Month Sales 1 105 2 135 3 120 4 105 5 90 6 120 7 145 8 140 9 100 10 80 11 100 12 110 Use ? = 0.2 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)
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| Month | Sales |
| 1 | 105 |
| 2 | 135 |
| 3 | 120 |
| 4 | 105 |
| 5 | 90 |
| 6 | 120 |
| 7 | 145 |
| 8 | 140 |
| 9 | 100 |
| 10 | 80 |
| 11 | 100 |
| 12 | 110 |
Use ? = 0.2 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)
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- Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?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.The following table reports the percentage of stocks in a portfolio for nine quarters: a. Construct a time series plot. What type of pattern exists in the data?b. Use trial and error to find a value of the exponential smoothing coefficient a thatresults in a relatively small MSE.c. Using the exponential smoothing model you developed in part b, what is the forecastof the percentage of stocks in a typical portfolio for the second quarter of year 3?
- 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)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)An investor bought a 5 ½% bond at 99. Compute the current yield. (Round answer to two decimal places.)
- A bank pays interest at a rate of 5%. What is the yearly multiplier if interest is compounded (a) three times a year? (b) continuously?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)For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83. Compare a three-month moving average forecast with an exponential smoothing forecast for α = 0.2. Which provides the better forecasts using MSE as the measure of model accuracy? Do not round your interim computations and round your final answers to three decimal places. Movingaverage Exponentialsmoothing MSE What is the forecast for next month? If required, round your answer to two decimal places.
- 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.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?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?
