Obtain residuals from prophet models and fit arma models

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Reference no: EM133693390

Data-driven Decision Making and Forecasting

Assessment - Fitting and evaluating ARIMA and VAR time series models

Your Tasks

In Class : Compare fitting a SARIMA model to fitting an ARMA model to residuals from a Prophet model, for two time series. Discuss the advantages and disadvantages of the two approaches.

In class:
At the beginning of the class, your lecturer will provide you with a dataset and a series of questions to answer. You will create a Word document with the answers to questions. At the end of class, submit your Word file via MyKBS.

Part A: Fit SARIMA models to the two time series and provide plots of the time series and predictions. Provide the acfs of the residuals.

Part B: Obtain residuals from Prophet models and fit ARMA models to these residuals.

Part C: Discuss the advantages and disadvantages of the two approaches.

You will then enter the "Video quiz" on MyKBS where you will need to:

Part D: Make a video lasting between 15 to 30 minutes of yourself answering the 7 multiple choice questions based on Workshop 8 material, explaining your reasoning as you progress.

Once you start the quiz you will have 30 minutes to complete it.

Say how confident you are about your responses, share your thought processes, and relate your answers to concepts learned in class.

Part E: Upload your video recording as instructed.
The data are sales of sparkling wine from KangaVineyard per month (litres) from January 1980 until December 1994. Read the time series
2024T1_A2_SPARKLING_Group
into Exploratory, where Group will be e.g. P1 for Perth 1.
Write the mean monthly sales, standard deviation of monthly sales, minimum and maximum monthly sales in the right hand column of Table 1 below.

Table 1 Descriptive statistics (litres) of monthly sparkling wine sales

statistic   Numerical value
mean
standard deviation
minimum
maximum
Fit SARIMA model, with predictions for 24 months ahead NB set Date\Time to MONNote the RMSE, MAPE, and the order of the model i.e. numerical values of p.d,q,P,D,Q in the second row of Table 2 below

Table 2 Within time series performance measures by forecasting method

Model   RMSE (1 decimal place)   MAPE (3 decimal place)
SARIMA order (p,d,q)(P,D,Q)
Prophet (additive seasonal)
Prophet (multiplicative seas.)
Prophet+ARMA(1,1)       Not applicable
Prophet+ARMA(4,0)       Not applicable

Insert the Forecasted plot below and give a detailed description in a caption "Figure 1 ...." below your plot.
Insert the Residual ACF plot below and give a detailed description in a caption "Figure 2 ...." below your plot. Comment briefly on the Residual ACF.
Give the forecast for December 1995, together with an approximate 80% prediction interval based on the RMSE.
Now fit Prophet , with predictions for 24 months ahead, with additive and with multiplicative seasonals (Seasonality Mode). Record the RMSE and MAPE in rows three and four of Table 2 above.
Choose the Prophet Seasonality Mode that gives the lower RMSE. Insert the Forecasted plot below and give a detailed description in a caption "Figure 3 ...." below your plot. Go to Data and Export Table Data as Excel.
Insert the Yearly plot, which shows seasonal variation, below. Give a detailed caption as "Figure 4 ....." below your plot. What are the approximate seasonal indices (as factors that multiply the trend) for December and January? [estimating the indices from the graph is ok.] Explain the seasonality.
Edit the Exported Excel File, by deleting forecasts beyond 1994, calculating RESIDUALS as observed sales less forecast and deleting columns that you don't need.
Fit ARMA(1,1) and ARMA(4,0) models to the RESIDUALS. NB Set both Set Parameters Automatically and Model with Seasonality to FALSE, and set the differencing parameters d, D to 0. Enter the RMSE values in Table 2 above.
Insert the Forecasted plot for the ARMA(4,0) model, and provide a suitable caption as ‘Figure 5....." below your plot.
You are writing a report for KangaVineyard that will include forecasts of sparkling sales for 1995-6. KangaVineyard management does not want comparisons of forecasting methods, they just want one set of forecasts. Which forecasting method would you choose to present? Justify your decision.

Reference no: EM133693390

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