4: Time series

Question 1

What is a time series?

Answer 1

A series of data points indexed in time order. Composed of two parameters:
1. The value of the variable of interest
2. The time when the value occurred

Question 2

What are some typical time series?

Answer 2

• With a trend
• With seasonality
• With trend and seasonality
• With a structural break
• With time-varying variance
• A stationary time series

Question 3

What is autocorrelation?

Answer 3

Autocorrelation (serial correlation) is the correlations of a variable Xt and each of its lags Xt-1, Xt-2, etc

Question 4

What does the autocorrelation function (ACF) provide?

Answer 4

The distribution of the correlations between a variable Xt and each of its lags Xt-1, Xt-2, etc, to identify a possible structure.

Question 5

What is the difference between ACF and PACF?

Answer 5

ACF = correlation between data and the lags. In PACF you do not include the correlation related to intermediary lags, you control for those variables.

Question 6

What are lags?

Answer 6

Previous value in the time series. The first lag of Yt is Yt-1

Question 7

What is an autoregressive model?

Answer 7

Trying to predict model X with its past value; studying the effect of X on X in the past, could be good predictors of current X.

Question 8

What is a stationary time series?

Answer 8

A stochastic process whose unconditional joint probability distribution does not change over time. Can try to identify stationarity visually.

A time series:
- without trend (it looks flat on the plot)
- without breaks
- without seasonality (periodic fluctuation)
- with constant variance over time

Question 9

What are two possible test for stationarity?

Answer 9

1. ADF test
2. KPSS test

Question 10

What is the ADF test?

Answer 10

Augmented Dickey-Fuller test.

• Test for unit root.
• Null hypothesis: a unit root is present.
• Alternative hypothesis: stationarity.
• Problem: high level of Type I error in the test

Question 11

What is the KPSS test?

Answer 11

Kwiatkowski-Phillips-Schmidt-Shin (KPSS)

• Test for trend stationarity
• Null hypothesis: absence of unit root
• Warning: this is not a proof of stationarity.

Absence of unit root = data are trend-stationary

Question 12

What is cross-sectional data?

Answer 12

Assumed that X influence Y all at once (standard OLS model)

Question 13

What is a distributed lag model (dynamic linear model)?

Answer 13

The effect of X on Y might not happen all at once, but over time, over several lags of the IV X. This is distributed lag.

Question 14

What are the betas called in a distributed lag model?

Answer 14

The lag weights

Question 15

What does dynamic models show?

Answer 15

Long-term effect X has on Y. Two kinds of effects:

• Cumulative. How long does it take to get back, how long they stay, different lags add up. Long-term effect of X on Y. Compute long-run cumulative dynamic multipliers: zero-period dyn mult=ß1, one-period = ß1+ß2.
• Contemporaneous. Effect in Y happen all at once with the variation of X.

ßq is the dynamic multiplier of period q-1

Question 16

What are the assumptions for distributed lag models?

Answer 16

• The usual assumptions of linear regression
• X is exogenous
• X is stationary

Question 17

What does exogeneity mean?

Answer 17

The explanatory variable (= IV) is NOT correlated with the error term

Question 18

What is endogeneity and what are the two main causes?

Answer 18

The opposite of exogeneity –> IV is correlated with error term.

1. The omitted variable bias: when an important predictor is missing in your mode.
2. The simultaneity bias: when Y is not only a response to X, but also a predictor of X.

Question 19

What characterises stationarity?

Answer 19

• no trend or seasonality
• no breaks
• no change in variance over time
• no unit root
• CONSTANT DISTRIBUTION OVER YOUR TIME SERIES

Question 20

What is seasonality?

Answer 20

Fluctuations that are periodic over time. At a fixed frequency.

Question 21

What is a trend?

Answer 21

Long-term increase or decrease