# Northeastern University Time Series Forecasting Project

### Description

The project consists of three parts. The submission of this project will consist of two attachments:1.A Word document that is prepared according to the APA standards of formatting. In the Word document, explain the experiments and their respective conclusions, and additional information as indicated in each problem

Either an Excel workbook or an R script file (.R file) that contains all the work and the calculations indicated in parts 1-3 of the project. Please save your Excel workbook or R script file

Part 1: Short-term Forecasting:

(i)Use a simple line plot of both time series to detect seasonal, irregular, or trend behaviors if any. Write a summary of your observations of both time series in your report.

(ii)Perform exponential smoothing to forecast both pricesfor period 253. Use successive values of 0.15, 0,35, 0.55, and 0.75for the smoothing parameter ?. Next, calculate the MAPD (Mean Absolute Percentage Deviation)of each forecast; and based on the MAPDs, determine the value of ?that has yielded the most accurate forecastfor each stock. In your report, describe your results; and explain whyin your opinionsuch valuesof ?haveyielded the most accurate forecasts for the two stocks.

(iii)Use your exponential smoothing forecast of part (ii) with ?=?.55and perform an adjusted exponential smoothing to forecast both prices for period 253. Use successive values of 0.15, 0.25, 0.45, and 0.85for the trend parameters?for both stocks. Next, calculatethe MAPEs(Mean Absolute Percentage Error) of your forecasts anddetermine the valuesof ?that haveprovided the most accurate forecasts for both stocks. In your report, describe your results and explain why, in your opinion,such valuesof ?have yielded the most accurate forecasts.

Part 2: Long-term Forecasting

(i)For each stock, use a 3-period weighted moving averages to forecast its value during periods 1 through 100. Use the weights 0.5(for the most recent period), 0.3 (for the period before the most recent), and 0.2 (for two periods ago). Next, use the observedvalue for period 101as the base of a linear trend, and use that linear trend to forecast the values of both stocks for periods 101 through 257. Write a summary of your results in your report. Describe how accurate this method of forecasting has been by comparing the forecasted values for periods 253-257 with their actual “Close”values on those specific days (Hint: check the actualvalues on https://finance.yahoo.com).

(ii)Calculate the MAPEs (Mean Absolute Percentage Error) of your forecasts in question (i) above andcompare them with the values obtained for your forecasts in Part 1.For each stock, describe which method has yielded a most accurate forecast.

Part 3: Regression:

(i)For each stock, use simple regression of stock values versus the time periods to predict its values for periods 1 through 257. In your report, describe how the accuracy of this prediction has been compared to the methods used in Parts 1 and 2 of this project

(ii)Perform a residual analysis of your simple regression to verify whether regression is appropriate to use for each of the given data. In particular, determine:

•Whether the residuals are independent

•Whether the residuals are homoscedastic

.•Whether the residuals are normally distributed by plotting a Normal probability plot of the residuals

•Whether the residuals are normally distributed by performing a Chi-squared test for Normality of the residuals

.After completing parts 1-3 and in your report, respond to the following question. Note this question is subjective, and it does not necessarily have only one correct answerat this stage of the course

.Question: Supposethat you have decided to form a portfolio ?(Pi)consisting of the above two stock types (denote a share value of AAPL by ?and that of HON by ?). You are however undecided as to what percentage of your investment should be allocated to the AAPL shares and what percentage should be allocated to HON shares. Let thesepercentages be denoted by P and Q respectively(Obviously, P + Q=100%). In your opinion, what are good values to select for P and Q 