a. Use the values values of Y for the next two months, using simple exponential smoothing with w = 0.7. b. Use the Holt model wvith w = 0.7 and v = 0.7 to forecast the values of Y for the next two months
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- 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)
- 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)1i. Suppose that a structure can withstand a flood with a peak discharge no greater than 1,950 m3/s and it has been designed to have an economic life span of 100 years. Determine the risk of failure assuming the Extreme Value Distribution when the mean and standard deviation of the annual flood series are 410m3/s and 280 m3/s, respectively. 1ii. What is the probability that at least one flood of ARI 50y (T=50y) will occur during the 30 year design life of a flood control project? 1iii. Consider a small, temporary (3 year design life) flood mitigation dam designed to contain a 20 year flood event. What is the risk that it will be overtopped at least once in the design life.What is the probability that the time of the first event that is observed to occur in a Poisson process with rate λ per unit time, after initiation at t = 0, occurs later than time t = t0, for fixed value t0 ? Justify your answer
- 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.By first calculating, and then combining, the number of counts in each individual 30- second period, what does student A determine as the average decay rate (in counts/sec), and what is its uncertainty?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.
- Old Faithful is a geyser located in Yellowstone National Park in Wyoming, USA. Millions of travelers come from afar to witness Old Faithful's eruptions each year. The data provided show the waiting time until the next eruption for 272272 Old Faithful eruptions in 1990. Suppose that prior to 1990, travelers to Yellowstone are told that Old Faithful is expected to erupt, on average, every 6969 minutes, and park scientists believe that this average is no longer true. Suppose that, based on historical data available over several decades, the scientists are comfortable assuming that all eruption waiting times have a known standard deviation of 17.24817.248 minutes. 54 74 62 85 55 88 85 51 85 54 84 78 47 83 52 62 84 52 79 51 47 78 69 74 83 55 76 78 79 73 77 66 80 74 52 48 80 59 90 80 58 84 58 73 83 64 53 82 59 75 90 54 80 54 83 71 64 77 81 59 84 48 82 60…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: 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)