Group Project

Project A – Smoothing out the Stock Market

Predicting the ups and downs of the stock market is a notoriously difficult task. On the other hand, if anyone could obtain accurate forecasts of future stock prices, then they could make a lot of money by buying up stocks at low prices and selling them later at higher prices. It is often useful just to predict whether the trend of a stock is upward or downward in the near future. In this project, you will use standard time series smoothing techniques to estimate trends in the S&P 500 Index.

Using the data set SP500.csv, perform multiple techniques to smooth the time series including simple moving averages with various window lengths and exponential moving averages.

1. Produce SMA trendlines with window sizes 10, 30, 60, and 120. Graph the trendlines on the same set of axes as the original graph and describe the results. What happens to the trendline as the window size increases?
2. Produce EMA trendlines with $\alpha =0.25,0.5$ and $0.75$. Graph the trendlines on the same set of axes as the original graph and describe the results. What happens to the trendline as the value of $\alpha$ increases?
3. Now compare your results from part a and part b. As a group, discuss the advantages and disadvantages of using SMA vs. EMA. What characteristics of the data are emphasized (or de-emphasized) by each method as the parameters (window size and $\alpha$, respectively) change.

Project B – ARIMA Analysis of Coal Consumption

As a group, explore the time series in the data set MonthlyCoalConsumption.xlsx.

1. Find the smallest order of differencing so that the time series becomes stationary.
2. Then run an ACF diagram and look for any spikes that might indicate periodicity of a seasonal component.
3. Run ARIMA analysis of the time series using the parameters for $p$ and $d$ established by your findings about periodicity and stationarity, trying different values of $q$. Evaluate the model’s accuracy by computing the AIC score for each combination of parameters.
4. As a group, decide which parameters $(p,d,q)$ you think will give the most accurate forecast. Then forecast up to 30 time units into the future and produce confidence intervals for your forecasts. Interpret your results by indicating how likely your forecasts are to be within a range of values.