AD 685 Project – Fall 2022
Instructions:
· Please complete the guided project by Tuesday, December 13, 11:59 PM (ET)
· Write your answer below each question and upload a “word doc” named LastName_FirstName.doc using the link on Blackboard.
Copyright By PowCoder代写 加微信 powcoder
· 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 consists 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 :
· “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:
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 15.2, 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
Specification
Regressors
Excess Ret(t-1)
Std. Error
Excess Ret(t-2)
Std. Error
Excess Ret(t-3)
Std. Error
Excess Ret(t-4)
Std. Error
Std. Error
-statistic
b. Are these results consistent with the theory of efficient capital markets?
c. Can you provide an intuition behind this result?
d. Repeat the calculations reported in Table 15.6, 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
Specification
Eatimation Period
1960:M1–2002:M12
1960:M1–2002:M12
1960:M1–1992:M12
Regressors
Excess Ret(t-1)
Std. Error
Excess Ret(t-2)
Std. Error
Change_ln_DP(t-1)
Std. Error
Change_ln_DP(t-2)
Std. Error
ln_DP(t-1)
Std. Error
Std. Error
F-statistic
e. Does the have any predictive power for stock returns?
f. Does “the level of the dividend yield” have any predictive power for stock returns?
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.
Zero Forecast
Constant Forecast
h. Does the ADL(1,1) model with the log dividend yield provide better forecasts than the zero or constant models?
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).
(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.
(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 .
(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, .
(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.
(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” . Is the AR(2) model stable? Explain.
(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?)
DATE_M EXRETURN LN_DIVYIELD
1931M01 5.9649584 -282.2329
1931M02 10.3053054 -293.2089
1931M03 -6.8408314 -287.8614
1931M04 -10.4480653 -278.2477
1931M05 -14.3580770 -265.4742
1931M06 12.8502610 -280.5102
1931M07 -6.6559179 -275.5950
1931M08 0.0461485 -278.4424
1931M09 -34.2583894 -247.1829
DATE_MEXRETURNLN_DIVYIELD
1931M015.9649584-282.2329
1931M0210.3053054-293.2089
1931M03-6.8408314-287.8614
1931M04-10.4480653-278.2477
1931M05-14.3580770-265.4742
1931M0612.8502610-280.5102
1931M07-6.6559179-275.5950
1931M080.0461485-278.4424
1931M09-34.2583894-247.1829
DATE_M EXRETURN LN_DIVYIELD
1931M01 5.9649584 -282.2329
1931M02 10.3053054 -293.2089
1931M03 -6.8408314 -287.8614
1931M04 -10.4480653 -278.2477
1931M05 -14.3580770 -265.4742
1931M06 12.8502610 -280.5102
1931M07 -6.6559179 -275.5950
1931M08 0.0461485 -278.4424
1931M09 -34.2583894 -247.1829
1931M10 7.6799039 -255.0321
1931M11 -9.5340623 -247.2558
1931M12 -14.6130526 -236.3433
1932M01 -1.3088847 -237.5438
1932M02 5.3918523 -245.9247
1932M03 -11.6910343 -237.7585
1932M04 -19.9650041 -220.8940
1932M05 -23.2280746 -201.7617
