Reading 13 - Time Series Analysis

Question 1

What is a linear trend?

Answer 1

a time series pattern that can be graphed using a straight line

Question 2

In its simplest form, what does a linear trend model equation look like?

Answer 2

Question 3

What is Ordinary least squares (OLS) regression?

Answer 3

Is used to estimate the coefficient in the trend line

Question 4

What is the equation for a time series that exhibits exponential growth?

Answer 4

Question 5

What is the general rule on whether to use a log-linear model or linear trend model?

Answer 5

If the variable grows at a constant rate, a log-linear model is most appropriate

If the variables increases over time by a amount, a linear trend model is most appropriate

Question 6

What is an autoregressive model (AR) ?

Answer 6

A model in which the dependent variable is regressed against one or more lagged values of itself.

** ie sales for a firm could be regressed against the sales for the firm in the previous month

Question 7

What would the equation for an autoregressive model look like?

Answer 7

x_t = b₀+b₁x_t-1+e_t

Question 8

Statistical inferences based on ordinary least squares estimates for an autoregressive model may be invalid unless the time series being modeled is covariance stationary.

What are the 3 conditions neccesary to be considered covariance stationary?

Answer 8

1. Constant and finite expected value
2. Constant and finite variance
3. Constant and finite covariance between values at any given lag

Question 9

What are the 3 steps to whether an autoregressive model (AR) is correctly specified (meaning it does not exhibit serial correlation) ?

Answer 9

1. Estimate the AR model being evaluated using a linear regression
2. Calculate the autocorrelations of the model’s residuals
3. Test whether te autocorrelations are significantly different from zero

Question 10

What is mean reversion?

& what is the basic equation to calculate it?

Answer 10

if a time series has a tendency to move toward its mean.

Question 11

What is the difference between in-sample forecasts and out-of-sample forecats?

Answer 11

In-sample are within the range of data (ie time period) used to estimate the model

Out-of-sample are made outside of the sample period.

Question 12

What is the root mean squared error criterion (RMSE) ?

Answer 12

Is used to compare the accuracy of autoregressive models in forecating out-of-sample values

**The model with the lower RMSE for the out-of-sample data will have lower forecast error and will be expected to have better predictive power in the future

Question 13

What is the random walk process?

Answer 13

The predicted value of the series in one period is equal to the value of the series in the previous period plus a random error term

Question 14

Do Random Walk or Random Walk with a Drift exhibit Covariance Stationarity?

Answer 14

No

Question 15

What are the two tests to determine if time series is covariance stationary?

Answer 15

1. Run an AR model and examine the autocorrelations
2. Perform a Dickey Fuller test

***#2 is the preffered test.

Question 16

What is it called when we transform a random walk time series to a covariance stationary time series?

Answer 16

First Differencing

This involves subtracting the value of the time series in the immediately preceeding period from the current value of the time series to define a new dependent variable, y.

Question 17

What is autoregressive conditional heteroskedasticity (ARCH) ?

Answer 17

When examining a single time series, if the variance of the residuals in one period is dependent on the variace of the residuals in a previous period.

Question 18

What is cointegration?

Answer 18

that two time series are economically linked or follow the same trend and that relationship is not expected to change

Question 19

Suppose that the time series designated as Y is mean reverting. If Yt+1 = 0.2 + 0.6 Yt, the best prediction of Yt+1 is:

Answer 19

The prediction is Yt+1 = b0 / (1-b1) = 0.2 / (1-0.6) = 0.5