AD 685 Project –Spring 2021 Instructions: · Please complete the guided project by May 8, 11:59 PM (ET). · Write your answer below each question and upload a “word doc” named LastName_FirstName.doc...

AD 685 Project –Spring 2021
Instructions:
· Please complete the guided project by May 8, 11:59 PM (ET).
· Write your answer below each question and upload a “word doc” named LastName_FirstName.doc using the link on Blackboard.
· 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.
This project consist of two parts:
· Part 1: Predicting Stock Returns.
· Part 2: Forecasting models for the rate of inflation.
Part 1: Predicting Stock Returns.
Data Description:
Documentation for Stock_Returns_1931_2002
This file contains 2 monthly data series over the 1931:1-2002:12 sample period.
· ExReturn: Excess Returns
· ln_DivYield: 100×ln(dividend yield). (Multiplication by 100 means the changes are interpreted as percentage points).
The data were supplied by Professor Motohiro Yogo of the University of Pennsylvania and were used in his paper with John Campbell:
· “Efficient Tests of Stock Return Predictability,” Journal of Financial Economics, 2006.
(Double click in the window below to access the data)
Some Background
exreturn: is the excess return on a broad-based index of stock prices, called the CRSP value-weighted index, using monthly data from 1960:M1 to 2002:M12, where “M1” denotes the first month of the year (January), “M2” denotes the second month, and so forth.
· The monthly excess return is what you earn, in percentage terms, by purchasing a stock at the end of the previous month and selling it at the end of this month, minus what you would have earned had you purchased a safe asset (a U.S. Treasury bill). The return on the stock includes the capital gain (or loss) from the change in price plus any dividends you receive during the month.
Calculating k-period stock returns:
One-period holding return:
Two-period holding return:
Other way
Three-period’s returns:
k-period’s returns:
When to apply a “buy and hold” strategy:
· If you have a reliable “forecast” of future stock returns then an active “buy and hold” strategy will make you rich quickly by beating the stock market.
· If you think that the stock market will be going up, you should buy stocks today and sell them later, before the market turns down. Forecasts based on past values of stock returns are sometimes called “momentum” forecasts: If the value of a stock rose this month, perhaps it has momentum and will also rise next month.
· If so, then returns will be autocorrelated, and the autoregressive model will provide useful forecasts. You can implement a momentum-based strategy for a specific stock or for a stock index that measures the overall value of the market.
· From another point of view, we can use autoregressive models to test a version of the efficient markets hypothesis (EMH). A strict form of the efficient markets hypothesis states that information observable to the market prior to period should not help to predict the return during period . If the (EMH) is false, then returns might be predictable. If so, then returns will be autocorrelated, and the autoregressive model will provide useful forecasts.
· For example, if you want to find out if returns are predictable (even if it is just a bit), estimate the following AR(1)
· A positive coefficient means “momentum,” past “good returns” mean higher future returns.
· A negative coefficient means “overreaction” or “mean reversion”. In this case, previous “good returns” mean lower future returns.
· Either way, if , then returns will be autocorrelated, and the autoregressive model will provide useful forecasts.
Note: In all your calculations use Huber-White heteroskedasticity consistent standard errors and covariance.
a. Repeat the calculations reported in Table 14.2, using the following regression specifications estimated over the 1960:M1–2002:M12 sample period.
AR(1) Model
AR(2) Model
AR(4) Model
    Autoregressive Models of Monthly Excess Stock Returns, 1960:M1–2002:M12
     
     
     
     
     
     
    Dependent variable: Excess returns on the CRSP value-weighted index
     
    (1)
    
    (2)
    
    (3)
    Specification
    AR(1)
     
    AR(2)
     
    AR(4)
    Regressors
     
     
     
     
     
    Excess Ret(t-1)
    0.0504
    
    0.0532
    
    0.05362
    Std. Error
    0.0512
    
    0.0508
    
    0.051
    z-value
    0.98
    
    1.047
    
    1.05
     
    
    
    
    
    
    Excess Ret(t-2)
    
    
    -0.0528
    
    
    Std. Error
    
    
    0.0481
    
    
    z-value
    
    
    1.1
    
    
     
    
    
    
    
    
    Excess Ret(t-3)
    
    
    
    
    
    Std. Error
    
    
    
    
    
    p-value
    
    
    
    
    
     
    
    
    
    
    
    Excess Ret(t-4)
    
    
    
    
    -0.05394
    Std. Error
    
    
    
    
    0.0476
    z-value
    
    
    
    
    1.13
     
    
    
    
    
    
    Intercept
    0.3116
    
    0.3284
    
    0.3391
    Std. Error
    0.1974
    
    0.1989
    
    0.2025
    z-value
    1.58
    
    1.65
    
    1.67
     
    
    
    
    
    
    Adj R^2
    0.001
    
    0.001
    
    -0.002
     
    
    
    
    
    
    Wald F-statistic
    1.306
    
    1.367
    
    0.721
    p-value
    0.37
    
    0.28
    
    0.43
    T=
      516
     
      516
     
      516
b. Are these results consistent with the theory of efficient capital markets?
These results are statistically not significant which tells us that these coefficients might be zero and there is not autocorrelation which tells us that the markets are efficient.
c. Can you provide an intuition behind this result?
This means that the stock returns can not be predicted from the past stock returns which tells us that the markets are efficient and no abnormal returns can be made.
d. Repeat the calculations reported in Table 14.6, using regressions estimated over the 1960:M1–2002:M12 sample period.
    Autoregressive Distributed Lag Models of Monthly Excess Stock Returns, 1960:M1–2002:M12
     