1932M06 -0.9714341 -204.7223
1932M07 28.5970311 -237.1678
1932M08 31.1136957 -272.7358
1932M09 -3.2352084 -272.8100
1932M10 -14.0117522 -265.5729
1932M11 -5.7386068 -264.5414
1932M12 4.3764421 -270.7398
1933M01 0.9535563 -274.1626
1933M02 -14.2299376 -263.9548
1933M03 1.5445859 -267.7878
1933M04 32.3073099 -302.1529
1933M05 19.1924877 -324.3895
1933M06 12.5264320 -338.1844
1933M07 -10.1223930 -328.6087
1933M08 11.4618379 -343.4021
1933M09 -11.1839596 -332.7242
1933M10 -8.6230478 -323.1439
1933M11 9.4773087 -330.0220
1933M12 1.9717464 -334.6379
1934M01 12.1731472 -345.0648
1934M02 -2.3945521 -342.0283
1934M03 0.4708646 -340.6425
1934M04 -1.8264310 -337.3806
1934M05 -7.3412476 -329.0570
1934M06 2.4830087 -330.3515
1934M07 -11.4629388 -316.3382
1934M08 5.7778848 -316.3660
1934M09 -0.2988386 -315.4241
1934M10 -2.0572232 -312.8846
1934M11 8.0662882 -320.8530
1934M12 0.3951357 -318.1672
1935M01 -3.2708263 -314.5120
1935M02 -2.0119031 -311.5611
1935M03 -3.8230702 -306.7842
1935M04 8.5629839 -315.4708
1935M05 3.4104471 -317.3147
1935M06 5.3335646 -321.4858
1935M07 7.1327794 -328.6475
1935M08 2.7351651 -332.1568
1935M09 2.3645830 -332.0547
1935M10 6.8017231 -337.6329
1935M11 5.0263630 -337.4944
1935M12 4.5014637 -340.3963
1936M01 6.3777364 -344.9823
1936M02 2.5627316 -346.0814
1936M03 0.8457263 -345.9888
1936M04 -8.1959630 -336.4404
1936M05 4.9146948 -335.7937
1936M06 2.5363792 -336.1503
1936M07 6.1857648 -340.6330
1936M08 1.1110944 -336.5401
1936M09 1.4515584 -335.3798
1936M10 6.7455042 -340.8827
1936M11 3.3560965 -329.0038
1936M12 0.1159950 -321.2782
1937M01 3.2043277 -324.4864
1937M02 1.3032316 -324.6322
1937M03 -0.4361027 -321.8466
1937M04 -7.7904360 -313.8231
1937M05 -0.8734557 -309.9933
1937M06 -4.1873018 -302.9138
1937M07 8.0525442 -310.7973
1937M08 -4.6745133 -304.7642
1937M09 -14.5402531 -288.0675
1937M10 -9.9798157 -278.3211
1937M11 -8.7234900 -268.3937
1937M12 -4.1654064 -263.9771
1938M01 0.8281418 -265.5344
1938M02 5.5645605 -271.7241
1938M03 -27.0199102 -245.4506
1938M04 13.5750094 -259.5059
1938M05 -3.9863740 -259.9150
1938M06 21.2006832 -284.0032
1938M07 6.9428206 -292.0001
1938M08 -2.7743666 -293.8418
1938M09 0.8666265 -298.6544
1938M10 7.4497135 -306.6715
1938M11 -1.8434093 -319.4468
1938M12 3.9773089 -329.2344
1939M01 -6.1468900 -323.2705
1939M02 3.4121664 -325.0125
1939M03 -12.6804215 -312.3877
1939M04 -0.2604986 -311.8563
1939M05 6.6326152 -316.5729
1939M06 -5.4831009 -310.0719
1939M07 9.6403296 -319.4949
1939M08 -6.8306778 -309.5483
1939M09 14.8326355 -323.2142
1939M10 -0.4145542 -322.9744
1939M11 -3.7295367 -309.5138
1939M12 2.9603150 -309.0883
1940M01 -2.4889310 -306.1745
1940M02 1.4169725 -305.1649
1940M03 1.8695682 -306.6719
1940M04 0.1450027 -305.6517
1940M05 -24.8694191 -276.2713
1940M06 6.4417197 -281.7801
1940M07 3.1956741 -284.4412
1940M08 2.3364807 -283.5389
1940M09 2.2710512 -284.9484
1940M10 2.9636985 -286.9011
1940M11 -1.6569815 -283.8112
1940M12 0.7037104 -283.4216
1941M01 -4.1323561 -279.3577
1941M02 -1.4959907 -276.6367
1941M03 0.9354067 -275.5241
1941M04 -5.4382362 -270.5914
1941M05 1.4137244 -270.4819
