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AD 685 Project – Fall 2023

Instructions:

· Please complete the guided project by December 19, 11:59 PM (ET)

· Type your response in a separate “word doc” named LastName_FirstName.doc

· Also, you must upload the work files from R (LastName_FirstName.prg). One for Part 1 and one for Part 2. Excel is not suitable for this project, and it will not be accepted.

· Do not use the forecast, quantmod or the strucchange package. You will not receive any score for responses associated with these packages.

· Upload 3 files (Word doc and 3 R files) on Blackboard

This project consists of two parts:

· Part 1: Predicting Stock Returns.

· Part 2: Forecasting models for the rate of inflation.

· Part 3: Cointegration Investigation.

Part 1: Predicting Stock Returns

a. Use the Autoregressive Distributed Lag Models to estimate the following over the 1990 January–2023 June sample period. For the unemployment rate variable, you only need to show the output from (t-6) and (t-1), whichever is applicable. For each block, you need to show the coefficients, (heteroskedastic standard error) and the associated p-value.

b. Are these results consistent with the theory of efficient capital markets and can you provide an intuition behind this result?

c. Do you think using the year-over-year change of unemployment rate is better than the level of unemployment rate for either regression? Explain.

d. Construct pseudo out-of-sample forecasts of excess returns with rolling 10-year window and the regression specifications below that begin in 2000 January (1^st month with 10-year available historical data).

Zero Forecast: the sample RMSFEs of always forecasting excess returns to be zero. 

Constant Forecast: (in which the recursively estimated forecasting model includes only an intercept

In R, this is equivalent to running lm(ER ~ 1). Note that you still need to use the rolling window to calculate the “Constant Forecast”. This means the constant forecast should change every month from 2000 January to 2023 June, because in each month, a new set of 10-year monthly data is incorporated into the regression.

ADL (2,12,2,2) specification as in (a):

e. Does the ADL (2,12,2,2) provide better forecasts than the zero or constant models? Can you suggest another economic variable to improve the forecast?

Part 2

Forecasting models for the rate of inflation - Guidelines

Go to FRED’s website (https://fred.stlouisfed.org/) and download the data for:

· Consumer Price Index for All Urban Consumers: All Items (CPIAUCSL) - Seasonally adjusted – Monthly Frequency – From 1947:M1 to 2017:M12

In this hands-on exercise you will construct forecasting models for the rate of inflation, based on CPIAUCSL.

For this analysis, use the sample period 1970:M01–2012:M12 (where data before 1970 should be used, as necessary, as initial values for lags in regressions).

a. 

(i) Compute the (annualized) inflation rate,

(ii) Plot the value of Infl from 1970:M01 through 2012:M12. Based on the plot, do you think that Infl has a stochastic trend? Explain. 

b. 

(i) Compute the first twelve autocorrelations of   

(ii) Plot the value of  from 1970:M01 through 2012:M12. The plot should look “choppy” or “jagged.”  Explain why this behavior is consistent with the first autocorrelation that you computed in part (i) for . 

c. 

(i) Compute Run an OLS regression of  on . Does knowing the inflation this month help predict the inflation next month? Explain.

(ii) Estimate an AR(2) model for Infl. Is the AR(2) model better than an AR(1) model? Explain.

(iii) Estimate an AR(p) model for . What lag length is chosen by BIC? What lag length is chosen by AIC?

(iv) Use the AR(2) model to predict “the level of the inflation rate” in 2013:M01—that is, .

d. 

(i) Use the ADF test for the regression in Equation (15.32) with two lags of  to test for a stochastic trend in . Does the Inflation rate has a unit root?

(ii) Is the ADF test based on Equation (15.32) preferred to the test based on Equation (15.33) for testing for stochastic trend in ? Explain.

(iii) In (i) you used two lags of . Should you use more lags? Fewer lags? Explain.

(iv) Based on the test you carried out in (i), does the AR model for  contain a unit root? Explain carefully. (Hint: Does the failure to reject a null hypothesis mean that the null hypothesis is true?)

e. Use the QLR test with 15% trimming to test the stability of the coefficients in the AR(2) model for “the inflation” . (You cannot use the strucchange package. You must demonstrate that you understand how the QLR test is structured) Is the AR(2) model stable? Explain.

f. 

(i) Using the AR(2) model for  with a sample period that begins in 1970:M01, compute pseudo out-of-sample forecasts for the inflation beginning in 2005:M12 and going through 2012:M12.

(ii) Are the pseudo out-of-sample forecasts biased?  That is, do the forecast errors have a nonzero mean?

(iii) How large is the RMSFE of the pseudo out-of-sample forecasts? Is this consistent with the AR(2) model for  estimated over the 1970:M01–2005:M12 sample period?

(iv) There is a large outlier in 2008:Q4. Why did inflation fall so much in 2008:Q4? (Hint: Collect some data on oil prices. What happened to oil prices during 2008?)

Part 3

Investigation of Cointegration Within the Stock Market

From the Time Series Lectures, you learned that when two data series are linearly dependent, the series are said to be cointegrated. Any exogenous forces that change this relationship are considered temporary and the series that behaves abnormally will presume to autocorrect its path to re-establish the preexisting linear relationship. This mechanism was historically exploited by investment analyst as one of the quantitative trading strategies. In this exercise, you will choose two stocks or financial instruments you believe to be closely “related” and use the Engle-Granger Augmented Dickey-Fuller test to determine whether it is worthwhile to construct a pair-trading strategy.

1) Pick two U.S. Stocks or financial instrument that you believe to be cointegrated and want to examine their feasibility for pair-trading. State the rationale AND elaborate of why you choose these two stocks. Here are some considerations or ideas on informing this decision:

a. Choose two companies that compete in the same market where they earn revenue from the same segment/group of end-users.

b. From the list of S&P 500 constituents, choose companies in the same GICS sector.

c. Plot the return charts. Have they moved in the same “pattern” historically?

2) Download the historical monthly stock return (10-Year) from Yahoo Finance.

3) When conducting the Engle-Granger Augmented Dickey-Fuller test, you should assume that you do not know the cointegrating coefficient between the stocks’ return. Therefore, you will need to perform a linear regression and estimate the residual.

In your write-up, please explain if two stock return series are cointegrated, how you will devise a pair-trading strategy to profit from a pattern drift? You must show me an illustrated (i.e. drawing is okay) sketches of how the strategy will profit. Sorry, you cannot just copy from ChatGPT; you need to demonstrate that you understand the concept of cointegration.