R语言代写 | Tests of Weak Form Efficiency

本次代写是R语言金融回归模型的一个作业

1. Autoregressive (AR) Model

You can test to see if the return data in your sample follow a random walk using the AR (1) model:

R_t= σ+ β₁ R_t-1 + ℇ_t   

where the dependent variable R_t is the return for the time t, and the independent variable R_t-1 is 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 H₀  if 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 H₀  if p-value is statistically significant)?

Do the result tell you anything about the EMH/ random walk model?

R_i= σ+ β₁ R_t-1 + ℇ_t…….(1)

(9)  Draw scatter plot and line charts to find evidence of Weak Form EMH/Random Walk Model.

2. 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.

R_T=β₁ D_1,t + β₂ D_2,t + β₃ D_3,t + β₄ D_4,t + β₅ D_5,t + ℇ_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):

R_T=β₁ D_1,t + β₂ D_2,t + β₃ D_3,t + β₄ D_4,t + β₅ D_5,t + ℇ_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.

R_T=β₁ D_1,t + β₂ D_2,t + β₃ D_3,t + β₄ D_4,t + β₅ D_5,t + ℇ_t