1941M06 5.6690182 -273.6835
1941M07 5.6727285 -278.8014
1941M08 0.0484734 -277.4169
1941M09 -0.7534793 -275.7809
1941M10 -5.2967249 -269.8969
1941M11 -1.9851582 -264.3471
1941M12 -4.8084770 -257.1187
1942M01 0.5585308 -257.6732
1942M02 -2.3212849 -255.3871
1942M03 -6.7906062 -247.8228
1942M04 -4.4204280 -243.0769
1942M05 5.9478990 -250.5445
1942M06 2.4463663 -252.9259
1942M07 3.3966978 -256.3961
1942M08 1.8225024 -260.1509
1942M09 2.5676822 -262.3913
1942M10 6.5402561 -269.8150
1942M11 0.1126999 -273.1240
1942M12 4.8182982 -278.9289
1943M01 7.2373533 -286.2952
1943M02 5.8063083 -292.1621
1943M03 5.9576437 -298.1285
1943M04 0.6552063 -298.7729
1943M05 5.5189914 -303.2376
1943M06 1.6597566 -304.0653
1943M07 -4.7654835 -299.4386
1943M08 1.2546190 -300.3024
1943M09 2.3633779 -300.8681
1943M10 -1.2590893 -300.0887
1943M11 -6.0419847 -292.0816
1943M12 6.1091653 -297.8191
1944M01 1.7434391 -299.1672
1944M02 0.3978740 -297.8578
1944M03 2.3725810 -299.4205
1944M04 -1.7632369 -297.9494
1944M05 5.0313643 -301.0066
1944M06 5.4898042 -305.4764
1944M07 -1.5513311 -303.8730
1944M08 1.4913020 -302.8358
1944M09 0.0116306 -303.8177
1944M10 0.2398562 -303.0885
1944M11 1.5035069 -301.6009
1944M12 4.1112842 -305.8558
1945M01 1.7726619 -307.4123
1945M02 6.3117292 -312.8948
1945M03 -4.0154050 -308.1800
1945M04 7.4655321 -315.3866
1945M05 1.7799658 -314.2980
1945M06 0.3868130 -316.0253
1945M07 -2.2793956 -313.6012
1945M08 5.8658314 -318.6487
1945M09 4.6645559 -322.6249
1945M10 3.8148624 -326.4407
1945M11 5.3119168 -330.7256
1945M12 1.1141825 -332.6506
1946M01 6.1065669 -338.0507
1946M02 -5.9927152 -330.9580
1946M03 5.7605549 -336.3052
1946M04 4.0360864 -339.7083
1946M05 3.9615780 -344.0075
1946M06 -4.0541142 -339.1279
1946M07 -2.6240252 -334.6942
1946M08 -6.6304651 -326.7493
1946M09 -10.5989750 -314.6444
1946M10 -1.4643089 -311.8465
1946M11 0.1154316 -312.1626
1946M12 4.9278189 -310.5973
1947M01 1.4761731 -311.3550
1947M02 -1.2095458 -307.1040
1947M03 -1.7306882 -304.3609
1947M04 -4.9256784 -298.2704
1947M05 -1.0465224 -294.1706
1947M06 5.1951343 -297.6524
1947M07 4.0287785 -301.3732
1947M08 -1.7978766 -297.6343
1947M09 -0.4779251 -295.0165
1947M10 2.3749414 -296.7623
1947M11 -1.8886898 -288.8601
1947M12 2.8634015 -289.9508
1948M01 -3.8447697 -285.6673
1948M02 -4.5258140 -279.7150
1948M03 7.8509270 -285.0924
1948M04 3.6202115 -288.0015
1948M05 7.1049653 -295.1071
1948M06 -0.0925725 -292.4918
1948M07 -5.2536893 -287.8241
1948M08 0.2928596 -285.2921
1948M09 -3.0705975 -280.6501
1948M10 5.7644902 -284.7139
1948M11 -9.5900348 -272.0175
1948M12 3.0677684 -273.1914
1949M01 0.2000379 -273.1405
1949M02 -3.0019621 -267.6639
1949M03 3.9074178 -270.3268
1949M04 -1.9140122 -267.6873
1949M05 -2.8781643 -263.3639
1949M06 0.2510303 -262.4166
1949M07 5.3117825 -267.6745
1949M08 2.5228796 -268.2921
1949M09 3.0705929 -272.1332
1949M10 3.0176701 -276.6784
1949M11 1.8167638 -272.3540
1949M12 5.0374261 -277.3051
1950M01 1.5196635 -278.5056
1950M02 1.3508391 -278.3361
1950M03 1.1157266 -278.6771
1950M04 3.8504859 -282.8544
1950M05 4.0974760 -283.5809
