Time Series Regression

Question 1

Time series data

Answer 1

Sample consistently repeating the same unit of observations over time - time series regression has emphasis on prediction and forecasting.

Question 2

Growth rates of Y between periods t and t-1

Answer 2

= ln(Y(t)) - ln(Y(t-1))
=approx.(Y(t)-Y(t-1))/Y(t-1)

Question 3

Autocorrelation

Answer 3

Correlation of a time series with its own lagged value

Question 4

Auto regressions

Answer 4

Regressionj models that relate a time series variable to its past (lagged) value - the order of the regression indicates the number of lags in the regression

Question 5

Forecast value and forecast error

Answer 5

If the error is negative this means that the model overpredicts growth in 2011

Question 6

Root mean forecast error

Answer 6

Question 7

Forecast intervals

Answer 7

Highlight the range of uncertainty around the model’s forecast

Question 8

pth order autoregressive model

Answer 8

Adding more lags to the model which can improve the model fit (Rsquare increase) in increase the model forecast accuracy (increse RMSFE)

Question 9

Autoregressive distributed lag models

Answer 9

Using ADL for modelling lagged impact of an independent variable on a dependent variable (included lags of the dependent variables)

the gammas are just the beta for the independent compared to the dependent

Question 10

Key assumptions of the ADL model

Answer 10

1. Zero conditional mean - the errors are independent
2. Large outliers unlikely
3. No perfect multicollinearity
4. Future tends to be like the past
5. The variables bcome independent as the number of lags included becomes larger

Question 11

Granger causality

Testing predictative content

Answer 11

Based on the D-stat associated with the joint test - do a different test for each set of lags (ie. different test of the lags significant for rural prices and urban prices)
- If the hypothesis are rejected this means they contain predictive content for P(t) conditional on all other variables in the ADL model

Question 12

How to choose the number of lags that should be included for AR(p) model

Answer 12

1. Bayes-Schwarz info criterion - calculate the BIC for the different orders and then choose the lowest BIC

Question 13

How to choose the number of lags that should be included for ADL models

Answer 13

Akaike information criterion - use this formula to find the BICS and then again choose the lowest BIC and this is the order (number of lags) that should be included.

Question 14

Steps to deseasonalise and detrend data

Answer 14