Assume that a time-series plot takes the form of that shown in the following graph: 80 60 40 40 20 20 -20 -40 0 2 6 8 10 12 Given this plot, which of the following models would likely give the best fit? ŷ = b + b₁t + b₁²² + b₁t³ ŷ = b + b₁t+ b₁²² ŷ = bob₁ + b₁t ŷ = b + b₁t + b₁²² + b3t³ + bât^
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- A method of smoothing a time series that uses successively, une qual weights for each of the K-values from the immediate past to come up with forecast for a time-period is the moving averagethe weighted moving averagethe trend projectionexponential smoothingWhy is it important that time series are “stationary” and what are the implications of non-stationary on OLS estimates? Outline an approach you could use to make a non-stationary series stationary. Discuss what is meant by cointegration and how you would test for it.find the first three parts of taylor time series:
- As a general rule, is it advisable to difference a time-series more than 1–2 times? Why or why not?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…find power series expansion of the function
- 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.Find power series representationThe lifetime of a bulb is modeled as a Poisson variable. You have two bulbs typesA and B with expected lifetime 0.25 years and 0.5 years, respectively. When abulb’s life ends, it stops working. You start with new bulb of type A at the start ofthe year. When it stops working, you replace it with a bulb of type B. When itbreaks, you replace with a type A bulb, then a type B bulb, and so on. 1. Find the expected total illumination time (in years), given you do exactly 3bulb replacements.2. Your replacements are now probabilistic. If your current bulb breaks, youreplace it with a bulb of type A with probability pp, and with type B withprobability (1 – pp). Find the expected total illumination time (in years),given you do exactly nn bulb replacements, and start with bulb of type A.Answer for part 2 exists in closed form in terms of n and p.
- Consider the following techniques of transforming time series data. Choose all that applyFind the power series representing the function 1/ (z-5) in the region |z - 4| < 1 .As a result of the experiment, data recorded in the form of a statistical series were obtained. find the range of variation and divide it into 9 intervals.