Problem Set #2Due by Sunday November 3rd, 2019Problem 1 (35).Consider the dataset about bitcoin (BTC) price, the time series is fromJanuary 1st, 2017 to October 18th, 2019.(1: Points 6) First read the BTC data, then plot the QQ plot, boxplot andkernel density estimates. Discuss any features you see in the QQ plot, boxplotand kernel density plot. Specifically, address the following questions: Do thedata appear to be normally distributed? If not, in what ways do they appearnon-normal? Are the data symmetrically distributed? If not, how are theyskewed? Do the data seem heavy tailed compared to a normal distribution?How do the left and right tails compare; is one tail heavier than the other?(2: Points 6) Next, conduct data transformation by taking the squarerootand log-arithm to get transformed data, denoted as sqrt.BTC andlog.BTC, respec-tively. Further plot QQ plots, boxplots and kernel densityestimates, discuss the features you see in the plot similar to question (1).(3: Points 6) Conduct Box–Cox transformation to the original data andestimate its parameter λ by maximum likelihood.(Hint: Zoom in on the high-likelihood region with the following function:boxcox (BTC～ 1, lambda=seq(0, 1, 1/100)); Also use package ”MASS”).(4: Points 6) Find a 99% confidence interval (CI) for λ.(5: Points 6) Try to fit a skewed t-distribution including R code (use package”fGarch” and function ”sstdFit”).(6: Points 5) What are the estimates using the skewed t-distribution?1Problem 2 (35).Consider the Gold price in USD data and this time series is observed fromJanuary 3rd, 2017 to October 18th, 2019 (notice that you might need toclean some invalid data in Excel).(1: Points 6) First r ead the Gold data calculate the corresponding l og r eturns(say Y ). Plot this time series of l og r eturns and write a brief description. Dothe series l ook stationary? Do the fluctuations i n the series seem to be of constantsize? If not, describe how the volatilit代写dataset、代做Python，Java，c/c++编y fluctuates. ( use f unction ”diff”).(2: Points 6) Plot the QQ plot, boxplot and kernel density estimates ofthe log re-turns and give some explanations.(3: Points 6) Fit the standardized t-distribution (std) to the log returns.Find MLEs of the mean, standard deviation, and the degrees-of-freedomparameter by using Maximum Likelihood Estimation. (use package ”fGarch”and function ”Optim”).(4: Points 6) Calculate the AIC and BIC values based on the aboveoptimazition.(5: Points 6) Modify the code so that the MLEs f or the skewed t-distribution arefound. I nclude your modified code with your work. What are the MLEs?(also usepackage ”fGarch” and function ”Optim”).(6: Points 5) Which distribution is selected by AIC, the t or the skewed tdistribution?Whichdistribution is selected by BIC, the t or the skewed tdistribution?2Problem 3. (30)Consider the dataset of IBM price shares in the time series observed fromJanuary 3rd, 2017 to October 18th, 2019.(1: Points 4) Read the IBM dataset and calculate its sample mean, standarddevi-ation, skewness and kurtosis. (need to use package ”fGarch”).(2: Points 4) Fit a t-distribution to the data and show the estimates (usefunction ”stdFit”).(3: Points 4) Try to bootstrap the sample mean 1000 times in two cases:model-free and model-based on t-distribution. (use functions ”sample” and”rstd”).(4: Points 4) Plot QQ plot and KDEs of ModelFree mean and ModelBasedmean. Also, plot side-by-side boxplots of the two samples. Describe any majordif-ferences between the model-based and model-free results. Include the plotswith your work.(5: Points 5) Find 95% bootstrap c onfidence i ntervals f or the sample mean using themodel-based and model-free bootstraps with digits=5.(6: Points 4) Estimate the bias of the sample mean of IBM based on modelfreeand model-based bootstraps.(7: Points 5) Estimate the mean squared error (MSE) of the sample meanof data IBM. (Notice that MSE=variance+bias2.)3转自：http://www.3daixie.com/contents/11/3444.html