forecasting

The purpose of the project:

Toyota Motor Corporation is a multinational automaker headquartered in Toyota, Aichi, Japan. In 2010, Toyota employed 317,734 people worldwide, and was the world’s largest automobile manufacturer in 2012 by production. The following data shows the demand of the Toyota car and The data is collected about it shows the monthly demand for cars for the years 2015 and 2016.

The data

Year	Time	Month	Demand (00)
2015	1	January	1560
2015	2	February	1680
2015	3	March	1710
2015	4	April	1740
2015	5	May	1680
2015	6	June	1752
2015	7	July	1680
2015	8	August	1560
2015	9	September	1650
2015	10	October	1800
2015	11	November	1860
2015	12	December	1800
2016	13	January	1530
2016	14	February	1650
2016	15	March	1620
2016	16	April	1710
2016	17	May	1680
2016	18	June	1620
2016	19	July	1530
2016	20	August	1620
2016	21	September	1560
2016	22	October
2016	23	November
2016	24	December

The data is retrieved from the https://www.automotiveworld.com/ website

Use this information to calculate.

a) Prepare a time-series plot of the data. Does the data appear to have a trend or seasonality?

b) Use the naïve method to forecast the demand for the last three months of 2016.

c) Use the moving average method with 4 periods, i.e., MA(4), to forecast the monthly demand for January 2016 through December 2016.

d) Use the exponential smoothing method with a=0.4 to forecast the monthly demand for January 2016 through December 2016. Use the actual demand observed in January 2015 as your initial forecast for January 2015 (That is, start the model in January 2015.

e) Using the data, prepare forecasts for October, November, December (2016) for the following models:

1. Naïve

2. Moving Average with 2 periods

3. Exponential Smoothing with alpha equal to 0.25. Assume the Forecast for period 3.

4. Regression Analysis

Determine the MSE, MAD and MAPE error for each forecasting method. Using the MAD and MAPE for comparison, which model performed the best? Which forecast do you choose for period September?

f) Fit a trend line to the data provided for January 2015 to December 2015. Using the equation of the trend line you found, forecast the monthly demand for January 2016 through December 2016.

g) Compute the MAD for each method, that is, the Naïve, MA(4), ES(0.4), and the trend line during January 2016 to September 2016.

h) Choose one of the time-series methods you analyzed thus far which will provide you the most reliable estimate and why? What are the demand forecasts for the last three months of 2016 if this method is used?