1950M06 -5.9167743 -277.6732
1950M07 1.4840914 -278.8721
1950M08 4.8139224 -276.6186
1950M09 4.6622585 -279.1079
1950M10 -0.2629690 -278.3174
1950M11 2.7520245 -271.6385
1950M12 5.4522928 -275.6421
1951M01 5.5058579 -280.4350
1951M02 1.3981423 -279.4692
1951M03 -2.2322648 -276.2853
1951M04 4.7261445 -281.0217
1951M05 -2.3989315 -275.4500
1951M06 -2.6691224 -272.1937
1951M07 6.7090653 -278.8001
1951M08 4.2824978 -282.6702
1951M09 0.7764988 -283.7056
1951M10 -2.4112268 -280.4308
1951M11 0.4896634 -286.6147
1951M12 3.3055381 -291.1463
1952M01 1.5389399 -292.9406
1952M02 -2.6285958 -287.6081
1952M03 4.3337649 -291.9950
1952M04 -5.1177023 -286.2958
1952M05 3.0730663 -288.5383
1952M06 3.7144603 -292.0184
1952M07 1.0317890 -292.4647
1952M08 -0.8459210 -292.0067
1952M09 -2.0985866 -289.1115
1952M10 -0.6539838 -288.8960
1952M11 5.6235558 -294.4102
1952M12 2.9020067 -297.0108
1953M01 -0.3272323 -297.4944
1953M02 -0.3033146 -295.6844
1953M03 -1.5303003 -294.0913
1953M04 -2.9398506 -291.6311
1953M05 0.4986701 -291.4048
1953M06 -1.8217395 -288.9287
1953M07 2.3499841 -291.2875
1953M08 -4.6652701 -285.9359
1953M09 0.1547320 -285.5778
1953M10 4.4703111 -290.2416
1953M11 2.7092758 -291.0687
1953M12 -0.0349409 -289.6072
1954M01 4.8263885 -294.2753
1954M02 1.8307097 -295.5540
1954M03 3.6298293 -298.3888
1954M04 4.0855807 -302.3883
1954M05 3.0364484 -304.4673
1954M06 1.0744861 -304.5849
1954M07 4.8695046 -309.5086
1954M08 -2.3391055 -304.9411
1954M09 6.1463909 -311.1655
1954M10 -1.7056478 -308.8780
1954M11 9.0969832 -314.0122
1954M12 5.3104152 -319.6504
1955M01 0.6222698 -320.3776
1955M02 3.0023628 -322.0301
1955M03 -0.2105682 -320.6014
1955M04 3.0712138 -323.6693
1955M05 1.0442669 -322.5585
1955M06 6.2926159 -328.6641
1955M07 1.8843901 -330.5911
1955M08 0.2753597 -328.2124
1955M09 -0.3864415 -327.1941
1955M10 -2.7831652 -324.3808
1955M11 6.7378970 -325.9142
1955M12 1.4592434 -326.6489
1956M01 -3.0719822 -321.8997
1956M02 3.6958931 -324.4590
1956M03 6.4381403 -330.7155
1956M04 0.3362472 -330.7558
1956M05 -5.2588052 -322.5470
1956M06 3.4298264 -325.5126
1956M07 4.8010187 -329.0417
1956M08 -3.1297390 -325.2606
1956M09 -5.3777209 -319.4365
1956M10 0.5124723 -318.3571
1956M11 0.5915190 -322.0438
1956M12 2.7784508 -324.0525
1957M01 -3.5220447 -320.3589
1957M02 -2.1169570 -316.7029
1957M03 2.1375438 -318.0645
1957M04 4.1431870 -321.4163
1957M05 3.3291380 -324.9244
1957M06 -0.8068079 -323.5386
1957M07 0.6644796 -323.5695
1957M08 -5.3928426 -318.0748
1957M09 -6.1855540 -311.1740
1957M10 -4.4609940 -306.8918
1957M11 2.2349580 -309.9494
1957M12 -4.0542935 -305.3377
1958M01 4.6294435 -310.6566
1958M02 -1.5326779 -308.1833
1958M03 3.2239594 -311.0601
1958M04 2.9476625 -313.7793
1958M05 2.3132852 -316.8587
1958M06 2.8765956 -318.9075
1958M07 4.3489254 -323.3758
1958M08 1.8481425 -326.1669
1958M09 4.5798164 -329.9894
1958M10 2.5580692 -332.7705
1958M11 2.8724547 -336.4850
1958M12 4.9698476 -341.9741
1959M01 0.6980741 -342.6276
1959M02 0.9119450 -343.7338
1959M03 0.2545711 -343.7612
1959M04 3.5753495 –
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