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- Given is a historical time series for job services demand in the prior 6 months. Month Demand 1 812 2 799 3 777 4 811 5 765 6 791 The Period 4 forecast by using exponential smoothing with 0.33 alpha = (in 2 decimal places)The following table shows the average price of tomatoes (in dollars per pound) in certain country from 2017 to 2021 Year Price 2017 1.715 2018 0.942 2019 0.916 2020 1.181 2021 1.614 Use 2017 as the base period to compute the simple index for this time series By what percentage did the price of tomatoes increase or decrease between 2017 and 2021? Calculate an exponential smoothed series for this time series, using ? = 0.6. Forecast the price of tomatoes in 2022.With the gasoline time series data from table 17.1, show the exponential smoothing forecasts using a = .1.a. applying the MSe measure of forecast accuracy, would you prefer a smoothing constant of a = .1 or a = .2 for the gasoline sales time series?b. are the results the same if you apply Mae as the measure of accuracy?c. What are the results if Mape is used?
- Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 73.7 Q2 82.5 Q3 108.1 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,733 Time 65.8 If the original value of the series in a Q4 was 2,197, then what is the seasonally adjusted value?At a police station in a large city, calls come in at an average rate of four calls per minute. Assume that the time that elapses from one call to the next has the exponential distribution. Take note that we are concerned only with the rate at which calls come in, and we are ignoring the time spent on the phone. We must also assume that the times spent between calls are independent. This means that a particularly long delay between two calls does not mean that there will be a shorter waiting period for the next call. We may then deduce that the total number ofcalls received during a time period has the Poisson distribution. Find the average time between two successive calls and find the probability that less than five calls occur within a minute.Explain the different factors that account for fluctuations in time series data
- The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y.Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 73.8 Q2 86.1 Q3 109.2 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,291 Time 54.9 In general, what quarter is the busiest time of the year? (please just answer 1, 2, 3, or 4)Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 72.9 Q2 84.3 Q3 108.6 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,796 Time 77.4 What is the forecast for period 51, if period 51 is a Q1? (please round your answer to 1 decimal place)
- Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 71.8 Q2 85 Q3 107.6 Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4. Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below: Coefficients Intercept 2,215 Time 59.3 If the original value of the series in a Q1 was 2,179, then what is the seasonally adjusted value? (please round your answer to 1 decimal place)The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a)Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?A share follows a discrete-time log-normal process with initial price ?=£3000, u=0.02, and o2=0.015, where the time-step is 1 year. Find the probability that a European call on the share with strike price £3300 and expiry date 4 years will be exercised. State your answer as a decimal to three significant figures.