Problem 1

A). If we computed the autocorrelation of this series would the lag-1 autocorrelation exhibit negative, positive, or no autocorrelation? How can you see this from the plot??

The time series plot appears to show a downward trend. If we were to compute the lag-1 autocorrelation it would show consecutive values that move in the same direction. This would likely exhibit positive autocorrelation.

B). Compute the autocorrelation and produce an ACT plot. Verify your answer to the previous question

Lag-1 shows a positive correlation of almost .10 which would indicate a positive correlation.

Problem 2

A). Create a time plot of the differenced series

## 
## Attaching package: 'lubridate'
## The following object is masked from 'package:base':
## 
##     date

B). Which of the following is/are relevant for testing whether this stock is a random walk?

The autocorrelations of the closing price series

The AR(1) slope coefficient for the closing price series

The AR(1) constant coefficient for the closing price series

The autocorrelations of the differenced series

c). Recreate the AR(1) model output for the Close price series shown in the left of Table 7.4. Does the AR Model indicate that this is a random walk? Explain how you reached your conclusion

## Series: wmstockts 
## ARIMA(1,0,0) with non-zero mean 
## 
## Coefficients:
##          ar1     mean
##       0.9574  53.1357
## s.e.  0.0188   1.3872
## 
## sigma^2 estimated as 0.9852:  log likelihood=-351.69
## AIC=709.39   AICc=709.48   BIC=719.94

calculate p-value from t-distribution

##       ar1 
## 0.0242599

calculate p-vlaue from normal distribution

##        ar1 
## 0.02339822

The P value is less that 0.04 in both examples indicating that this is not a random walk.

D). What are the implications of finding that a time series is a random walk? Choose the correct statements(s) below

The implications of finding that a time series is not a random walk are that it is impossible to obtain useful foreacsts of the series and; that the changes in the series from one period to the other are random