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- The following ratio-to-moving averages for the seasonally adjusted series were found by the decomposition method applied on a time series representing quarterly sales for January 2018 to December 2020 period: a. Calculate the Seasonal Index for every quarter. b. If the trend is described by the trend line T^ = 1,000 + 30 t, what is the forecast for the fourth quarter of 2021?canton Supplies, inc., is a service firm that employs approximately 100 individuals.Managers of canton Supplies are concerned about meeting monthly cash obligations andwant to develop a forecast of monthly cash requirements. Because of a recent changein operating policy, only the past seven months of data that follow are considered to berelevant.Month 1 2 3 4 5 6 7Cash Required ($1000s) 205 212 218 224 230 240 246a. construct a time series plot. What type of pattern exists in the data?b. Using Minitab or excel, develop a linear trend equation to forecast cash requirementsfor each of the next two months.The table below shows percentage changes (xi) in the Dow-Jones index over the first five trading days of each of thirteen years and also the corresponding percentage changes (yi) in another index. xi yi 1.5 14.9 0.2 -9.2 -0.1 19.6 2.8 20.3 2.2 -3.7 -1.6 27.7 -1.3 22.6 5.6 2.3 -1.4 11.9 1.4 27.0 1.5 -4.3 -4.7 20.3 1.1 4.2 1- Calculate the sample correlation and interpret. 2- Test at the 1% significance level, against a two-sided alternative, the null hypothesis that the population correlation is 0. Thanks.
- Suppose we have the following returns for large-company stocks and Treasury bills over a six-year period: Year Large-Company US Treasury Bill 1 3.97 6.59 2 14.34 4.42 3 19.23 4.29 4 −14.45 7.32 5 −31.94 5.28 6 37.47 5.38 a. Calculate the arithmetic average returns for large-company stocks and T-bills over this time period. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. Calculate the standard deviation of the returns for large-company stocks and T-bills over this time period. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the arithmetic average risk premium over this period? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer…Consider the following time series data: 1 2 3 4 5 6 7 26 15 22 14 21 25 17 PART 1.Compute MSE using the most recent value as the forecast for the next period and then calculate the forecast for month 8. PART 2.Compute MSE using the average of all the data available as the forecast for the next period. What is the forecast for month 8?consider the following time series data.t 1 2 3 4 5 6 7yt10 9 7 8 6 4 4a. construct a time series plot. What type of pattern exists in the data?b. develop the linear trend equation for this time series.c. What is the forecast for t = 8?
- Consider the following techniques of transforming time series data. Choose all that applyWhich of the following statements are true: (1) If both the actual and seasonally adjusted dairy production figures increase then the actual increase was bigger than it usually is. (2) Increases and decreases in seasonally adjusted series cannot be caused by regular seasonal events. (3) If New Zealand suffers a widespread drought this coming summer then a decrease in the actual value of agricultural output is possible but there would be no change in the seasonally adjusted value. Select one: a.(1) and (2) b.(1) and (3) c.(2) and (3) d.(1), (2) and (3)consider the following time series data.Month 1 2 3 4 5 6 7Value 24 13 20 12 19 23 15a. compute MSe using the most recent value as the forecast for the next period. Whatis the forecast for month 8?b. compute MSe using the average of all the data available as the forecast for the nextperiod. What is the forecast for month 8?c. Which method appears to provide the better forecast?
- Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series: Quarter Seasonal Index Q1 73.9 Q2 84.1 Q3 107.1 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 2,964 Time 50.7 What is the trend projection of the series for period 119? (please round your answer to 1 decimalA customer comment phone line is staffed from 8:00 a.m. to 4:30 p.m. five days a week. Records are available that show the number of calls received every day for the last five weeks as shown in the following table. Assume the time series has seasonality without trend. Week Day Number 1 M 29 T 13 W 15 TH 14 F 22 2 M 24 T 9 W 15 TH 13 F 25 3 M 33 T 14 W 16 TH 12 F 20 4 M 26 T 12 W 15 TH 17 F 23 5 M 25 T 10 W 19 TH 16 F 24 (a) Solve for the forecast equation that minimizes the sum of squared error. x1 = 1 if Monday, 0 otherwise; x2 = 1 if Tuesday, 0 otherwise; x3 = 1 if Wednesday, 0 otherwise; x4 = 1 if Thursday, 0 otherwise. t = (b) Forecast the five days of Week 6. Week 6 Monday forecast callsWeek 6 Tuesday forecast callsWeek 6 Wednesday forecast callsWeek 6 Thursday forecast callsWeek 6 Friday forecast callsUsing the time series data in the table, respond to the following items. Period Sales 1 $ 615 2 676 3 761 4 710 5 784 6 801 7 852 8 698 9 1,193 10 1,115 11 1,231 12 1,259 13 1,495 14 1,229 15 1,652 16 1,337 17 1,673 18 1,613 Please show work, thanks.