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x1 x2 x3 x4 x5 0.955277552 2.361917595 0.993418774 -0.848964256 -1.083709078 0.645082785 2.534616862 -0.149652234 -0.053987543 0.522730438 1.33003082 3.357724309 1.449752607 1.25769613 -0.484063396 0.627756149 3.313935597 -0.532045937 -1.793432546 -0.662355752
x1 | x2 | x3 | x4 | x5 |
0.955277552 | 2.361917595 | 0.993418774 | -0.848964256 | -1.083709078 |
0.645082785 | 2.534616862 | -0.149652234 | -0.053987543 | 0.522730438 |
1.33003082 | 3.357724309 | 1.449752607 | 1.25769613 | -0.484063396 |
0.627756149 | 3.313935597 | -0.532045937 | -1.793432546 | -0.662355752 |
1.440358362 | 4.091506839 | 1.865995111 | 1.231836973 | -0.249944598 |
-0.868643107 | 2.404562365 | -2.361439196 | -0.941032387 | -0.495003858 |
-1.067776316 | 0.855873575 | 0.82137504 | 0.610041886 | -1.17562397 |
2.414395658 | 3.099094518 | 1.757295626 | -1.394856681 | -0.281221414 |
-1.044189092 | 1.435086523 | -2.450025592 | 1.757685815 | 2.394009661 |
2.3388686 | 3.486937818 | 4.298889074 | 1.109635385 | 1.21016442 |
-0.604679121 | 2.184871133 | -4.04379038 | -1.130250915 | -2.650018167 |
1.104372086 | 2.852268992 | 4.339404389 | -2.605046986 | -1.169528646 |
..... | ||||
Problem 5 (15 pts). Each column of the "Dataset.xlsx" corresponds to a realization of some stochastic process. Sketch the time plot and correlogram for each one of the time series using the command using Rstudio acf(x, lag.max =20). Interpret the correlogram of each realized time series data and then decide which one of the MA(1), MA(2),AR(1),RW (with or without drift), or white noise processes are most suitable to model the underlying stochastic processes. You should present your final models by writing their corresponding equations explicitly. Find a relatively reasonable set of estimates for the parameters of each model by trial and error, e.g., for a candidate AR(1) model you may plug in different values for 1 and w2, and thereafter compare the plot of the computed sample ACF of your time series against the plot of the theoretical ACF of your proposed AR(1) process. Please note that there is no need to submit your R implementations. However, it is important to demonstrate the procedure by which you have carried out the trial and error step and eventually obtained the estimates for parameters of each model. It will be further informative to present a figure comprised of three horizontal subplots: 1- time plot, 2- correlogram, and 3- theoretical ACF (sketched according to the estimates of parameters obtained earlier) for each process
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