STAT603留学生代做、代做Mathematical Sciences、代写R、R编程设计 调试

日期：2019-05-26 11:18

Auckland University of Technology

School of Engineering, Computer and Mathematical Sciences

STAT603: Forecasting

Assignment 2

Outline: The purpose of this assignment is to assess your analytical and

computing skills on the material covered.

Total: 30 marks and three questions. This assignment contributes 15% towards

your final grade in this paper.

Due: 9am, on Wednesday 29 May 2019.

Submission:

Only .pdf files will be accepted. For instance you can use (but not

restricted to) Word to edit your assignment and then export it to pdf,

or you can make use of R scripts and then use knitr to compile it.

Your answers must be submitted as a soft copy in a single ‘.pdf’ file

including signed SECMS assignment cover sheet (otherwise your assignment

won’t be marked).

The filename must include 1) your lastname, 2) your firstname, and 3)

your student id. For instance, if John White submits his assignment,

this must be a file with extension .pdf and named as “White John 123456789”.

Submission channel will be announced later.

Report/Assignment: Your assignment must be self-contained and self–

explanatory. Any R code, output, scientific reference, and any other resource

required to complete your assignment must be embedded in the document

and properly referred (or cited) to.

Page Limit: Maximum number of pages is 10 including graphs and R code.

Data: Quarterly total beer available for consumption (million litres) in New

Zealand from Quarter 1, 2010 to Quarter 3, 2017

Filename: NZ_TotalBeer_Quarterly.xlsx.

Software: Each computing task involved with this assignment must be carried

out using R or RStudio.

Plagiarism: If this is the case for your project, your case will be

referred to an appropriate university’s office.

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Tasks/Questions:

1. Question 1 – ETS (14 marks)

(a) Plot the series and discuss the main features of the data including

stationarity (2 marks).

(b) Forecast the next two years using (1) simple exponential smoothing,

(2) Holt’s linear trend, and Holt’s (3) damped trend. Plot

the series and the forecasts. Merely based on this plot, discuss

the adequacy of these methodologies to forecast from this series.

Justify your answer (4 marks).

(c) Repeat Part (b) with Holt-Winters’ seasonal methods. Discuss

whether additive or multiplicative seasonality is necessary. Justify

your answer (4 marks).

(d) Compare the mean squared error (MSE) and the mean absolute

error (MAE) of the one-step-ahead and four-step-ahead forecasts

from the above methods in (b)-(c). You must report your results

in a Table (see, e.g., Lab-Question 3, Week 8 – Monday). Comment

on the adequacy of these methodologies towards forecasting.

Which method appears as more accurate to forecast this time series?

Does this selection depend on the number of pre–specified

(steps–ahead) forecasts? Justify your answer (4 marks).

2. Stationarity (4 marks)

(a) Plot the autocorrelation function (ACF) and the partial ACF

(PACF), and (a) discuss the stationarity of the series. Does you

answer here conform with your answer in Question 1 – (a)?

(b) Should the series be differenced? Justify your answer (2 marks).

(b) Find an appropriate Box-Cox transformation and order of differencing

to obtain stationary data (2 marks). Note: Justify your

answer whatsoever, even if no Box–Cox transformation is needed.

3. ARIMA (12 marks)

(a) By studying the appropriate graphs of the series in R, propose

an appropriate ARIMA(p, d, q) structure to model the series.

Justify your answer (1 mark).

(b) Should a constant be included in the model? Explain (1 mark).

(c) Write the proposed model using backshift notation (1 mark).

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(d) Fit the model using R functions and examine the residuals. Is the

proposed model satisfactory? Justify your answer (2 marks).

(e) Forecast four periods ahead. Check your forecasts by hand to

make sure you know how they have been calculated (2 marks).

HINT: See https://otexts.com/fpp2/arima-forecasting.html .

(f) Create a plot of the series with forecasts and prediction intervals

for the four forecasted periods (1 mark).

(g) Now, let auto.arima() choose an ARIMA structure. Does auto.arima

return the same model (the one you chose)? If not, which model

do you think is better? Justify your answer (2 mark).

(h) Which method do you think is best between ETS and ARIMA?

(2 mark).

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