(c) Use a smoothing constant of a = 0.6 to compute the exponential smoothing forecasts. (Round your answers to two decimal places.) Time Series Value Yt Month t 1 2 3 4 5 6 7 8 9 10 11 12 105 135 120 105 90 120 145 140 100 80 100 110 Forecast Fr
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![(b) Use α = 0.4 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)
Month t
1
2
3
4
5
6
7
8
9
10
11
12
Time Series Value
Yt
105
135
120
105
90
120
145
140
100
80
100
110
Forecast Ft
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- 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.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)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?
- Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 72.8 Q2 83.2 Q3 108.8 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 2,570 Time 53.9 What is the forecast for period 49, if period 49 is a Q3? (please round your answer to 1 decimal place)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.Use power series to solve the initial value problem
- Joe is a student who is conducting experiments with a series of lightbulbs. He started with 10 identical lightbulbs, each with an exponentially distributed lifetime with a mean of 200 hours. Joe wants to know how long it will take until the last bulb burns out (or fails). At noontime, Joe stepped out to get some lunch with 6 bulbs still on. Assume that Joe came back and found that none of the 6 bulbs has failed. (a) After Joe came back, what is the expected time until the first bulb failure? (b) What is the expected length of time between the fourth bulb failure and the fifth bulb failure?A corporate bond that pays 4% per annum semi-annually has a yield of 3% p.a. withcontinuous compounding and a remaining life of 1.5 years (immediate after couponpayment). The yield on a similar risk-free bond is 2% p.a. with continuous compounding. The risk-free rates are 1% p.a. with continuous compounding for all maturities.Assume that the unconditional probability of default per every six months is a constantand that defaults can happen at the end of every six months (immediate before couponpayment). The recovery rate is 40%. Estimate the unconditional probability of defaultusing the “more exact calculation”.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)
- Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series. Use rounded for two decimal places values for intermediate calculations. Use minus sign for negative values.Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: 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 coefficients from a regression of the deseasonalized series on Time are given below: If the original value of the series in a Q4 was 2494, then what is the seasonally adjusted value? (please round your answer to 1 decimal place)Suppose that the length of a phone call in minutes follows exponential distribution with parameter λ=8. If some one comes ahead of you in queue of telephone booth, then find the probability that you have to wait between 10 and 20 minutes.