Week 1 - Time series models

Question 1

What are the 3 characteristics of time series models and briefly explain them?

Answer 1

1. Time trends - This is being able to determine whether there is a clear increase or decrease in the data in the long term.
2. Seasonality - This refers to fluctuations In the data with regular fixed periods and is generally associated with the same aspect of the calendar, for example sales are usually higher in quarter 4.
3. Cyclical - Occurs when data exhibits rises and falls that are not of a fixed frequency, which are often due to economic conditions and follow a business cycle.

Question 2

What is a dynamic model?

Answer 2

A dynamic model is a model which takes into account lags which are delays in response between X and Y as it often takes time to adjust to changes.

Question 3

What is the general response to a increase in Yt due to an increase in Xt

Answer 3

In general: Change in y+j/ change in x1t = B5[Change in y+j]/Change in x1t

Question 4

What are the 2 LR responses to an increase in Yt due to an increase in Xt?

Answer 4

1. B1 + B2 + B3 / 1-B5

2. Change in Y/Change in X = (B1 + B2 + B3)/1-B5

Question 5

What are the 4 assumptions of the time series models?

Answer 5

1. E[ et | y1,y2,…,yt-1)=0 , excluding yt, this is contemporaneous exogeneity, as this does not include yt.
2. V[et | yt-1]= theta squared
3. Cov (et, et-j|yt-1)=0, shocks are unrelated
4. et|yt-1 is normally distributed with a mean of 0 and a variance of theta squared

Question 6

What is the assumption of random sampling replaced with?

Answer 6

1. Stationarity

2. Weak dependence

Question 7

State and explain the 3 assumptions of stationarity?

Answer 7

1. E(Yt)= U for all T, this is the expected value of Yt= a constant u(mue) for all time. It doesn’t matter what time period you pick you expect the time series data to be the same.
2. V(Yt)= Theta squared, the variance of Yt is a constant theta squared, for all time. This means the uncertainty of the variation of GDP is the same in all time periods.
3. Cov(Yt,Yt-h)= Sigma h for all time periods. This means that the covariance between the data of 1900 and 1920(20 years apart) is the same as the covariance between 2000 and 2020(20 years apart)

Question 8

Explain weak dependency

Answer 8

• Cov(Yt,Yt-h) →0 as h→infinity
• The association between yt and yt-100 starts getting very small as the time period between the two periods you are looking at increases.

Question 9

What does dependency means for the OLS estimator?

Answer 9

• The OLS estimator is no longer unbiased, which means the OLS estimator is not equal to the true coefficient in small samples, but it is unbiased in big samples.
• The assumption will also mean the OLS estimator will not be exactly normally distributed but as the sample gets larger by the central limit theorem it will be approx normal distributed, and when hypothesis testing you use chai squared and normal distributions instead of F and t test.