# Question: a what is the definition of market efficiency for a...

###### Question details

(a) What is the definition of market efficiency for a fixed horizon? Is it possible to have deviations from efficiency in a market that is efficient? Explain.

(b)Describe collective data snooping and individual data snooping in your own words, and briefly discuss the differences between them.

(c) Forecast optimality is judged by comparing properties of a given forecast with those that we know are true. An optimal forecast generates forecast errors which, given a loss function, must obey some properties. Under a mean-square-error loss function, what three properties must the optimal forecast error ${e}_{t+h|t}\equiv {Y}_{t+h}-{\stackrel{\u02c6}{Y}}_{t+h|t}^{\ast}$ for a horizon h possess?

For the remaining two sub-questions of the exercise, consider a forecast ${\stackrel{\u02c6}{Y}}_{t+1|t}$of a variable ${Y}_{t+1}$. You have 100 observations of ${\stackrel{\u02c6}{Y}}_{t+1|t}$and ${Y}_{t+1}$, and decide to run the following regression:

Yt+1 = α + βYˆ t+1|t + ετ

The results you obtain are given in Table I:

Estimate | Std Error | |

α | -0.0081 | 0.0052 |

β | 1.6135 | 0.2399 |

Table I. Regression results

(d) What null hypothesis should we set up in order to test for forecast optimality? Can this test be conducted with the information given?

(e) Explain what can be inferred from Table I.