Consider the following time series data for the real consumption of households and government, at current PPPS (in billions 2017USS). In year 2018, the first lagged value of the real consumption is and the first difference is Year | 2015 | 2016| 2017 | 2018 | 2019 1 3 4 5 t rcon, | 1267 | 1307 | 1375 | 1413 O A. 1307; -38 B. 1375; 38. O C. unknown; unknown. O D. 1413; unknown
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- Look at the four plots in Figure 14.2—the US unemployment rate, thedollar-pound exchange rate, the logarithm of the index of industrial production, and the percentage change in stock prices. Which of these seriesappears to be non-stationary? Which of them appears to resemble a randomwalk?Which of the time series forecasting methods would not be used to forecast seasonal data?In 1998 El Salvador had a gini index of 54.50 and 26 years later had a gini index of 38. What does this tell us about the distribution of income throughout El Salvador?
- 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.A time series variable generally is correlated with one or more of its laggedvalues; that is, it is serially correlated. Explain How?Which of the following time series forecasting methods would not be used to forecast seasonal data?
- Suppose that the first Section of Applied Stat class ends at 13:20 and the second starts at 13:30 with ten minutes break. Professor, who teaches both sections, wants to go to bathroom during the break. Suppose that the time that takes for professor to go to bathroom and come back to the classroom has an exponential distribution with the mean of 6.7 minutes. Find the probability that the professor will be late for class for less than 3 minutes (round to 3 decimal places).Explain the different factors that account for fluctuations in time series dataSuppose that historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine whether the proportion of new car buyers that trade in their old car has statistically significantly decreased, what is the p-value? (please round your answer to 4 decimal places)
- The time to failure of a certain type fo electrical component is assumed to follow an exponential distribution with a mean of 4 years. The manufacturer replaces free all components that fail while under guarantee. If the manufacturer wants to replace a maximum of 3% of the ocmponents, for how long should the manufacturer's stated guarantee on the component be?Ten days of data on the S&P Dynamic Futures Index are as follows: 3.1) Construct a time series plot. What type of pattern exists in the data? 3.2) Use trial and error to find a value of the exponential smoothing coefficient that results in a relatively small MAE. You should try at least 5 values before making any conclusions.The operator of a pumping station has observed that demand for waterduring early afternoon hours has an approximately exponential distribution with mean 1000cfs (cubic feet per second).a) Find the probability that the demand will exceed 700 cfs during the early afternoonon a randomly selected day.b) What water-pumping capacity should the station maintain during early afternoons sothat the probability that demand will be below the capacity on a randomly selectedday is 0.995?c) Of the three randomly selected afternoons, what is the probability that on at least twoafternoons the demand will exceed 700 cfs? 2. Let Y1 and Y2 be random variables with joint density functionf(y1, y2) = (6/7(y^2+y1y2/2) 0 < y1 < 1, 0 < y2 < 2,0, elsewherea) Find marginal density functions. Are Y1 and Y2 independent?b) Find P(0 < Y1 < 0.3, −2 < Y2 < 1).c) Find P(0.6 < Y1 < 1|0 < Y2 < 1). 3.The joint density function of Y1 and Y2 is given byf(y1, y2) = (y1 + y2), 0 <…