2017)Looking for a new perspective in life, you travel to Australia for an internship in a service consulting company. Your first project involves working with a major hotel group that hired your firm to improve operations planning. As a starting point for the project, your boss asks you to develop a forecasting tool to estimate the quarterly volume of overnight trips in Australia. An overnight trip is a trip where a traveler spends at least one night at their destination.The hotel group’s business model requires them to make key staffing and pricing decisions two quarters (6 months) in advance. The forecasting horizon is two quarters (thus, in the last quarter of 2017, you are forecasting overnight trips in the second quarter of 2018). A snapshot of the data is below. The raw quarterly data is available in this link: (attached). The time unit is Quarters, and the observations are thousands of overnight trips. Question 1 (20 points)Implement the Holt-Winters method for forecasting demand in Australia. You can use Excel or any programming language you want. Pre-existing implementations of the Holt-Winters method cannot be used. Note that the season, in this case, has four periods (L = 4) corresponding to the four quarters of the year. Initialize the parameters of the Holt-Winters method according to the initialization procedure discussed in class. The inputs of your implementation of Holt-Winters will be the data, the season length L, the forecast horizon 𝜏τ = 2 quarters, and parameters 𝛼,𝛽,α,β, and 𝛾γ. The output should be the 2-quarter forecast between Q3 2000 and Q2 2018. In the same graph, plot the 2-quarter forecast for the quarters between Q3 2000 and Q2 2018 for 𝛼=𝛽=𝛾=0.3α=β=γ=0.3 as well as the actual trips between Q3 2000 and Q4 2017.Question 2 (10 points)The next step is to tune the parameters 𝛼,𝛽,α,β, and 𝛾γ . Since we care about the forecast two quarters out, find parameters that give a “low” Mean Squared Error (MSE) between the two-quarter forecast (𝜏τ = 2) and the actual number of trips between Q3 2000 and Q4 2017. Recall that the MSE between a vector 𝐱=(𝑥1,...,𝑥𝑇)x=(x1,...,xT) and 𝑦=(𝑦1,...,𝑦𝑇)y=(y1,...,yT) is defined as 1𝑇∑𝑇𝑡=1(𝑥𝑡−𝑦𝑡)21T∑t=1T(xt−yt)2 .Explain how you searched for a “good” 𝛼,𝛽,α,β, and 𝛾γ . How do you interpret the values of 𝛼,𝛽,α,β, and 𝛾γ that you found?Question 3 (10 points)Produce a point forecast (i.e., a number) for Q2 2018. How would you refine this forecast? How would you estimate this forecast's potential error? (Qualitative answers for the questions suffice).Part 2: Forecasting Competition The daily number of COVID-19 vaccines given in the USA is ramping up. In this part of the assignment, your group’s goal is to forecast the daily number of vaccines given in the USA for the eight days between March 31st and April 7th (included) of 2021. Your forecast will be compared with the numbers collected by Our World in Data (https://ourworldindata.org/ (Links to an external site.)). The raw data per state (and for the whole USA) is available here: https://github.com/owid/covid-19-data/blob/master/public/data/vaccinations/us_state_vaccinations.csv (Links to an external site.) .A shorter version of this data with only US vaccinations is available here: (attached) (the data updated on 03/28 is here (attached)). A snapshot of the data is below. Produce a forecast using the Holt-Winters method and show your implementation and rationale for choosing lues of 𝛼,𝛽,α,β, and 𝛾γ.Your forecast will be evaluated using the Mean Squared Error. Namely, let (𝑓1,...,𝑓8)(f1,...,f8) be your forecast for the days between March 31st and April 7th. Let (𝑑1,…,𝑑8)(d1,…,d8) be the actual number of vaccinations. The MSE, in this case, is 18∑8𝑡=1(𝑓𝑡−𝑑𝑡)218∑t=18(ft−dt)2 .Part 3: Qualitative Forecasting You have accepted the position of Demand Planning Analyst in the Retail Fulfillment Operations team at Apple. One of your most exciting tasks is to estimate the demand for new products being launched in the near future. This task is challenging because, due to long lead times and manufacturing planning, Apple's management must make these forecasts well in advance, sometimes even a year before the launch date.Yesterday, you were assigned to the team responsible for Apple’s next-generation phone, the iPhone Z. Your task is to forecast how many iPhone Z units will sell globally during the first year after launch. The launch date is nine months from now, but you must make the final forecast soon. Once the forecast has been made, the company places one large order to its suppliers. After the order is placed, you cannot update the order quantity.Your task is certainly not an easy one, and some “out-of-the-box” thinking is required. This is an open-ended exercise that will motivate the discussion on forecasting in our next class. It is an opportunity to be creative and to think about different forecasting methods.No need to source data or be very specific. A few paragraphs (or slides) for each question will suffice.Question 1 (10 points)Qualitatively describe at least two different approaches to forecasting the future demand (if possible, base your answers on the methods described in class). Briefly explain the advantages, limitations, and any assumptions behind each approach. What data would you need for each forecasting method, and who would you have to engage with to collect this data?Question 2 (10 points)Suppose that you want to use the Newsvendor model to estimate the optimal order quantity for the iPhone Z. This, however, requires a forecast that describes the distribution of the future demand. Explain if and how you would use your approaches in Question 1 to construct a demand distribution for the iPhone Z.Question 3 (10 points)After delivering your report on demand forecasting for the iPhone Z, the executive team is impressed. They invite you to be a part of Apple’s most ambitious secret project: The Apple iCar. This revolutionary electric vehicle features level 4 autonomous driving capabilities, and its modular and elegant design is set to disrupt the auto industry. You are tasked with estimating the demand for this vehicle during the first year after launch. Propose two methods for estimating the demand for this new product. What are some of the advantages and limitations of each method?