ETF 5952 : Quantitative Methods for Risk Analysis - Accounting and Finance Assignment Help

Assignment Task

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Question 1
To answer this questions, use the data “VIC”, which contains Covid-19 positive cases and Google mobility data in Victoria State. More precisely, the data set contains the following variables: 
• date: date 
• case: the number of positive cases reported 
• case.lagX: lagged “case” variable with lag of X days (X = 1,...,5). 
• retail: mobility trends for places such as restaurants, cafs, shopping centres, theme parks, museums, libraries and cinemas. 
• grocery: mobility trends for places such as supermarkets, food warehouses, farmers markets, specialty food shops and pharmacies. 
• park: mobility trends for places like national parks, public beaches, marinas, dog parks, plazas and public gardens. 
• transit: mobility trends for places that are public transport hubs, such as underground, bus and train stations. 
• work: mobility trends for places of work. 
• house: mobility trends for places of residence. 
The last six variables are based on information from Android phones and measures relative mobility. See “Mobility Report” provided by Google for more details. 
1. Estimate autoregressive (AR) model with lag order of 1, 2,...,5 and report the estimation result. Notice that AR(k) means that yt = α0 + α1yt−1 + · · · + αkyt−k +  t. 
2. Compare the AR(1),..., AR(5) models by using AIC and BIC. Explain which model is the optimal according to those inforamtion criterion (less than 30 words). Also, provide a time series plot of “case” with fitted values from the optimal model. 
3. Use the six variables from Google mobility data. Provide time series plots (you can plot each series at a different figure, if you prefer). Explain if the six variables share similar trend. 
4. Use the six variables of mobility and estimate factor model (PCA): 
E[xt,j ] = φj,1νt,1 + φj,2νt,2 + · · · + φj,6νt,6. 
Here, jth variable vary over time t. Latent factors νt,1, . . . , νt,6 depend on time and factor loading φj,1, . . . , φj,6 depend on the variable index j. Plot variance of all estimated factors and explain contri butions of the factors to variations in the mobility variables (no more than 30 words). 
5. Report estimated factor loadings and interpret the effect of the first factor on the mobility variables (no more than 40 words). 
6. The data set contains the mobility variables with 7 days lag, because there are a few days lags between infection and positive test result. Estimate the AR(5) model with the six mobility variables. Can you interpret all the estimation result regarding effects of the six mobility variables on positive case numbers? (Answer Yes or No). Explain a possible reason for your answer (no more than 40 words). 
Question 2 
We use “Boston” of an R-package “MASS”, which contains information on housing values in suburbs of Boston. Before your analysis, read an instruction for MASS regarding the data, which can be found on the web. 
1. Regress log of median housing value on the rest of variables (including an intercep i.e., a constant term) in the data set and report the estimation result. Provide interpretation of the effect of crime on median housing value (no more than 30 words). 
2. If you apply for AIC or BIC to select regressors (except the constant term) at the model of Qeustion 2.2, then how many models do you have to estimate? 
3. Set a seed to be “123”, and use lasso (gamlr) to estimate the model in Question 2.1. Use cross-validation method to choose the tuning parameter for lasso and report only the estimated coefficients. Notice that there are two methods: min-cv and 1se-rule and report both. For each of the methods, provide interpretation of the effect of crime on median housing value (no more than 30 words). 
4. Use lasso (gamlr) to estimate the model in Question 2.1 with AICc (not AIC) and BIC. For each case, report estimation result and provide interpretation of the effect of crime on median housing value (no more than 30 words). 

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