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这是一篇作业是R语言金融回归模型的一个作业

Autoregressive (AR) Model

You can test to see if the return data in your sample follow a random walk using the AR (1) model:
Rt= σ+ β1Rt-1+t
where the dependent variable Rtis the return for the time t, and the independent variable Rt-1is the return lagged one period for time t-1 .
You can create a one-period lag of return either manually in excel or you simply do that in SPSS, for instance, by using the LAG function under the Transform>Compute variables menu.
You should report and discuss your results.
(1)Create BP_1 Variable for t-1 {Hints: Transform….create time series…}
(2)Compute stock return of BP (BP_Ret) {Transform….Compute Variable ….((BP-BP_1)/BP_1)*100
(3)Create a Lag Variable for BP_Ret_1 for t-1 {Hints: Transform…Create time series…}
(4)Compute Logarithmic stock return of BP (BP_LogRet) {Transform…Compute Variable…(Ln(BP)-LN(BP_1)*100
(5)Do a formal test of independence to test H0: No Autocorrelation { Hints: Analyse…Forecasting …Autocorrelation…Variables (BP_Return), Display (Autocorrelation and Partial Autocorrelation). Can you reject H0: No Autocorrelation (e.g Reject H0if p-value is statistically significant) How do you interpret the results
(6)Repeat question 5 with BP share prices (instead of BP_Return).Do you observe any difference
(7)Estimate Autoregressive 1 (AR1) Model with and without constant term). Do the results tell you anything about the random walk model
(8)In order to test Weak Form EMH , estimate the following AR(1) Model with the BP_Return (with constant term). Can you reject H0: β=0 (e.g. Reject H0if p-value is statistically significant)
Do the result tell you anything about the EMH/ random walk model
Ri= σ+ β1Rt-1+t…….(1)
(9)Draw scatter plot and line charts to find evidence of Weak Form EMH/Random Walk Model.

Day of the Week Effect

In this part, you will test and see if the data show any seasonal effects over days of the week.
RT=β1D1,t+ β2D2,t+ β3D3,t+ β4D4,t+ β5D5,t+t
Note that there is no constant in the above regression; if you want to include a constant you can have only 4 dummy variables. Again, you should report and comment on your findings.
(1)Convert DATES into DAYS: Transform….Date & Time Wizard….Extract a part of a date or time variable…Date or time (DATE) and unit to extract (DAY OF WEEK)…Finish.
(2)Convert DAYS into NUMBERS (e.g., Mon=1, Fri=5): Transform…Automatic Recode…..choose New Variable name (DAYS2)….Recode starting from lowest to highest ….Use the same recoding scheme for all variables…}
(3)Create DUMMY Variables from DAYS2 (D1 FOR Monday,D2 for Tuesday,D3 for Wednesday,D4 for Thursday and D5 for Friday): Transform….Recode into different variable…Use Old & New Value option…….
(4)In order to investigate the seasonal effect on financial markets (calendar anomalies),estimate the following OLS regression (or Dummy Variable regression) model to test `Day-of-the-Week-Effect` (WITHOUT CONSTANT):
RT=β1D1,t+ β2D2,t+ β3D3,t+ β4D4,t+ β5D5,t+t
Where,
D1 = 1 if the return is on a Monday and 0 otherwise
D2 = 1 if the return is on a Tuesday and 0 otherwise
D3 = 1 if the return is on a Wednesday and 0 otherwise
D4 = 1 if the return is on a Thursday and 0 otherwise
D5 = 1 if the return is on a Friday and 0 otherwise
(5)Estimate the Following OLS regression (or Dummy Variable regression) model to test if `Monday return` is statistically significant than other days of the week. State Null and alternative hypotheses.
RT=β1D1,t+ β2D2,t+ β3D3,t+ β4D4,t+ β5D5,t+t