    
    
    
    
     
    Dependent variable: Excess returns on the CRSP value-weighted index
     
     
     
    (1)
    
    (2)
    
    (3)
    Specification
    ADL(1,1)
     
    ADL(2,2)
     
    ADL(1,1)
    Eatimation Period
    1960:M1–2002:M12
     
    1960:M1–2002:M12
     
    1960:M1–1992:M12
    Regressors
     
     
     
     
     
    Excess Ret(t-1)
    0.05894
    
    0.0418
    
    0.0782
    Std. Error
    0.158
    
    0.162
    
    0.0567
    p-value
    0.711
    
    0.796
    
    0.167
     
    
    
    
    
    
    Excess Ret(t-2)
    
    
    -0.2132
    
    
    Std. Error
    
    
    0.193
    
    
    p-value
    
    
    0.27
    
    
     
    
    
    
    
    
    Change_ln_DP(t-1)
    0.0858
    
    -0.0115
    
    
    Std. Error
    0.157
    
    0.163
    
    
    p-value
    0.585
    
    0.94
    
    
     
    
    
    
    
    
    Change_ln_DP(t-2)
    
    
    -0.1613
    
    
    Std. Error
    
    
    0.185
    
    
    p-value
    
    
    0.3843
    
    
     
    
    
    
    
    
    ln_DP(t-1)
    
    
    
    
    0.0262
    Std. Error
    
    
    
    
    0.0116
    p-value
    
    
    
    
    0.023
     
    
    
    
    
    
    Intercept
    0.30945
    
    0.3716
    
    8.9872
    Std. Error
    0.199
    
    0.208
    
    3.9122
    p-value
    0.12
    
    0.061
    
    0.0216
     
    
    
    
    
     
    Adj R^2
    -0.001
    
    -0.001
    
    0.013
     
    
    
    
    
    
    F-statistic
    0.653
    
    0.897
    
    3.683
    p-value
    0.43
    
    0.28
    
    0.11
    Obs =
     516
    
     516
     
     396
e. Does the have any predictive power for stock returns?
None of the t statistics for this model suggests that the coefficients are different from zero. Hence, we can come to the conclusion that it is not significant.
f. Does “the level of the dividend yield” have any predictive power for stock returns?
Yes. It does have predictive power for stock returns because the coefficient is statistically significant and we reject the hypothesis that it is zero.
g. Construct pseudo out-of-sample forecasts of excess returns over the 1993:M1–2002:M12 period, using the regression specifications below that begin in 1960:M1.
ADL(1,1) specification:
Constant Forecast: (in which the recursively estimated forecasting model includes only an intercept)
Zero Forecast: the sample RMSFEs of always forecasting excess returns to be zero.
    Model
    RMSFE
    Zero Forecast
    3.995428
    Constant Forecast
    4.000221
    ADL(1, 1)
    4.04375
h. Does the ADL(1,1) model with the log dividend yield provide better forecasts than the zero or constant models?
No ADL(1,1) model does not provide better forecasts than zero or the constant models because they have even lower RMSFEs.
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 (    ) - 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 .
The difference in the inflation does not have any correlation and hence the autocorrelation function will lead to no sign of correlation which can be observed in the chart below. This is due to stochastic trend of the inflation observed in the first part.
c.
(i) Compute Run an OLS regression of on . Does knowing the inflation this month help predict the inflation next month? Explain.
Knowing this month’s inflation does not help the next month’s inflation since the coefficient in the AR1 model is not statistically significant. Also, the stochastic trend in the inflation suggested that the inflation could be random values.
(ii) Estimate an AR(2) model for Infl. Is the AR(2) model better than an AR(1) model? Explain.
As far as the AR(2) model is concerned the AIC or BIC values have not been able to distinguish the two models since both the values are exact same. Also, the coefficient value is marked as NA and hence not able to distinguish the two models.
(iii) Estimate an AR(p) model for . What lag length is chosen by BIC? What lag length is chosen by AIC?
Lag 1 has been chosen by the 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 (14.31) with two lags of to test for a stochastic trend in .
(ii) Is the ADF test based on Equation (14.31) preferred to the test based on Equation (14.32) for testing for stochastic trend in ? Explain.
Yes ADF test based on equation 14.31 is more preferred as compared to the other test due to the fact that
(iii) In (i) you used two lags of . Should you use more lags? Fewer lags? Explain.
We can use more lags. More lags can be used like 3 or 6 or 12 to understand if there is any seasonality in the trends. Once we do that we can try and add a factor to compensate for the seasonality.
(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?)
Based on the ADF test we can understand if there is stationarity in the time series or not. We have a higher p value and hence we can not reject the null hypothesis and we fail to reject the null hypothesis. This tells us that there is a unit root and stationarity is not present.
e. Use the QLR test with 15% trimming to test the stability of the coefficients in the AR(2) model for “the inflation” . 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...