Quantitative Analysis/ Questions and Answers

ECON1061 – Final Assessment, Semester 1 2021 Instructions: 1. Answer all questions in a new Word document. DO NOT copy the questions in this file to your answer sheet as this will affect your Turnitin score. Do not include a coversheet. Your answer sheet should only include your full name, student number, and answers to the questions. 2. Please label your answer to each question clearly – e.g., Question 1 a. 3. Font “Arial” size 11 is recommended. There is no page or word limit. 4. The assessment is due by 14 June at 11.59pm (Melbourne Time). 5. The assessment is worth a total of 40 marks and accounts for 40% of the total grade for this course. 6. Students will only get ONE attempt to submit the file on Canvas. No multiple submissions are allowed so please only submit the last and final version of your answers. You will not be able to check your Turnitin score. 7. This is an individual piece of assessment. Submission will be verified via Turnitin for any form of plagiarism. The assessment should contain your own work and you can’t copy or have someone else complete any part of the work for you. By submitting this assessment, you are declaring that you have read, understood and agree to the content and expectations of the Assessment declaration. (Links to an external site.) (Links to an external site.) Good luck! QA Team Question 1 The below graph plots the daily prices of Gold over time. a) Examine the plot and describe the issues that may arise when trying to forecast future Gold prices given this time series data. Offer solutions to these issues. (2 marks). b) Offer a suitable forecasting method for this data. (2 marks). Question 2 For each of the below ACF plots which are obtained for a time series data of 4 different variables of interest: a) Explain the ACF plot. (2 marks). b) Describe what the raw data is likely to look like over time. (2 marks). c) What kind of variable is this plot likely to characterise (e.g., stock prices, exchange rates, temperature, etc.)? (2 marks). 1) 2) 3) 4) Question 3 The following ACF plots were produced for raw data of monthly sales of two different variables, A and B. a) Explain which variable is likely to be easier to forecast. (3 marks). b) Explain how your answer to part a) would change if these were residuals of an ARIMA model instead of “raw data of monthly sales”. (3 marks). Variable A: Variable B: Question 4 For the following time series plots, explain what type of transformation, if any, would make the variance more stable. (3 marks). 1) 2) Question 5 The following monthly sales (in thousands of AUS dollars) of chocolate boxes have been recorded for January, February, March, and April, respectively: 8, 8, 5, 9. Focusing on sales forecast accuracy for the month of April only, explain which of the following forecasting method would you recommend: the Naïve method, the Average method, or the Simple exponential smoothing method (assuming alpha=0.8 and initial state of 7)? (3 marks). Question 6 The variable income (yearly) is examined in a regression setting where the predictor variable is lag (1) of income and the following output is produced. a) Write down the regression equation. (3 marks). b) Interpret the meaning of the slope. (3 marks). c) A dummy variable for gender (male=0, female=1) was added to the model. Interpret its coefficient of -0.2. (3 marks). us_change %>% model(TSLM(log(Income) ~ log(LagIncome))) %>% report() #> Series: Consumption #> Model: TSLM #> #> Residuals: #> Min 1Q Median 3Q Max #> -2.5824 -0.2778 0.0186 0.3233 1.4223 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 0.5445 0.0540 10.08 < 2e-16 *** #> Log(LagIncome) 1.1000 0.0467 5.82 2.4e-08 *** #> — #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1 #> #> Residual standard error: 0.591 on 196 degrees of freedom #> Multiple R-squared: 0.147, Adjusted R-squared: 0.143 #> F-statistic: 33.8 on 1 and 196 DF, p-value: 2.4e-08 Question 7 The following plots have been obtained for a time series. a) Suggest an appropriate ARIMA model. (2 marks). b) The following ARIMA output has been obtained from R. Based on this output, which model would you recommend for forecasting? (2 marks). ## .model sigma2 log_lik AIC AICc BIC ar_roots ma_roots ## ## 1 arima011 17.1 -1388. 2788. 2788. 2813. ## 2 arima110 17.1 -1389. 2790. 2790. 2815. ## 3 auto 17.4 -1392. 2798. 2798. 2827. c) If your selected model in part b) above has a p-value of 0.13 in the Ljung-Box test, would you recommend using this model? Explain why or why not. (2 marks). Question 8 Examining the below R output, explain what model was selected for forecasting? (3 marks). Model: LM w/ ARIMA(1,1,1)(2,0,0)[7] errors